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[null,"Command","Description"]
[null,"!","Syntax: value!\n\nFactorial. Returns the factorial of a positive integer. For non-integers, ! = Γ(x + 1). This calculates the Gamma function. \n\nExample: 6! returns 720\n"]
[null,"%","Syntax: %(x, y)\n\nx percent of y. Returns (x/100)*y. \n\nExample: %(20,50) returns 10\n"]
[null,"%CHANGE","Syntax: %CHANGE(x, y)\nPercent change from x to y. Returns 100*(y-x)/x.\n%CHANGE(20,50) returns 150\n"]
[null,"%TOTAL","Syntax: %TOTAL(x, y)\nPercent total; the percentage of x that is y. Returns 100*y/x.\n%TOTAL(20,50)  returns 250.\n"]
[null,"(","Parentheses.\nInserts a pair of parentheses.\n"]
[null,"*","Syntax: Object1×Object2\nMultiplication.\nReturns the result of multiplying Object1 and Object2. The objects may be numerical values or expressions that return numerical results. The objects may also be lists or matrices of appropriate dimensions.\n\nExample: 3*2 returns 6\n"]
[null,"+","Syntax: Object1 + Object2\nAddition.\nReturns the result of adding Object2 to Object 1. The objects may be numerical values or expressions that return numerical results. The objects may also be lists or matrices of appropriate dimensions.\n\nExample: 3+2 returns 5\n\n"]
[null,"-","Syntax: Object1 - Object2\nSubtraction.\nReturns the result of subtracting Object2 from Object 1. The objects may be numerical values or expressions that return numerical results. The objects may also be lists or matrices of appropriate dimensions.\n\nExample: 3-2 returns 1\n"]
[null,".*","Syntax: .*(Lst||Mtrx,Lst||Mtrx)\n\nPerforms an element-by-element multiplication of 2 lists or 2 matrices.\n\nExample:  [[1,2],[3,4]] .* [[3,4],[5,6]] returns [[3,8],[15,24]]\n\n\n\n\n"]
[null,".+","Syntax: matrix .+ real/complex or real/complex .+ matrix\n\nAdds the real/complex to each element of the matrix\n\nExample: [1,2].+3 returns [4,5]\n"]
[null,".-","Syntax: matrix .- real/complex or real/complex .- matrix\n\nSubstract the real/complex to each element of the matrix (or the reverce as appropriate)\n\nExample: [3,4].-2 returns [1,2]\n"]
[null,"./","Syntax: ./(Lst||Mtrx,Lst||Mtrx)\n\nPerforms an element-by-element division of 2 lists or 2 matrices.\n\nExample:  [[1,2],[3,4]] ./ [[3,4],[5,6]] returns [[1/3,1/2],[3/5,2/3]]  \n\n"]
[null,".^","Syntax: .^(Mtrx,Intg(n))\n\nCalculates the power of each element of the matrix.\n\nExample:  [[1,2],[3,4]] .^ 3 returns [[1,8],[27,64]] \n\n"]
[null,"/","Syntax: Object1/Object2\nDivision.\nReturns the result of dividing Object1 by Object2. The objects may be numerical values or expressions that return numerical results. The objects may also be lists or matrices of appropriate dimensions.\n\nExample: 3÷2 returns 1.5\n"]
[null,":=","Syntax: variable := object\nAssigns object to variable.\nExamples:\nA := 3 stores the value 3 in the variable A\nF1 := 3-X makes F1(X)=3-X\nM5 := [1, 2] stores a vector in M5\n\n"]
[null,"<","Syntax: Value1 < Value2\n<: Less than or equal to. \nTests whether or not Value1 is less than Value2. Returns 1 if true, 0 if false.\n\nExample: 2 ≤ 1 returns 0\n"]
[null,"<=","Syntax: Value1 ≤ Value2\n ≤: Less than or equal to. \nTests whether or not Value1 is less than Value 2. Returns 1 if true, 0 if false.\n\nExample: 2 ≤ 1 returns 0\n\nAlternative: <=\n"]
[null,"<>","Syntax: Value1 ≠ Value2\n≠: Not equal to. \nTests if Value1 is not equal to Value 2. Returns 1 if true, 0 if false. \n\nExample: 3 ≠ 5 returns 1\n\nAlternatives: <>\n"]
[null,"=","Syntax: Value1 == Value2\n==: equal to. \nTests is Value1=Value2. Returns 1 if true, 0 if false.\n\nExample: 3==2 returns 0\n"]
[null,"==","Syntax: Value1 == Value2\n==: equal to. \nTests is Value1=Value2. Returns 1 if true, 0 if false.\n\nExample: 3==2 returns 0\n"]
[null,">","Syntax: Value1 > Value2\n>: Greater than. \nTests whether or not Value1 is greater than Value 2. Returns 1 if true, 0 if false.\n\nExample: 2 > 1 returns 1\n\n"]
[null,">=","Syntax: Value1 ≥ Value2\n≥: Greater than or equal to. \nTests whether or not Value 1 is either greater than or equal to Value2. Returns 1 if true, 0 if false.\n\nExample: 3 ≥ 4 returns 0\n\nAlternative: >=\n"]
[null,"^","Syntax: Value1^Value2\nExponentiation.\nReturns the result of raising Value1 to the power of Value2.\n\nExample: 2^3 returns 8\n\n"]
[null,"`","Syntax: QUOTE(expression)\n\nReturns the expression unchanged and un-evaluated.\nThis function is mostly used with the STO▶ command in order to store a function in a function variable. For example if you want to store SIN(X) in F1.you cannot do SIN(X)►F1 as SIN(X) would be evaluated and a numerical result would be stored into F1. QUOTE(SIN(X))►F1 will store SIN(X) in F1.\n"]
[null,"a2q","Syntax: a2q(Mtrx,VectVar)\n\na2q(A,X)=the quadratic form q associated to A, X=vector of variables.\n\nExample: a2q([[1,2],[4,4]],[x,y]) returns x^2+6*x*y+4*y^2\n\n"]
[null,"abcuv","Syntax: abcuv(Polya,Polyb,Polyc,[Var])\n\nReturns [u,v] suchthat au+bv=c for 3 polynomials a, b, and c.\n\nExample: abcuv(x^2+2*x+1,x^2-1,x+1) returns [1/2,-1/2]\n"]
[null,"about","Syntax: about(Var(a))\n\nReturns the hypothesis made with assume on the variable a.\n\nExample: about(n) returns n\n\n\n"]
[null,"ABS","Syntax: ABS(expr) or ABS(matrix)\n\nFor numerical arguments, returns the absolute value of the expression. For matrix arguments, returns the returns the Frobenius (Euclidean) norm of the array.\n\nExample: ABS(-3.14) returns 3.14 and ABS([[1,2],[3,4]]) returns 5.47722557505\n\n\n\n"]
[null,"abscissa","Syntax: abscissa(Pnt or Vect)\n\nReturns the abscissa of a point or a vector.\n\nExample: abscissa(point(1+2*i)) returns 1\n\n\n"]
[null,"ACOS","Syntax: ACOS(Value)\nACOS: the inverse cosine function.\nThis Shift-key combination returns the inverse cosine of Value.  The output depends on the Angle Measure setting.\n\nExample: ACOS(-1) returns 3.14159265359\n\n\n"]
[null,"acos2asin","Syntax: acos2asin(Expr)\n\nReplaces arccos(x) by π/2-arcsin(x) in the argument Expr.\n\nExample: acos2asin(acos(x)+asin(x)) returns π/2-asin(x)+asin(x)\n\n\n"]
[null,"acos2atan","Syntax: acos2atan(Expr)\n\nReplaces arccos(x) by π/2-arctan(x/√(1-x^2)) in the argument.\n\nExample: acos2atan(2*acos(x)) returns 2*(π/2-atan(x/(√(1-x^2))))\n\n\n"]
[null,"ACOSH","Syntax: ACOSH(value)\n\nInverse hyperbolic cosine.\n\nExample: ACOSH(1.54308063482) returns 1\n"]
[null,"ACOT","Syntax: ACOT(value)\n\nArc cotangent. The function derived from the inverse of the Cotangent function.\n\nExample: ACOT(1) returns 45 in degree mode\n"]
[null,"ACSC","Syntax: ACSC(value)\n\nArc cosecant. The function derived from the inverse of the Cosecant function.\n\nExample: ACSC(1) returns 90 in degree mode\n"]
[null,"ADDCOL","Syntax: ADDCOL(matrixname, vector, column_number)\nAdd Column. Inserts values from vector into a column before column_number in the specified matrix. The size of vector must be the same as the number of rows in the matrix matrixname.\n\n\n\n"]
[null,"additionally","Syntax: additionally(Expr)\n\nMake an additional assumption about a variable.\n\nExample:  assume(n,integer);additionally(n>5) returns DOM_INT,n\n\n\n"]
[null,"ADDROW","Syntax: ADDROW(matrixname, vector, row_number)\nAdd Row. Inserts values from vector into a row before row_number in the specified matrix. The size of vector must be the same as the number of columns in the matrix matrixname. \n"]
[null,"affix","Syntax: affix(Point) or affix(Vector)\n\nReturns the coordinates of a point or both the x- and y-lengths of a vector as a complex number.\n\nExamplea:\naffix(point(3,2)) returns 3+2*i\n if GA is a point at (1, -2), then affix(GA) returns 1-2*i.\n\n"]
[null,"algvar","Syntax: algvar(Expr)\n\nList of the variables by ascending algebraic extension order.\n\nExample: algvar(√x+y) returns [[y],[x]]\n\n\n"]
[null,"ALOG","Syntax: ALOG(value)\n\nThe common antilogarithm. This is more accurate than 10^x due to limitations of the power function.\n\nExample: ALOG(2) returns 100\n"]
[null,"alog10","Syntax: alog10(Expr)\n\nFunction x->10^x.\n\nExample: alog10(3) returns 1000\n\n\n"]
[null,"altitude","Syntax: altitude(point1, point2, point3)\n\nGiven three non-collinear points, draws the altitude of the triangle defined by the three points that passes through the first point. The triangle does not have to be drawn.\n\nExample: altitude(A, B, C) draws a line passing through point A that is perpendicular to BC.\n\n\n"]
[null,"AND","Syntax: Value1 AND Value2\nLogical AND. \nReturns 1 if both value1 and value2 are non-zero; otherwise returns 0.\n\nExample: 3 AND 2 returns 1\n"]
[null,"angle","Syntax: angle(Vertex, Point2, Point3)\n\nReturns the measure of a directed angle. The first point is taken as the vertex of the angle as the next two points in order give the measure and orientation.\n\nExample: angle(GA, GB, GC) returns the measure of ∡BAC\n\n"]
[null,"angleat","Syntax: angleat(Vertex, Point2, Point3, Point4)\n\nUsed in Symbolic view. Given the three points of an angle and a fourth point as a location, displays the measure of the angle defined by the first three points, with a label, at the location in the Plot view given by the fourth point. The first point is the vertex of the angle.\n\nExample: angleat(GA, GB, GC, point(0,0)) displays “aA=” at the origin, followed by the measure of ∡BAC.\n"]
[null,"angleatraw","Syntax: angleatraw(Pnt(A)),Pnt(B),Pnt(C),(Pnt or Cplx(z0)))\nangleatraw(A,B,C,z0) displays at point(z0), the value of the measure of the angle (AB,AC).\n\n"]
[null,"Ans","Syntax: ANS\nANS: Last answer.\nReturns the result of the last calculation made in Home view to its full precision. The variable ANS is different from the numbers in Home's history. A value in ANS is stored internally with the full precision of the calculated result, whereas the displayed numbers match the display mode.\n\n"]
[null,"append","Syntax: append((Lst||Seq|| Set,Elem)\n\nAppend an element to a list.\n\nExample: append([1,2,3],4) returns [1,2,3,4]\n"]
[null,"apply","Syntax: apply(Fnc(f),Lst(l))\n\nApply the function f at the elements of the list l (option matrix for a matrix).\n\nExample: apply(x->x^3,[1,2,3]) returns [1,8,27]\n\n\n"]
[null,"approx","Syntax: approx(Expr,[Int])\n\nNumerical evaluation of the first argument (we can give the number of digits as second argument).\napprox(expression) works also and does the same thing.\n\nExample: approx(2/3) returns 0.666666666667  \n\n\n"]
[null,"ARC","Syntax: ARC(G, x, y, r, [[∠1, ∠2],[color]])\n\nDraws a circle on GROB G, centered at (x, y), with radius r. If ∠1 and ∠2 are specified, draws an arc from ∠1 to ∠2 using the current angle mode.\n"]
[null,"ARC_P","Syntax: ARC_P(G, x, y, r, [[∠1, ∠2],[color]])\n\nDraws a circle on GROB G, centered at (x, y), with radius r. If ∠1 and ∠2 are specified, draws an arc from ∠1 to ∠2 using the current angle mode.\n"]
[null,"arcLen","Syntax: arcLen(Expr, Real1, Real2)\n\nReturns the length of the arc of a curve between two points on the curve. The curve is an expression, the independent variable is declared, and the two points are defined by values of the independent variable.\n\nThis command can also accept a parametric definition of a curve. In this case, the expression is a list of 2 expressions (the first for x and the second for y) in terms of a third independent variable.\n\nExamples:\narcLen(x^2, x, -2, 2) returns 9.29….\narcLen({sin(t), cos(t)}, t, 0, π/2) returns 1.57…\n\n"]
[null,"area","Syntax: area(Circle) or area(Polygon) or area(Expr, x=value1..value2)\n\nReturns the area of a circle or polygon. Can also return the area under a curve between two points.\n\nExamples:\nIf GA is defined to be the unit circle, then area(GA) returns π.\narea(4-x^2/4, x=-4..4) returns 64/3 or 21.333…\n\n"]
[null,"areaat","Syntax: areaat(Polygon, Pnt||Cplx(z0))\nDisplays at point(z0), with a legend, algebraic area of a circle or of a (star) polygon (e.g. triangle, square, ...).\n\n"]
[null,"areaatraw","Syntax: areaatraw(Polygon, Pnt||Cplx(z0))\nDisplays at point(z0), algebraic area of a circle or of a (star-)polygon (e.g. triangle, square, ...).\n\n"]
[null,"ARG","Syntax: ARG(x+yi)\n\nThe ARG function finds the angle determined by a complex number.\n\nExample: ARG(3+3i) returns 45 in degree mode.\n\n"]
[null,"ASC","Syntax: ASC(\"string\")\n\nReturns a vector containing the ASCII codes of string.\n\nExample: ASC(\"AB\") returns [65, 66]\n\n"]
[null,"ASEC","Syntax: ASEC(value)\n\nArc secant. The function derived from the inverse of the Secant function.\n\nExample: ASEC(1) returns 0 in degree mode\n"]
[null,"ASIN","Syntax: ASIN(Value)\nASIN: the inverse sine function.\nThis Shift-key combination returns the inverse sine of Value. The output depends on the Angle Measure setting.\n\nExample: ASIN(1) returns 1.57079632679\n\n"]
[null,"asin2acos","Syntax: asin2acos(Expr)\n\nReplaces arcsin(x) by π/2-arccos(x) in the argument.\n\nExample: asin2acos(acos(x)+asin(x)) returns π/2-acos(x)+acos(x)\n\n\n"]
[null,"asin2atan","Syntax: asin2atan(Expr)\n\nReplaces arcsin(x) by arctan(x/√(1-x^2)) in the argument.\n\nExample: asin2atan(2*asin(x)) returns 2*atan(x/(√(1-x^2)))\n\n\n"]
[null,"ASINH","Syntax: ASINH(value)\n\nInverse hyperbolic sine.\n\nExample: ASINH(1.17520119365) returns 1\n"]
[null,"assume","Syntax: assume(Expr)\n\nMake an assumption on a variable.\n\nExample: assume(a>0) returns a\n\n\n"]
[null,"ATAN","Syntax: ATAN(Value)\nATAN: the inverse tangent function.\nThis Shift-key combination returns the inverse tangent of Value.  The output depends on the Angle Measure setting.\n\nExample: ATAN(0) returns 0\n\n\n"]
[null,"atan2acos","Syntax: atan2acos(Expr)\n\nReplaces arctan(x) by π/2-arccos(x/√(1+x^2)) in the argument.\n\nExample: atan2acos(atan(2*x) returns π/2-acos((2*x)/√(1+(2*x)^2))\n\n\n"]
[null,"atan2asin","Syntax: atan2asin(Expr)\n\nReplaces arctan(x) by arcsin(x/√(1+x^2)) in the argument Expr.\n\nExample: atan2asin(atan(y/x) returns asin((y/x)/√(1+(y/x)^2))\n\n\n"]
[null,"ATANH","Syntax: ATANH(value)\n\nInverse hyperbolic tangent.\n\nExample: ATANH(.761594155956) returns 1\n"]
[null,"atrig2ln","Syntax: atrig2ln(Expr)\n\nRewrites the expression Expr containing inverse trigonometric functions with equivalent logarithmic functions.\n\nExample: atrig2ln(atan(x)) returns (i*ln((i+x)/(i-x)))/2\n\n\n"]
[null,"barycenter","Syntax: barycenter([Point1, Weight1], [Point2, Weight2],…,[Pointn, Weightn])\n\nCalculates the hypothetical center of mass of a set of points, each with a given weight (a real number). Each point, weight pair is enclosed in square brackets as a vector.\n\nExample: barycenter([–3,1],[3,1],[4,2]) returns point(2,0)\n\n\n"]
[null,"basis","Syntax: basis(Lst(vector1,..,vectorn))\n\nExtract a basis from a spanning set of vectors.\n\nExample: basis([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]) returns [[-3,0,3],[0,-3,-6]]\n\n\n"]
[null,"BEGIN","Syntax: BEGIN commands; END;\nDefines a set of commands to be executed in a block.\n\nExample Program SQM1\n\nEXPORT  SQM1(X)\nBEGIN\nRETURN X^2-1;\nEND;\n\nThis program defines a user function named SQM1(X). From the Home view, entering SQM1(8) returns 63.\n\n"]
[null,"Beta","Syntax: Beta(Expr,Expr)\n\nReturns Gamma(x)*Gamma(y)/Gamma(x+y).\n\nExample: Beta(3,2) returns 1/12\n\n\n"]
[null,"BINOMIAL","Syntax: BINOMIAL(n, k, p)\n\nBinomial probability density function. Computes the probability of k successes out of n trials, each with a probability of success, p.\nReturns Comb(n,k) if there is no third argument. Note that n and k are integers with k=n.\n\nExample: BINOMIAL(4, 2, 0.5) returns 0.375\n\n"]
[null,"BINOMIAL_CDF","Syntax: BINOMIAL_CDF(n, p, k)\n\nCumulative binomial distribution function. Returns the probability of k or fewer successes out of n trials, with a probability of success, p for each trial. Note that n and k are integers with k=n.\n\nExample: BINOMIAL_CDF(4, 0.5, 2) returns 0.6875\n\n"]
[null,"BINOMIAL_ICDF","Syntax: BINOMIAL_ICDF(n, p, q)\n\nInverse cumulative binomial distribution function. Returns the number of successes, k, out of n trials, each with a probability of p, such that the probability of k or fewer successes is q.\n\nExample: BINOMIAL_ICDF(4, 0.5, 0.6875) returns 2\n\n"]
[null,"bisector","Syntax: bisector(Point1, Point2, Point3)\n\nGiven three points, creates the bisector of the angle defined by the three points whose vertex is at the first point. The angle does not have to be drawn in the Plot view.\n\nExamples:\nbisector(GA, GB, GC) draws the bisector of ∡BAC.\nbisector(0,-4i,4) draws the line given by y=–x\n\n"]
[null,"BITAND","Syntax: BITAND(int1[, int2..,intn])\nBitwise logical AND. Takes n integers as input and returns their bitwise logical AND.\nExample: BITAND(20, 13) returns 4\n\n"]
[null,"BITNOT","Syntax: BITNOT(int)\nBitwise logical NOT. Takes one integer as input and returns its bitwise not.\n\n"]
[null,"BITOR","Syntax: BITOR(int1[, int2..,intn])\nBitwise logical OR. Takes n integers as input and returns their bitwise logical OR.\nExample: BITOR(9, 26) returns 27\n\n"]
[null,"BITSL","Syntax: BITSL(int1[, int2])\n\nBitwise shift left. Takes one or two integers as input and returns the result of shifting the bits in the first integer to the left by the number of places indicated by the second integer. If there is no second integer, then the bits in the first integer are shifted to the left one place.\n\nExamples: BITSL(28, 2) returns 112\nBITSL(5) returns 10\n\n"]
[null,"BITSR","Syntax: BITSR(int1[, int2])\n\nBitwise shift right. Takes one or two integers as input and returns the result of shifting the bits in the first integer to the right by the number of places indicated by the second integer. If there is no second integer, then the bits in the first integer are shifted to the right one place.\n\nExamples: BITSR(112, 2) returns 28\nBITSR(10) returns 5\n\n"]
[null,"BITXOR","Syntax: BITXOR(int1[, int2..,intn])\nBitwise logical exclusive OR (XOR). Takes n integers as input and returns their bitwise XOR.\nExample: BITXOR(9, 26) returns 19\n\n"]
[null,"black","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"BLIT","Syntax: BLIT([trgtG], [dx1, dy1], [dx2, dy2], srcG, [sx1, sy1], [sx2, sy2], [c]) \nCopies the region of graphic srcG between point (sx1, sy1) and (sx2, sy2) into the region of trgtG between points (dx1, dy1) and (dx2, dy2). Does not copy pixels from srcG that are color c.\n\nThe defaults for the optional arguments are:\ntrgtG=G0\nsrcG=G0\nsx1, sy1=srcGRB top left corner\nsx2, sy2=srcGRB bottom right corner\ndx1, dx2=trgtGRB top left corner\ndx2, dy2=calculated so destination area is the same as source area\nc=all pixel colors\n\n"]
[null,"BLIT_P","Syntax: BLIT_P([trgtG], [dx1, dy1], [dx2, dy2], srcG, [sx1, sy1], [sx2, sy2], [c])\nCopies the region of graphic srcG between point (sx1, sy1) and (sx2, sy2) into the region of trgtG between points (dx1, dy1) and (dx2, dy2). Does not copy pixels from srcG that are color c.\n\nThe defaults for the optional arguments are:\ntrgtG=G0\nsrcG=G0\nsx1, sy1=srcGRB top left corner\nsx2, sy2=srcGRB bottom right corner\ndx1, dx2=trgtGRB top left corner\ndx2, dy2=calculated so destination area is the same as source area\nc=all pixel colors\n\n"]
[null,"blue","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"bounded_function","Argument returned by limit. Indicates that the function is bounded.\n\n"]
[null,"BREAK","Syntax: BREAK [n];\n\nExits from expression local loop structure.\nExample:\nFOR A FROM 1 TO 10 DO\n  B:= (A+3) MOD 5\n  IF B==1 THEN BREAK;\n  END;\nEND;\n\nIf n is specified, allow to exit n loop structures. \n"]
[null,"breakpoint","Syntax: breakpoint(Intg)\nAdds a breakpoint.\n\n"]
[null,"B→R","Syntax: B→R(#integer)\n\nTransform an integer into a real number.\n"]
[null,"canonical_form","Syntax: canonical_form(Trinom(a*x^2+b*x+c),[Var])\n\nCanonical form of a second degree polynomial.\n\nExample: canonical_form(2*x^2-12*x+1) returns 2*(x-3)^2-17\n\n\n"]
[null,"CAS","Syntax: CAS(expression) or CAS.function(...) or CAS.variable[(...)]\n\nEvalute an expression or variable using the CAS.\nNote that outputs in numerical mode are transformed into strings or lists of expressions for symbolic matrices.\n\n\n\n"]
[null,"CASE","Starts a \"CASE...END\" branch structure.\nSyntax: \n\n     CASE \n     IF test1 THEN commands1 END\n     IF test2 THEN commands2 END\n     ...\n      IF testN THEN commandsN END\n     [DEFAULT] [commandsD]\n     END;\n\nEvaluates test1. If true, executes commands1 and ends the CASE. Otherwise, evaluates test2. If true, executes commands2. Continues evaluating tests until a true is found. If no true test is found, executes commandsD, if provided.\n\n\n\n"]
[null,"cat","Syntax: cat(SeqObj)\n\nEvaluates the arguments, then concatenates them into a string.\n\nExample: cat(\"aaa\",c,12*3) returns \"aaac3\"\n\n\n"]
[null,"CEILING","Syntax: CEILING(value)\n\nLeast integer greater than or equal to value.\n \nExample: CEILING(3.2) returns 4 and CEILING(-3.2) returns -3\n"]
[null,"center","Syntax: center(Circle)\n\nReturns the center of a circle\n\nExample: center(circle(x^2+y2–x–y)) returns point(1/2,1/2)\n"]
[null,"cFactor","Syntax: cFactor(Expr)\n\nFactorisation of the expression in C (on the Gauss integers if there are more than 2 variables).\n\nExample: cFactor(x^2*y+y) returns (x+i)*(x-i)*y\n\n\n"]
[null,"CHAR","Syntax: CHAR(list or vector) or CHAR(integer)\n\nReturns the string corresponding to the ASCII character codes in vector, or the single character associated with integer.\n\nExample: CHAR(65) returns \"A\" and CHAR({82, 77, 72}) returns \"RMH\"\n"]
[null,"charpoly","Syntax: charpoly(Mtrx,[Var])\n\nList of the coefficients of the characteristic polynomial of a matrix or characteristic polynomial of a matrix with the second argument as variable.\n\nExample: charpoly([[1,2],[3,4]]) returns poly1[1,-5,-2]\n\n\n"]
[null,"CHECK","Syntax: CHECK(n)\nChecks (selects) the corresponding symbolic definition field in the current app. The integer n must be between 0 and 9 for most apps. For Statistics 1-Var and Statistics 2-Var apps, n must be between 1 and 5.\n\nFor example, CHECK(3) would check F3 if the current app is Function. Then a checkmark would appear next to F3 in Symbolic view,  F3 would be plotted in Plot view, and evaluated in Numeric view.\n"]
[null,"chinrem","Syntax: chinrem([Lst||Expr,Lst||Expr],[Lst||Expr,Lst||Expr])\n\nChinese remainder for polynomials written as matrices.\n\nExample: chinrem([[1,2,0],[1,0,1]],[[1,1,0],[1,1,1]]) returns [[2,2,1] [1,1,2,1,1]].\n\n\n"]
[null,"CHISQUARE","Syntax: CHISQUARE(n, x)\n\nChi-square probability density function. Computes the probability density of the Chi-squared distribution at x, given n degrees of freedom.\n\nExample: CHISQUARE(2, 3.2) returns 0.100948258997\n"]
[null,"CHISQUARE_CDF","Syntax: CHISQUARE_CDF(n, k)\n\nCumulative χ² (Chi-squared) distribution function. Returns the lower-tail probability of the χ² probability density function for the value x, given n degrees of freedom.\n\nExample: CHISQUARE_CDF(2, 6.1) returns 0.952641075609\n"]
[null,"CHISQUARE_ICDF","Syntax: CHISQUARE_ICDF(n, p)\n\nInverse cumulative χ² (Chi-squared) distribution function. Returns the value x such that the χ² lower-tail probability of x, with n degrees of freedom, is p.\n\nExample: CHISQUARE_ICDF(2, 0.952641075609) returns 6.1\n"]
[null,"cholesky","Syntax: cholesky(Mtrx)\n\nFor a numerical symmetric matrix A, returns L matrix such that A=L*tran(L).\n\nExample: cholesky([[3,1],[1,4]]) returns [[3*√3/3,0],[√3/3,11/3*√33/11]]\n\n\n"]
[null,"CHOOSE","Syntax: CHOOSE(var, “title”, “item1”, “item2”,[…\"item14\"]) or CHOOSE(var,\"title\",{\"item1\"...\"itemN\")\n\nDisplays a choose box with the given title and containing items with the strings \"item1\", etc. If the user choose an object, var will be updated to contain the number of the selected object (an integer, 1, 2, 3, …); otherwise, stores zero in var if the user exits without choosing.\n\nReturns true (non zero) if the user selects an object, otherwise return false (0).\n"]
[null,"chrem","Syntax: chrem(LstIntg(a,b,c....),LstIntg(p,q,r,....))\n\nChinese remainders for integers.\n\nExample: chrem([2,3],[7,5]) returns [-12,35]\n\n"]
[null,"Ci","Syntax: Ci(Expr)\n\nCosine integral int(cos(t)/t,t=-∞..x).\n\nExample: Ci(1.0) returns 0.337403922901\n\n\n"]
[null,"circle","Syntax:circle(Point1, Point2) or circle(Point1, Point 2-Point1) or circle(equation)\n\nDraws a circle, given the endpoints of the diameter, or a center and radius, or an equation in x and y.\n\nExamples:\ncircle(GA, GB) draws the circle with diameter AB.\ncircle(GA, GB-GA) draws the circle with center at point A and radius AB.\ncircle(x^2+y^2=1) draws the unit circle.\n\nThis command can also be used to draw a clockwise arc.\ncircle(GA, GB, 0, π/2) draws a quarter-circle with diameter AB.\n\n\n\n"]
[null,"circumcircle","Syntax: circumcircle(Point1, Point2, Point3)\n\nDraws the circumcircle of a triangle; that is, the circle circumscribed about a triangle.\n\nExample: circumcircle(GA, GB, GC) draws the circle circumscribed about ΔABC\n\n\n"]
[null,"coeff","Syntax: coeff(Expr,[Var], [Term])\n\nReturns the list of coefficients of a polynomial with respect to the second argument or the coefficient of the term whose degree is Term.\n\nExamples: \ncoeff(x^3+2) returns [1,0,0,2]\ncoeff(2*y^2-3,y,0) returns -3\n\n"]
[null,"col","Syntax: col(Mtrx(A),Intg(n)||Interval(n1..n2))\n\nReturns the column n or the sequence of the columns n1...n2 of the matrix A, or optional argument of count,count_eq,count_inf,count_sup.\n\nExample: col([[1,2,3],[4,5,6],[7,8,9]],1) returns [2,5,8]   \n\n\n"]
[null,"colDim","Syntax: coldim(Mtrx)\n\nNumber of columns of a matrix.\n\nExample: coldim([[1,2,3],[4,5,6]]) returns 3 \n\n\n"]
[null,"collect","Syntax: collect(Expr or {Expr1, Expr2,...,Exprn})\nCollects likes terms in a polynomial expression (or of a list of polynomial expressions).\n\nExample: collect(x+2*x+1-4) returns 3*x-3\n\n\n"]
[null,"COLNORM","Syntax: COLNORM(matrix)\n\nColumn Norm. Finds the maximum value (over all columns) of the sums of the absolute values of all elements\n\nExample: COLNORM([[1,2],[3,4]]) returns 6\n"]
[null,"COMB","Syntax: COMB(n, r)\n\nCombinations. Returns the number of combinations (without regard to order) of n things taken r at a time: n!/(r!(n-r))\n\nExample: COMB(5,2) returns 10 \n"]
[null,"comDenom","Syntax: comDenom(Expr,[Var(var)])\n\nReturns the expression after reduction at the same denominator: the numerator and the denominator are developed [according to the powers of the variable var].\n\nExample: comDenom(1/x+1/y^2+1) returns (x*y^2+x+y^2)/(x*y^2)  \n\n\n"]
[null,"common_perpendicular","Syntax: common_perpendicular(Line(D1),Line(D2))\n\nDraws the common perpendicular of the lines D1 and D2.\n\n\n"]
[null,"companion","Syntax: companion(Poly,Var)\n\nCompanion matrix of a polynomial (an=1).\n\nExample: companion(x^2+5x-7,x) returns [[0,7],[1,-5]]\n\n\n"]
[null,"compare","Syntax: compare(Obj(arg1),Obj(arg2))\n\nReturns 1 if  type(arg1)<type(arg2) or if type(arg1)=type(arg2) and arg1<arg2, else returns 0.\n\nExample: compare(1,2) returns 1\n\n\n"]
[null,"complexroot","Syntax: complexroot(Poly(P),Real(l),[Cplx(a)],[Cplx(b)])\n\nReturns the list of the vertices of the squares (side<=l) containing roots of P [inside the rectangle with opposed vertices a and b] with their mulitiplicity.\n\nExample: complexroot(x^5-2*x^4+x^3+i,0.1) returns [[[(-21-12*i)/32,(-18-9*i)/32],1],[[(6-15*i)/16,(-6-21*i)/(16-16*i)],1],[[(27+18*i)/(16+16*i),(24-3*i)/16],1],[[(6+27*i)/(16+16*i),(9+6*i)/8],1],[[(-15+6*i)/(16+16*i),(-3+12*i)/16],1]]\n\n\n"]
[null,"CONCAT","Syntax: CONCAT(value1, value2, [..value16])\n\nConcatenation. Concatenates (joins) items into a list.\n \nExample: CONCAT({1,2,3}, 4) returns  {1,2,3,4} and CONCAT(1,2,3,4) returns {1,2,3,4}\n"]
[null,"COND","Syntax: COND(matrix)\n\nCondition Number. Finds the 1-norm (column norm) of a square matrix.\n\nExample: COND([[1,2],[3,4]]) returns 21\n"]
[null,"conic","Syntax: conic(Expr)\n\nPlots the graph of a conic section defined by an expression in x and y.\n\nExample:  conic(x^2+y^2-81) draws a circle with center at (0,0) and radius of 9\n\n\n"]
[null,"CONJ","Syntax: CONJ(x+yi)\n\nComplex Conjugate. Reverses the sign of the imaginary part of a complex number.\n\nExample: CONJ(3+4i) returns 3-4i\n"]
[null,"contains","Syntax: contains((Lst(l) or Set(l)),Elem(e))\n\nTests if a set contains an expression (returns the index+1 or 0).\n\nExample: contains(%{0,1,2,3%},2) returns 3\n\n\n"]
[null,"content","Syntax: content(Poly,[Var])\n\nReturns the gcd of the coefficients of the polynomial Poly.\n\nExample: content(2*x^2+10*x+6) returns 2\n\n\n"]
[null,"CONTINUE","Syntax CONTINUE [n];\n\nTransfers execution in a loop to the start of the next iteration of the nth upper loop (default current loop).\n"]
[null,"CONVERT","Syntax: CONVERT(Value_Unit1, 1_Unit2)\nConverts Value in Unit1 to the corresponding value in compatible Unit2.\n\nExample: CONVERT(20_m, 1_ft) returns 65.6167979003_ft\n\nAlternative: 20_m ► _ft\n"]
[null,"convexhull","Syntax: convexhull(Lst)\n\nConvex hull of a list of 2D points.\n\nExample: convexhull(0,1,1+i,1+2i,-1-i,1-3i,-2+i) returns 1-3*i,1+2*i,-2+i,-1-i\n\n\n"]
[null,"coordinates","Syntax: coordinates(Pnt or Cplx or Vect)\n\nReturns the list (resp matrix) of the abscissa and of the ordinate of a point or a vector (resp of points or vectors).\n\nExample: coordinates(point(1+2*i)) returns [1,2]\n"]
[null,"CopyVar","Syntax: CopyVar(Var(var1),Var(var2))\n\nCopy the storage without evaluation of var1 into var2.\n\n\n"]
[null,"correlation","Syntax: correlation(Lst||Mtrx,[Lst])\n\nReturns the correlation of the elements of its argument.\n\nExample: correlation([[1,2],[1,1],[4,7]]) returns 33/(6*√31)\n\n\n"]
[null,"COS","COS: the cosine function.\nSyntax: COS(Value)\n\nReturns the cosine of Value. Value is interpreted as either degrees or radians, depending on the setting of Angle Measure in Home Modes or Symbolic Setup.\n\nExample: in radian mode, COS(π) returns -1.\n"]
[null,"cos2sintan","Syntax: cos2sintan(Expr)\n\nReplaces cos(x) by  sin(x)/tan(x) in the argument.\n\nExample: cos2sintan(cos(x)) returns sin(x)/tan(x) \n\n\n"]
[null,"COSH","Syntax: COSH(value)\n\nHyperbolic cosine.\n\nExample: ASINH(1.17520119365) returns 1\n"]
[null,"COT","Syntax: COT(value)\n\nCotangent. The Cotangent function; that is, cos(x)/sin(x).\n\nExample: COT(45) returns 1 in degree mode\n"]
[null,"count","Syntax: count(Fnc(f),(Lst||Mtrx)(l),[Opt(row||col)])\n\nReturns f(l[0])+f(l[1])+...+f(l[size(l)-1]).\n\nExample: count((x)->x,[2,12,45,3,7,78]) returns 147 \n\n\n"]
[null,"covariance","Syntax: covariance(Lst||Mtrx,[Lst])\n\nReturns the covariance of the elements of its argument.\n\nExample: covariance([[1,2],[1,1],[4,7]]) returns 11/3\n\n\n"]
[null,"covariance_correlation","Syntax: covariance_correlation(Lst||Mtrx,[Lst])\n\nReturns the list of the covariance and the correlation of the elements of its argument.\n\nExample: covariance_correlation([[1,2],[1,1],[4,7]]) returns [11/3,33/(6*√31)] \n\n\n"]
[null,"cpartfrac","Syntax: cpartfrac(RatFrac)\n\nPerforms partial fraction decomposition in C of a fraction.\n\nExample: cpartfrac((x)/(4-x^2)) returns 1/((x-2)*-2)+1/((x+2)*-2) \n\n\n"]
[null,"crationalroot","Syntax: crationalroot(Poly(P))\n\nReturns the list of complex rational roots of P without indicating the multiplicity.\n\nExample: crationalroot(2*x^3+(-5-7*i)*x^2+(-4+14*i)*x+8-4*i) returns [(3+i)/2,2*i,1+i] \n\n\n"]
[null,"CROSS","Syntax: CROSS(vector1, vector2)\n\nCross Product. Finds the cross product of vector1 with vector2.\n\nExample: CROSS([1,2],[3,4]) returns [0, 0, -2]\n"]
[null,"CSC","Syntax: CSC(value)\n\nCosecant. The Cosecant function; that is, 1/sin(x)\n\nExample: CSC(90) returns 0 in degree mode\n"]
[null,"cSolve","Syntax: csolve(Eq,Var)\n\nReturns the solutions, including comlex solutions, of Eq, for Var. If Eq is an expression, solves Eq=0.\n\nExample: csolve(x^4=1,x) returns {1,-1,-i,i}\n"]
[null,"cumSum","Syntax: cumSum(Lst(l)||Seq||Str)\n\nReturns the list (or the sequence or the string) lr where the elements are the cumulative sum of the list l:lr[k]=sum(l[j],j=0..k) (or lr=sum(l[j],j=0..k )$(k=0..size(l)-1)).\n\nExample: cumSum([0,1,2,3,4]) returns [0,1,3,6,10]\n\n\n"]
[null,"curl","Syntax: curl(Lst(A,B,C),Lst(x,y,z))\n\nReturns the curl of a vector. curl([A,B,C],[x,y,z])=[dC/dy-dB/dz,dA/dz-dC/dx,dB/dx-dA/dy].\n\nExample: curl([2*x*y,x*z,y*z],[x,y,z]) returns [z-x,0,z-2*x]\n\n"]
[null,"curve","Syntax: curve(Expr)\nReserved word.\n\n"]
[null,"cyan","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"cyclotomic","Syntax: cyclotomic(Expr)\n\nGenerates a vector representing the nth cyclotomic polynomial.\n\nExample: cyclotomic(20) returns [1,0,-1,0,1,0,-1,0,1]\n\n"]
[null,"cZeros","Syntax: cZeros(Expr,[Var]) or cZeros(ListExpr, ListVar)\n\nReturns the roots, including complex roots, of Expr (that is, the solution of Xpr=0) or the matrix where the lines are the solutions of the system : Expr1=0,Expr2=0....\n\nExample: cZeros(x^4-1) returns [1,-1, i, -i] \n\n\n"]
[null,"C→PX","Syntax: C→PX(x, y)  or C→PX({x, y}) \n\nTransform cartesian coordinates into pixel coordinates. Returns a list.\n"]
[null,"DEBUG","Executes a program in debug mode.\nSyntax: DEBUG(ProgramName(arguments))\n"]
[null,"degree","Syntax: degree(Poly)\n\nReturns the degree of the polynomial Poly.\n\nExample: degree(x^4+x) returns 3 \n\n\n"]
[null,"DELCOL","Syntax: DELCOL(matrixname ,column_number)\nDelete Column. Deletes the column column_number from the matrix matrixname.\n"]
[null,"delcols","Syntax: delcols(Mtrx(A),Interval(n1..n2)||n1)\n\nReturns the matrix where the columns n1..n2 (or n1) of the matrix A are deleted. \n\nExample: delcols([[1,2,3],[4,5,6],[7,8,9]],1..1) returns [[1,3],[4,6],[7,9]] \n\n\n"]
[null,"DELROW","Syntax: DELROW(matrixname, row_number)\nDelete Row. Deletes the row row_number from the matrix matrixname.\n"]
[null,"delrows","Syntax: delrows(Mtrx(A),Interval(n1..n2)||n1)\n\nReturns the matrix where the rows n1..n2 (or n1) of the matrix A are deleted. \n\nExample: delrows([[1,2,3],[4,5,6],[7,8,9]],1..1) returns [[1,2,3],[7,8,9]] \n\n\n"]
[null,"deltalist","Syntax: deltalist(Lst)\n\nReturns the list of the difference of two terms in succession.\n\nExample: deltalist([1,4,8,9]) returns [3,4,1]  \n\n\n"]
[null,"denom","Syntax: denom(a/b)\n\nSimplified Denominator. For the integers a and b, returns the denominator of the fraction a/b after simplification.\n\nExample: denom(10/12) returns 6\n"]
[null,"desolve","Syntax: desolve(Eq,[TimeVar],Var)\n\nSolves a differential equation.\n\nExample: desolve(y''+y=0,y) returns G_0*cos(x)+G_1*sin(x)   \n\n\n"]
[null,"DET","Syntax: DET(matrix)\n\nDeterminant of a square matrix.\n\nExample: DET([[1,2],[3,4]]) returns -2\n"]
[null,"diag","Syntax: diag(Lst(l)||Mtrx(A))\n\nReturns either the diagonal matrix with diagonal l or the diagonal of A.\n\nExample: diag([1,2],[3,4]) returns [1,4]\n\n\n"]
[null,"diff","Syntax: diff(Expr,[Var or ListVar])\n\nReturns the derivative of an expression with respect to a given variable. You can use the differentiation template in the Template menu as well.\n\nExamples: \ndiff(x^3-x) returns 3*x^2-1\ndiff(sin(x)-cos(y), x) returns cos(x)\ndiff(sin(x)-cos(y), y) returns sin(y)\n"]
[null,"DIFFERENCE","Syntax: DIFFERENCE({list1}, ...{listN})\n\nReturns a list of the elements that are not common between 2 or more of the lists.\n\nExample: DIFFERENCE({1,2,3},{2,4,8}) returns {1,3,4,8}\n"]
[null,"DIM","Syntax: DIM(string)\n\nReturns the number of characters in string.\n\nExample: DIM(\"12345\") returns 5\n"]
[null,"DIMGROB","Syntax: DIMGROB(G, w, h, [color]) or DIMGROB(G, w, h, list)\n\nSets the dimensions of GROB G to w*h. Initializes the graphic G with color or with the graphic data provided in list. If the graphic is initialized using graphic data, then list is a list of integers. Each integer, as seen in base 16, describes one color every 16 bits.\n\nColors are in A1R5G5B5 format (ie, 1 bit for alpha channel, and 5 bits for R, G and B).\n \n\n"]
[null,"DIMGROB_P","Syntax: DIMGROB_P(G, w, h, [color]) or DIMGROB(G, list)\n\nSets the dimensions of GROB G to w*h. Initializes the graphic G with color or with the graphic data provided in list. If the graphic is initialized using graphic data, then list is a list of integers. Each integer, as seen in base 16, describes one color every 16 bits.\n\nColors are in A1R5G5B5 format (ie, 1 bit for alpha channel, and 5 bits for R, G and B). \n"]
[null,"Dirac","Syntax: Dirac(Real)\n\nFunction derivative of Heaviside.\n\nExample: Dirac(1) returns 0\n\n\n"]
[null,"distance","Syntax: distance((Pnt or Cplx),(Pnt or Cplx or Curve))\n\nCalculates the distance between 2 points, or a point and a curve.\n\nExample: distance(0,1+i) returns √2\n\n\n"]
[null,"distance2","Syntax: distance2(point1, point2) or distance2(point, curve)\n\nReturns the square of the distance between two points or between a point and a curve.\n\nExamples:\ndistance2(1+i, 3+3i) returns 8.\nif GA is the point at (0, 0) and GB is defined as plotfunc(4-x^2/4), then distance (GA, GB) returns 12.\n\n"]
[null,"distanceat","Syntax: distanceat(GeoObj(A),GeoObj(B),(Pnt or Cplx))\n\ndistanceat(A,B,z0) displays at point(z0), with a legend, the distance between 2 geometrical objects.\n\nExample:  A:=point(0);B:=point(1+i);distanceat(A,B,(1+i)/2)) returns √2\n\n\n"]
[null,"distanceatraw","Syntax: distanceatraw(Point1, Point2, Point3) or distanceatraw(Point1, Curve, Point3)\n\nThis command is used in Symbolic view. Similar to distanceat(), this commmand returns the distance between two points or between a point and a curve and places that measurement at the location of Point3 in the Plot view. The distance is unlabeled.\n\nExamples\ndistanceatraw(1+I, 3+3i, point(0,0)) returns 2.828…or 2√2 and places that measure at the origin in Plot view.\n\nIf GA is the point at (0, 0) and GB is defined as plotfunc(4-x^2/4), then distanceat(GA, GB, GA) returns 3.464… or 2√3 and places this measure in Plot view at (0,0).\n\nDefine A:=point(0) and B:=point(1+i); then distanceatraw(A,B,(1+i)/2)) returns  √2 and places this measurement at (1/2, 1/2)\n\n\n \n"]
[null,"divergence","Syntax: divergence(Lst(A,B,C),Lst(x,y,z))\n\nReturns the divergence of a vector. divergence([A,B,C],[x,y,z])=dA/dx+dB/dy+dC/dz.\n\nExample: divergence([x^2+y,x+z+y,z^3+x^2],[x,y,z]) returns 2*x+3*z^2+1\n\n\n"]
[null,"divis","Syntax: divis(Poly(P) or LstPoly)\n\nReturns the list of divisors of a polynomial.\n\nExample: divis(x^2-1) returns [1,x-1,x+1,(x-1)*(x+1)]\n\n\n"]
[null,"division_point","Syntax: division_point(Point1, Point2, Realk) or division_point(Cplx1, Cplx2, Cplxk)\n\nFor two points A and B, and a numerical factor k, returns a point C such that C-B=k*(C-A). The two points may be referenced by name or represented by a complex number.\n\nExample: division_point(0,6+6*i,4) returns point (8,8)\n\n\n"]
[null,"divpc","Syntax: divpc(Poly1,Poly2,Integer)\n\nReturns the n-degree Taylor polynomial for the quotient of 2 polynomials.\n\nExample: divpc(x^4+x+2,x^2+1,5) returns the 5th-degree polynomial x^5+3*x^4-x^3-2*x^2+x+2\n"]
[null,"DO","Syntax: FOR var FROM start TO (or DOWNTO) finish [STEP increment] DO command(s) END;\n\nSets variable var to start; then, for as long as this variable’s value is less than or equal to (or more than for a DOWNTO) finish, executes  command(s) and adds (or substract for DOWNTO) 1 (or increment) to var. \n\nFOR A FROM 1 TO 10 STEP 2\n  DO \n    PRINT(A); \nEND;\n\nwill print  1 3 5 7 9\n"]
[null,"DOT","Syntax: DOT(matrix1, matrix2)\n\nDot Product. Finds the dot product of two arrays, matrix1 and matrix2.\n\nExample: DOT([1,2],[3,4]) returns 11\n"]
[null,"DRAWMENU","Syntax: DRAWMENU({text...}) or DRAWMENU(text..)\n\nDraw a menu containing the items specified\n"]
[null,"DrawSlp","Syntax: DrawSlp(Reala, Realb, Realm)\n\nGiven three real numbers m, a, b, draws a line with slope m that passes through the point (a, b).\n\nExample: DrawSlp(2,1,3) draws the line given by y=3x–5\n\n\n"]
[null,"e","Syntax: e\nNatural logarithm base, internally represented as 2.71828182846\n"]
[null,"EDITLIST","Syntax: EDITLIST(listname)\nStarts the List Editor and displays the specified list. If used in programming, returns to the program when user presses OK (menu key). \n\nExample:\n EDITLIST(L1) edits list L1.\n"]
[null,"EDITMAT","Syntax: EDITMAT(matrixname)\nStarts the Matrix Editor and displays the specified matrix. If used in programming, returns to the program when user presses OK (menu key). \nExample\n EDITMAT(M1) edits matrix M1.\n"]
[null,"egcd","Syntax: egcd((Poly or Lst),(Poly or Lst),[Var])\n\nReturns the extended greatest common divisor of 2 polynomials.\n\nExample: egcd((x-1)^2,x^3-1) returns [-x-2,1,3*x-3] \n\n\n\n"]
[null,"Ei","Syntax: Ei(Expr)\n\nExponential integral int(exp(t)/t,t=-∞..x)\n\nExample: Ei(1.0) returns 1.89511781636 \n\n\n"]
[null,"EIGENVAL","Syntax: EIGENVAL(matrix)\n\nDisplays the eigenvalues in vector form for matrix.\n\nExample: EIGENVAL([[1,2],[3,4]]) returns [5.37228132327 -.372281323269]\n"]
[null,"eigenvals","Syntax: eigenvals(Mtrx)\n\nReturns the sequence of the (calculable) eigenvalues of a matrix.\n\nExample: eigenvals([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) returns 3,-3,-3 \n\n\n"]
[null,"eigenvects","Syntax: eigenvects(Mtrx)\n\nComputes the eigenvectors of a diagonalizable matrix.\n\nExample: eigenvects([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) returns [[1,-3,-3],[-2,0,-3],[1,3,-3]] \n"]
[null,"EIGENVV","Syntax: EIGENVV(matrix)\n\nEigenvectors and Eigenvalues for a square matrix. Displays a list of two arrays. The first contains the eigenvectors and the second contains the eigenvalues.\n\nExample: EIGENVV([[1,2],[3,4]]) returns { [[eigenvectors]],[[eigenvalues]] }\n"]
[null,"eigVc","Syntax: eigVc(Mtrx)\n\nComputes the eigenvectors of a diagonalizable matrix.\n\nExample: eigVc([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) returns [[1,-3,-3],[-2,0,-3],[1,3,-3]] \n\n\n"]
[null,"eigVl","Syntax: eigVl(Mtrx(A))\n\nReturns the Jordan matrix associated to A when the eigenvalues are calculable.\n\nExample: eigVl([[4,1],[-4,0]]) returns [[2,1],[0,2]]\n\n\n"]
[null,"element","Syntax: element(object, real) or element(real1..real2)\n\nCreates a point on a geometric object whose abscissa is a given value or creates a real value on a given interval. \n\nExamples:\nelement(plotfunc(x^2),–2) creates a point on the graph of  y = x^2. Initially, this point will appear at (–2,4). You can move the point, but it will always remain on the graph of its function.\n\nelement(0..5) creates a value of 2.5 initially. Tapping on this value and pressing Enter enables you to press a cursor key to increase or decrease the value in a manner similar to a slider bar. Press Enter again to close the slider bar. The value you set can be used as a coefficient in a function you subsequently plot.\n"]
[null,"ellipse","Syntax: ellipse(Point1, Point2, Point3) or ellipse(Point1, Point2, Realk)\n\nDraws an ellipse, given the foci and either a point on the ellipse or a scalar that is one half the constant sum of the distances from a point on the ellipse to each of the foci.\n\nExamples:\nellipse(GA, GB, GC) draws the ellipse whose foci are points A and B and which passes through point C.\n\nellipse(GA, GB, 3) draws an ellipse whose foci are points A and B. For any point P on the ellipse, AP+BP=6.\n\n\n\n"]
[null,"ELSE","Starts an \"IF...THEN...END\" or \"IF...THEN...ELSE...END\" branch structure.\n\nSyntax: IF test THEN command(s) [ELSE commands] END;\nEvaluates test. If test is true (non 0), executes command(s); otherwise, executes the comands in the ELSE clause nothing happens.\n\nIF A<1 \n  THEN PRINT(\"A IS SMALLER THAN 1\"); \n  ELSE PRINT(\"A IS LARGER THAN 1\"); \nEND;\n"]
[null,"END","Ends a structure, either a block, a test, a loop or a branch.\n"]
[null,"equation","Syntax: equation(curve) or equation(point)\n\nReturns the Cartesian equation of a curve in x and y, or the Cartesian coordinates of a point.\n\nExamples:\nequation(line(1-i,i)) returns y=-2*x+1\nIf GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as circle(GA, GB-GA), then equation(GC) returns  x^2 + y^2 =1.\n\n"]
[null,"equilateral_triangle","Syntax: equilateral_triangle(Point1, Point2, [Var]) \n\nDraws an equilateral triangle defined by one of its sides; that is, by two consecutive vertices. The third point is calculated automatically, but is not defined symbolically. If a lowercase variable is added as a third argument, then the third point is labeled with the variable name and the coordinates of the third point are stored in that variable. The orientation of the triangle is counterclockwise from the first point.\n\n\nExample: equilateral_triangle(point(0,0), point(1,0)) draws the equilateral trangle through the points at (0,0), (1,0), and (1/2, √3/2).\n"]
[null,"erf","Syntax: erf(Real(x0))\n\nReturns the approximate value of 2/√π*int(exp(-t^2),t,0,x0)\n\nExample: erf(1) returns 0.84270079295\n\n\n\n\n"]
[null,"erfc","Syntax: erfc(Real(x0))\n\nReturns the approximate value of 2/√π*int(exp(-t^2),t,x0,∞).\n\nExample: erfc(1) returns 0.15729920705\n\n\n\n\n"]
[null,"euler","Syntax: euler(x);\n\nEuler’s phi (or totient) function. Takes a positive integer x and returns the number of positive integers less than or equal to x that are coprime to x.\n\nExample: euler(6) returns 2\n"]
[null,"EVAL","Syntax: EVAL(expression)\n\nEvaluates the expression. Usefull in programs where parameters are passed non evaluated with QUOTE\n"]
[null,"evalc","Syntax: evalc(Expr)\n\nReturns a complex expression simplified with the format real+i*imag\n\nExample: evalc(1/(x+y*i)) returns x/(x^2+y^2)+(i)*(-y)/(x^2+y^2) \n\n\n"]
[null,"evalf","Syntax: evalf(Expr,[Int])\n\nNumerical evaluation of the first argument (we can give the number of digits as second argument).\napprox(expression) works also and does the same thing.\n\nExample: evalf(2/3) returns 0.666666666667  \n\n\n"]
[null,"even","Syntax: even(Intg(n))\n\nReturns 1 if the integer is even, else returns 0.\n\nExample: even(6) returns 1\n\n\n"]
[null,"exact","Syntax: exact(Expr)\n\nConverts the expression to a rational or real expression. \n\nExample: exact(1.4141) returns 14141/10000\n"]
[null,"exbisector","Syntax: exbisector(Point1, Point2, Point3)\n\nGiven three points that define a triangle, creates the bisector of the exterior angles of the triangle whose common vertex is at the first point. The triangle does not have to be drawn in the Plot view.\n\nExamples:\nexbisector(GA, GB, GC) draws the bisector of the exterior angles of ΔABC whose common vertex is at point A.\n\nexbisector(0,–4i,4) draws the line given by y=x\n\n\n"]
[null,"excircle","Syntax: excircle(Point1, Point2, Point3)\n\nexcircle(A,B,C) draws the A-excircle of the ABC triangle.  \n\nDraws one of the excircles of a triangle, a circle tangent to one side of the triangle and also tangent to the extensions of the other two sides.\n\nExample: excircle(GA, GB, GC) draws the circle tangent to BC and to the rays AB and AC.\n\n"]
[null,"EXECON","Syntax: EXECON(\"expression with &\", lists or matrices)\n\nReturns a matrix or list composed of the result of the evaluation of the expression after replacement of & by each item in the input.\nExample: EXECON(\"&1+1\", {1,2,3}) returns {2,3,4}\n\nIf EXECON has only 1 list or matrix input, using & followed by a number A (between 1 and 9) will replace &A by the element i+A-1 of the input.\nExample: EXECON(\"&2-&1\", { 1, 4, 3, 5}\") returns {3, -1, 2} - the difference between 2 successive elements.\n\nIf EXECON has 2 or more lists or matrices input, using & followed by a number A (between 1 and 9) will replace &1 by the element from the Ath input.\nExample: EXECON(\"&1+&2\", {1,2,3},{4,5,6}) returns {5,7,9}\n\nIf EXECON has 2 or more lists or matrices as input, using & followed by 2 numbers A and B (between 1 and 9) will reaplace &AB by the element i+B-1 of the Ath input.\nExample: EXECON(\"&22-&1\", {1,2,3},{4,5,6,7}) returns {4,4,4}\n\nNote that for matrix input, the elements are treated as if the matrix was a vector.\n"]
[null,"EXP","Syntax: EXP(value)\nThe natural exponential. This is more accurate than e^x due to limitations of the power function.\n"]
[null,"exp2pow","Syntax: exp2pow(Expr)\n\nTransforms an expression of the form exp(n*ln(x)) to x^n.\n\nExample: exp2pow(exp(3*ln(x))) returns x^3\n\n\n"]
[null,"exp2trig","Syntax: exp2trig(Expr)\n\nTransforms the complex exponential into sine and cosine.\n\nExample: exp2trig(exp-(i*x)) returns cos(x)-i*sin(x)  \n\n\n"]
[null,"expand","Syntax: expand(Expr )\n\nFull distribution of multiplication and division over addition and subtraction.\n\nExample: expand((x+y)*(z+1)) returns y*z+x*z+y+x\n"]
[null,"expexpand","Syntax: expexpand(Expr)\n\nExpands exponentials usinng the identity exp(a*f(x))=(exp(f(x)))^a.\n\nExample: expexpand(exp(3*x)) returns exp(x)^3  \n\n\n"]
[null,"EXPM1","Syntax: EXPM1(value)\n\nExponent minus 1. This is more accurate than EXP when x is close to zero.\n\nExample: EXPM1(.23) returns .258600009929\n"]
[null,"exponential_regression","Syntax: exponential_regression(Lst||Mtrx(A),[Lst])\n\nReturns the coefficients (a,b) of y=b*a^x : it is the best exponential that approximates the points where the coordinates are the rows of A (or the 2 lists).\n\nExample: exponential_regression([[1.0,2.0],[0.0,1.0],[4.0,7.0]]) returns 1.60092225473,1.10008339351  \n\n\n"]
[null,"EXPORT","Syntax: \nVariable declaration: EXPORT var_1[:=value][, more variables];\nforward function declaration: EXPORT function(params); \nNormal function declaration: or EXPORT function[(params)]\nBEGIN\nEND;\n\nIn a program, declares a list of exported variable or an exported function.\n\n"]
[null,"EXPR","Syntax: EXPR(string)\n\nParses string into a number or expression.\n\nExample: EXPR(\"2+3\") returns 5\n"]
[null,"extract_measure","Syntax: extract_measure(Var)\n\nReturns the definition of a geometric object. For a point, that definition consists of the coordinates of the point. For other objects, the definition mirrors their definition in Symbolic view, with the coordinates of their defining points supplied.\n\nExamples: \nextract_measure(angleatraw(0,1,1+i,1)\nextract_measure(distanceatraw(0,1+i,(1+i)/2)) returns √2\n\n\n"]
[null,"ezgcd","Syntax: ezgcd(Poly,Poly)\n\nReturns the GCD of 2 polynomials with at least 2 variables, with the ezgcd algorithm.\n\nExample: ezgcd(x^2-+3*x-xy-3*y,x^2-y^2) returns x-y\n\n\n"]
[null,"f2nd","Syntax: f2nd(Frac or RatFrac)\n\nReturns the list built with the numerator and the denominator of the simplified fraction.\n\nExample: f2nd(42/12) returns [7,2]\n\n\n"]
[null,"factor","Syntax: factor(Expr)\n\nFactorizes a polynomial.\n\nExample: factor(x^4-1) returns (x-1)*(x+1)*(x^2+1) \n\n\n"]
[null,"factor_xn","Syntax: factor_xn(Poly)\n\nFactorizes x^n in P\\the polynomial Poly (n=degree of polynomial P).\n\nExample: factor_xn(x^4-1) returns x^4*(1-x^-4) \n\n\n"]
[null,"factorial","Syntax: factorial(Intg(n)|| Real(a) )\n\nfactorial(n)=n!. For non-integers, factorial(a)=a! = G(a + 1). This calculates the Gamma function. \n\nExample: factorial(4) returns 24\n\n\n"]
[null,"factors","Syntax: factors(Poly) or factors({Poly1, Poly2, ..., Polyn})\n\nReturns the list of prime factors of a polynomial; each factor followed by its multiplicity.\n\nExample: factors(x^4-1) returns [x-1,1,x+1,1,x^2+1,1] \n\n\n"]
[null,"fcoeff","Syntax: fcoeff(Root1, Oder1, Root2, Order2, ..., Rootn, Ordern)\n\nReturns the polynomial described by a list of roots, each followed by its order.\n\nExample: fcoeff([1,2,0,1,3,-1]) returns ((x-1)^2)*x*(x-3)^-1 \n"]
[null,"fft","Syntax: fft(Vect or (Vect(L),Intg(a),Intg(p))\n\nFast Fourier Transform in R or in the field Z/pZ, with a as primitive n-th root of 1 (n=size(L)).\n\nExample: fft([1,2,3,4,0,0,0,0]) returns [10.0,-0.414213562373-7.24264068712*(i),-2.0+2.0*i,2.41421356237-1.24264068712*i,-2.0,2.41421356237+1.24264068712*i,-2.0-2.0*i] \n\n\n"]
[null,"FILLPOLY","Syntax: FILLPOLY([G], {coordinates...} or [Coordinates], Color, [Alpha])\n\nFills the polygon specified by the provided Cartésian coordinates using the color provided.\nIf Alpha (0 to 255) is provided, the polygon is drawn with trensparency.\n\nExample: FILLPOLY([(0,0),(1,1),(2,0),(3,-1),(2,-2)], #FF, 128)\n"]
[null,"FILLPOLY_P","Syntax: FILLPOLY_P([G], {coordinates...} or [Coordinates], Color, [Alpha])\n\nFills the polygon specified by the provided pixel coordinates using the color provided.\nIf Alpha (0 to 255) is provided, the polygon is drawn with trensparency.\n\nExample: FILLPOLY_P([(20,20),(120,120),(150,20),(180,150),(50,100)], #FF, 128)\n"]
[null,"FISHER","Syntax: FISHER(n, d, x)\n\nF (Fisher or Fisher-Snedecor) probability density function. Computes the probability density at the value x, given numerator n and denominator d degrees of freedom.\n\nExample: FISHER(5, 5, 2) returns 0.158080231095\n"]
[null,"FISHER_CDF","Syntax: FISHER_CDF(n, d, x)\n\nCumulative F (Fisher or Fisher-Snedecor) distribution function. Returns the lower-tail probability of the F probability density function for the value x, given numerator n and denominator d degrees of freedom. \n\nExample: FISHER_CDF(5, 5, 2) returns 0.76748868087\n"]
[null,"FISHER_ICDF","Syntax: FISHER_ICDF(n, d, p)\n\nInverse cumulative F (Fisher or Fisher-Snedecor) distribution function. Returns the value x such that the F lower-tail probability of x, with numerator, n and denominator, d degrees of freedom, is p.\n\nExample: FISHER_ICDF(5, 5, 0.76748868087) returns 2\n"]
[null,"FLOOR","Syntax: FLOOR(value)\n\nGreatest integer less than or equal to value.\n\nExample: FLOOR(-3.2) returns -4\n\n"]
[null,"fMax","Syntax: fMax(Expr,[Var])\n\nReturns the abscissa of the maximum of the expression.\n\nExample: fMax(-x^2+2*x+1,x) returns 1\n\n\n"]
[null,"fMin","Syntax: fMin(Expr,[Var])\n\nReturns the abscissa of the minimum of the expression.\n\nExample: fMin(x^2-2*x+1,x) returns 1\n\n\n"]
[null,"FNROOT","Syntax: FNROOT(expression, variable, [guess], [guess2])\n\nFunction root-finder (like the Solve app). Finds the value for variable at which expression most nearly evaluates to zero. Uses guess as initial estimate. \n\nExample: FNROOT(M*9.8/600-1, M, 1) returns 61.2244897959\n"]
[null,"FOR","Syntax: FOR var FROM start TO (or DOWNTO) finish [STEP increment] DO command(s) END;\n\nSets variable var to start; then, for as long as this variable’s value is less than or equal to (or more than for a DOWNTO) finish, executes  command(s) and adds (or substract for DOWNTO) 1 (or increment) to var. \n\nFOR A FROM 1 TO 10 STEP 2\n  DO \n    PRINT(A); \nEND;\n\nwill print  1 3 5 7 9\n"]
[null,"format","Syntax: format(Real,Str(\"f4\"||\"s5\"||\"e6\"))\n\nTransforms the real into a string with the indicated format (f=float,s=scientific,e=engineering).\n\nExample: format(9.3456,\"s3\") returns 9.35\n\n\n"]
[null,"FP","Syntax: FP(value)\n\nReturns the Fractional part of value.\n\nExample: FP (23.2) returns .2\n"]
[null,"fracmod","Syntax: fracmod(Expr(Xpr),Intg(n))\n\nReturns the fraction a/b such as a/b=Xpr mod n, -√n/2<a<=√n/2 and 0<=b<√n/2\n\nExample: fracmod(41,121) returns 2/3 \n\n\n"]
[null,"FREEZE","Syntax: FREEZE\nPrevents the screen from being redrawn after the program ends. Leaves the modified display on the screen for the user to see.\n"]
[null,"froot","Syntax: froot(RatPoly(F))\n\nReturns the list of roots and poles of F with their mulitiplicity.\n\nExample: froot((x^5-2*x^4+x^3)/(x-3)) returns [0,3,1,2,3,-1] \n\n\n"]
[null,"fsolve","Syntax: fsolve(Expr,Var,[Guess or Interval],[Method])\n\nNumerical solution of an equation or a system of equations.\n\nExample: fsolve(cos(x)=x,x,-1..1) returns [0.739085133215] \n\n\n"]
[null,"function_diff","Syntax: function_diff(Fnc(f))\n\nReturns the derivative function of the function f.\n\nExample: function_diff(sin) returns  (`x`)->cos(`x`)\n\n\n"]
[null,"Gamma","Syntax: Gamma(Real(x0))\n\nCalculus of Gamma at a point x0 (Gamma(n+1)=n! for n integer).\n\nExample: Gamma(5) returns 24\n\n\n"]
[null,"gauss","Syntax: gauss(Expr,VectVar)\n\nSplits a quadratic form as a sum/difference of square.\n\nExample: gauss(x^2+2*a*x*y,[x,y]) returns (a*y+x)^2+(-y^2)*a^2 \n\n\n"]
[null,"gbasis","Syntax: gbasis(ListPoly, ListVar)\n\nReturns the Groebner basis of the ideal spanned by the list of polynomials.\n\nExample: gbasis({x^2-y^3,x+y^2},{x,y}) returns [y^4-y^3,x+y^2] \n\n\n"]
[null,"gcd","Syntax: gcd(Poly1, Poly2)\n\nReturns the greatest common divisor of 2 polynomials of several variables. Can also be used as integer gcd.\n\nExamples: \ngcd(x^2-4,x^2-5*x+6) returns x-2\ngcd(45,30) returns 15\n"]
[null,"GETBASE","Syntax: GETBASE(#integer)\n\nReturns the base used for display for this integer.\n\n0: system, 1: bin, 2: oct, 3: dec, 4: hex\n"]
[null,"GETBITS","Syntax: GETBITS(#integer)\n\nReturns the number of bits used for calculations with this integer.\n\n"]
[null,"GETKEY","Syntax: GETKEY\nReturns the ID of the first key in the keyboard buffer, or -1 if no key was pressed since the last call to GETKEY. Key IDs  are integers from 0 to 50, numbered from top left (key 0) to bottom right (key 50).\n\n0= Apps\n1= Symb\n2= Up\n3= Help\n4= Esc\n5= Home\n6= Plot\n7= Left\n8= Right\n9= View\n10= Cas\n11= Num\n12= Down\n13= Menu\n\nAfter that, the keys are number from top left (14= Vars) to bottom right (50= +)\n"]
[null,"GETPIX","Syntax: GETPIX([G], x, y)\nReturns the color of the pixel of G with coordinates (x,y).\n"]
[null,"GETPIX_P","Syntax: GETPIX_P([G], x, y)\nReturns the color of the pixel of G with coordinates (x,y).\n"]
[null,"GF","Syntax: GF(Intg(p), Intg(n))\n\nCreates a Galois Field of characteristic p with p^n elements.\n\nExample: GF(5,9) returns GF(5,k^9-k^8+2*k^7+2*k^5-k^2+2*k-2,[k,K,g],undef) \n\n\n"]
[null,"grad","Syntax: grad(Expr, ListVars)\n\nReturns the gradient of the expression Expr.\n\nExample: grad(2*x^2*y-x*z^3,[x,y,z]) returns [2*2*x*y-z^3,2*x^2,-x*3*z^2]\n\n\n"]
[null,"gramschmidt","Syntax: gramschmidt(Basis(B),ScalarProd(Sp))\n\nReturns an orthonormal base of E of base B for the scalar product Sp.\n\nExample: gramschmidt([1,1+x],(p,q)->integrate(p*q,x,-1,1)) returns [1/(√2),(1+x-1)/(√6)/3]\n\n\n"]
[null,"greduce","Syntax: greduce(Poly, ListPoly, ListVar)\n\nReturns the remainder of the division of a polynomial by a Groebner basis.\n\nExample: greduce(x*y-1,{x^2-y^2,2*x*y-y^2,y^3},{x,y}) returns (1/2)*y^2-1 \n\n\n"]
[null,"green","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"GROBH","Syntax: GROBH(G)  \nReturns the height of G.\n"]
[null,"GROBH_P","Syntax: GROBH_P(G)  \nReturns the height of G.\n\n \n"]
[null,"GROBW","Syntax: GROBW(G)  \nReturns the width of G.\n\n"]
[null,"GROBW_P","Syntax: GROBW_P(G)  \nReturns the width of G.\n\n \n"]
[null,"half_line","Syntax: half_line(Point1, Point2)\n\nGiven 2 points, draws a ray from the first point through the second point.\n\nExample: half_line(0, 1+i) draws a ray starting at the origin and passing through the point at (1,1)\n\n\n"]
[null,"halftan","Syntax: halftan(Expr)\n\nTransforms sin(x), cos(x) and tan(x) as a function of tan(x/2).\n\nExample: halftan(sin(x)) returns (2*tan(x/2))/((tan(x/2))^2+1)  \n\n\n"]
[null,"halftan_hyp2exp","Syntax: halftan_hyp2exp(Expr)\n\nTransforms the trigonometric functions in tan(x/2) and hyperbolic functions into expontials.\n\nExample: halftan_hyp2exp(sin(x)+sinh(x)) returns (2*tan(x/2)/((tan(x/2))^2+1)+(exp(x)-1/exp(x))/2  \n\n\n"]
[null,"halt","Syntax: halt(NULL)\n\nPuts a program in step-by-step debug mode.\n\n\n"]
[null,"hamdist","Syntax: hamdist(Intg,Intg)\n\nBit Hamming distance.\n\nExample: hamdist(0x12,0x38) returns 3\n\n\n"]
[null,"harmonic_conjugate","Syntax: harmonic_conjugate(Line or Pnt,Line or Pnt,Line or Pnt)\n\nReturns the harmonic conjugate of 3 points or of 3 parallel or concurrent lines or the line of conjugates of a point in respect to 2 lines.\n"]
[null,"harmonic_division","Syntax: harmonic_division(Pnt or Line,Pnt or Line,Pnt or Line,Var)\n\nReturns the 4 points (resp lines) and affects the last argument, such as the 4 points (resp lines) are in a harmonic division.\n\n\n"]
[null,"has","Syntax: has(Expr,Var)\n\nChecks if a variable is in an expression.\n\nExample: has(x+y,x) returns 1\n\n\n\n"]
[null,"head","Syntax: head(Vect or Seq or Str)\n\nShows the first element of a vector or a sequence or a string.\n\nExample: head(1,2,3) returns 1 \n\n\n"]
[null,"Heaviside","Syntax: Heaviside(Real)\n\nFunction equal to 0 if x<0 and 1 if x>=0\n\nExample: Heaviside(1) returns 1 \n\n\n"]
[null,"hermite","Syntax: hermite(Integer)\n\nReturns nth Hermite polynomial.\n\nExample: hermite(3) returns 8*x^3-12*x\n\n\n"]
[null,"hessenberg","Syntax: hessenberg(Mtrx(A))\n\nMatrix reduction to Hessenberg form. Returns [P,B] such that B=inv(P)*A*P.\n\nExample: hessenberg([[1,2,3],[4,5,6],[7,8,1]]) returns [[[1,0,0],[0,4/7,1],[0,1,0]],[[1,29/7,2],[7,39/7,8],[0,278/49,3/7]]]  \n\n\n"]
[null,"hessian","Syntax: hessian(Expr,LstVar)\n\nReturns the hessian matrix of the expression Expr.\n\nExample: hessian(2*x^2*y-x*z,[x,y,z]) returns [[4*y,4*x,-1],[2*2*x,0,0],[-1,0,0]]\n\n\n"]
[null,"hexagon","Syntax: hexagon(Point1, Point2, [Var1, Var2, Var3, Var4])\n\nDraws a regular hexagon defined by one of its sides; that is, by two consecutive vertices. The remaining points are calculated automatically, but are not defined symbolically. The orientation of the hexagon is counterclockwise from the first point.\n\nExamples:\nhexagon(0,6) draws a regular hexagon whose first two vertices are at (0, 0) and (6, 0).\n\nhexagon(0,6, a, b, c, d) draws a regular hexagon whose first two vertices are at (0, 0) and (6, 0)l labels the other four vertices a, b, c, and d, and stores the coordinates into the CAS variables a, b, c, and d. You do not have to define variables for all four remaining points, but the coordinates are stored in order. For example, hexagon(0,6, a) stores just the third point into the CAS variable a.\n\n"]
[null,"hilbert","Syntax: hilbert(Intg(n))\n\nReturns the order n Hilbert matrix:  Hjk=1/(j+k+1) j,k=1..n\n\nExample: hilbert(4) returns [[1,1/2,1/3,1/4],[1/2,1/3,1/4,1/5],[1/3,1/4,1/5,1/6],[1/4,1/5,1/6,1/7]] \n\n\n"]
[null,"→HMS","Syntax:  →HMS(value)\nDecimal to hours-minutes-seconds. \nChange the way a number is displayed to HMS format.\n  →HMS(8.5) returns 8°3\n"]
[null,"HMS→","Syntax: HMS→(value)\nHours-minutes-seconds to decimal.\nForces a number to be displayed in decimal format if it was previously displayed in DMS format\n HMS→(8°30) returns 8.5\n"]
[null,"homothety","Syntax: homothety(Point, Realk, Object)\n\nDilates a geometric object, with respect to a center point, by a scale factor.\n\nExamples: \n\nhomothety(GA, 2, GB) creates a dilation centered at point A that has a scale factor of 2. Each point P on geometric object B has its image P’ on ray AP such that AP’=2AP.\n\nhomothety(point(0,0),1/3,point(9,9)) creates an image point at (3,3)\n"]
[null,"hyp2exp","Syntax: hyp2exp(ExprHyperb)\n\nTransforms the hyperbolic functions with the exponential function.\n\nExample: hyp2exp(cosh(x)) returns (exp(x)+1/exp(x))/2  \n\n\n"]
[null,"hyperbola","Syntax: hyperbola(Point1, Point2, Point3) or hyperbola(Point1, Point2, Realk)\n\nDraws a hyperbola, given the foci and either a point on the hyperbola or a scalar that is one half the constant difference of the distances from a point on the hyperbola to each of the foci.\n\nExamples:\nhyperbola(GA, GB, GC) draws the hyperbola whose foci are points A and B and which passes through point C.\n\nhyperbola(GA, GB, 3) draws a hyperbola whose foci are points A and B. For any point P on the hyperbola, |AP-BP|=6.\n\n"]
[null,"iabcuv","Syntax: iabcuv(Intg(a),Intg(b),Intg(c))\n\nReturns [u,v] such as au+bv=c for 3 integers a,b,c\n\nExample: iabcuv(21,28,7) returns [-1,1] \n\n\n"]
[null,"ibasis","Syntax: ibasis(Lst(Vect,..,Vect),Lst(Vect,..,Vect))\n\nBasis of the intersection of two vector spaces.\n\nExample: ibasis([[1,0,0],[0,1,0]],[[1,1,1],[0,0,1]]) returns [[-1,-1,0]]\n\n\n"]
[null,"ibpdv","Syntax: ibpdv(Expr1,Expr2,[Var],[Real1],[Real2])\n\nIntegration by parts of Expr1=u(Var)*v'(Var) with Expr2= v'(Var) (or 0) as 2nd argument. You can specify a variable of integration and also the bounds of integration (Real1 and Real2). \n\nExample: ibpdv(x*ln(x),1) returns (-1/4)*x^2+(1/2)*(x^2)*ln(x)\n\n \n\n\n"]
[null,"ibpu","Syntax: ibpu(Expr1,Expr2,[Var],[Real1],[Real2])\n\nIntegration by parts of Expr1=u(Var)*v'(Var) with Expr2= u(Var) (or 0) as 2nd argument. You can specify a variable of integration and also the bounds of integration (Real1 and Real2). \n\nExample: ibpu(ln(x),ln(x),x,1,3) returns [3*ln(3),-1]\n"]
[null,"ichinrem","Syntax: ichinrem([a,p],[b,q]))\n\nInteger Chinese Remainder Theorem for two equations. Takes two lists [a, p] and [b, q] and returns a list of two integers, [r, n], such that x≡r mod n. In this case, x is such that x≡a mod p and x≡b mod q; also, n=p*q. \n\nExample: ichinrem([2, 7], [3, 5]) returns [-12, 35]\n"]
[null,"icontent","Syntax: icontent(Poly,[Var])\n\nReturns the GCD of the integer coefficients of a polynomial.\n\nExample: icontent(24x^3+6x^2-12x+18) returns 6\n\n\n"]
[null,"id","Syntax: id(Seq)\n\nThe name of the identity function (R^n-> R^n)\n\nExample: id(1,2,3) returns 1,2,3 \n\n\n"]
[null,"IDENMAT","Syntax: IDENMAT(n)\n\nIdentity matrix. Creates a square matrix of dimension n x n whose diagonal elements are 1 and off-diagonal elements are zero.\n\nExample: IDENMAT(2) returns [[1,0],[0,1]]\n"]
[null,"identity","Syntax: identity(Intg(n))\n\nReturns the identity matrix of specified dimension n.\n\nExample: identity(3) returns [[1,0,0],[0,1,0],[0,0,1]]\n\n"]
[null,"idivis","Syntax: idivis(a)\n\nInteger divisors. Returns a list of all the factors of the integer a.\n\nExample: idivis(12) returns [1, 2, 3, 4, 6, 12]\n\n"]
[null,"iegcd","Syntax: iegcd(a,b)\n\nExtended greatest common divisor for two integers. Returns [u,v,igcd(a,b)] such that a*u+b*v=igcd(a,b).\n\nExample: iegcd(14, 21) returns [-1, 1, 7]\n"]
[null,"IF","Starts an \"IF...THEN...END\" or \"IF...THEN...ELSE...END\" branch structure.\n\nSyntax: IF test THEN command(s) [ELSE commands] END;\nEvaluates test. If test is true (non 0), executes command(s); otherwise, executes the comands in the ELSE clause nothing happens.\n\nIF A<1 \n  THEN PRINT(\"A IS SMALLER THAN 1\"); \n  ELSE PRINT(\"A IS LARGER THAN 1\"); \nEND;\n"]
[null,"ifactor","Syntax: ifactor(a)\n\nPrime factorization. Returns the prime factorization of the integer a as a product. Can be used with STO▶.\n\nExample: ifactor(150) returns  2*3*5^2\n\n"]
[null,"ifactors","Syntax: ifactors(a)\n\nPrime factors. Similar to ifactor, but returns a list of the factors of the integer a with their multiplicities.\n\nExample: ifactors(150) returns [2, 1, 3, 1, 5, 2]\n"]
[null,"IFERR","Syntax: IFERR commands1 THEN commands2 [ELSE commands3] END;\n\nExecutes sequence of commands1. If an error occurs during execution of commands1, execute sequence of commands2. Otherwise, execute sequence of commands3.\n\nMany conditions are automatically recognized by the HP Prime as error conditions and are automatically treated as errors in programs. This command facilitates error-trapping of such errors.\n"]
[null,"ifft","Syntax: ifft(Vect)\n\nInverse Fast Fourier Transform.\n\nExample: ifft([100.0,-52.2842712475+6*i,-8.0*i,4.28427124746-6*i,4.0,4.28427124746+6*i,8*i,-52.2842712475-6*i]) returns [0.99999999999,3.99999999999,10.0,20.0,25.0,24.0,16.0,-6.39843733552e-12]\n\n\n"]
[null,"IFTE","Syntax: IFTE(Expr, Trueclause, Falseclause)\nIf...Then...Else... \nIf Expr evaluates true (1), evaluates Trueclause; if not, evaluates Falseclause.\n\nExample: IFTE(2<3, 5-1, 2+7) returns 4\n"]
[null,"igcd","Syntax: igcd(a, b)\n\nGreatest common divisor. Returns the integer that is the greatest common divisor of the integers a and b.\n\nExample: igcd(24, 36) returns 12\n"]
[null,"ihermite","Syntax: ihermite(Mtrx(A))\n\nHermite normal form of a matrix with coefficients in Z: returns U,B such that U is invertible in Z, B upper triangular and B=U*A\n\nExample: ihermite([[1,2,3],[4,5,6],[7,8,9]]) returns [[-3,1,0],[4,-1,0],[-1,2,-1]],[[1,-1,-3],[0,3,6],[0,0,0]]\n\n\n"]
[null,"ilaplace","Syntax: ilaplace(Expr,[Var],[IlapVar])\n\nInverse Laplace transform of a rational fraction.\n\nExample: ilaplace(1/(x^2+1)^2) returns (-x)*cos(x)/2+sin(x)/2 \n\n\n"]
[null,"IM","Syntax: IM(x+yi)\n\nImaginary Part. Returns the imaginary part of a complex number.\n\nExample: IM(3+4i)  returns 4\n"]
[null,"incircle","Syntax: incircle(Point1, Point2, Point3)\n\nDraws the incircle of a triangle, the circle tangent to all three sides of the triangle.\n\nExample: incircle(GA, GB, GC) draws the incircle of ΔABC.\n\n"]
[null,"INPUT","Syntax: INPUT(var,[“title”], [“label”], [“help”], [reset])\nor INPUT({vars},[“title”], [{“labels”}], [{“help”}], [{reset}])\n\nStarts a dialog box with header title and one field named label (with value default), displaying help at the bottom. The dialog box includes CANCEL and OK menu keys. If the user presses the OK menu key, the variable var is updated and 1 is returned. If the user presses the CANCL menu key, var is not updated and 0 is returned.\n"]
[null,"INSTRING","Syntax: INSTRING(string1, string2)\nReturns the index of the first occurrence of string2 in string1. Returns 0 if str2 is not present in str1. Note that the first character in a string is in position 1.\n\nExample:\nINSTRING(\"vanilla\", \"van\") returns 1\nINSTRING(\"banana\",\"na\") returns 3\nINSTRING(\"ab\",\"abc\") returns 0\n\n"]
[null,"int","Syntax: int(Expr,[Var],[Real1,Real2])\n\nIntegral (definite or indefinite). You can specify a variable of integration as well as the bounds ofr integration. You can use the integration template in the Template menu as well.\n\nExamples: \nint(1/x) returns ln(abs(x))\nint(sin(x),x,0,π) returns 2\n\n\n"]
[null,"inter","Syntax: inter(Curve1, Curve2)\n\nReturns the intersections of two curves as a vector.\n\nExample: inter(8-x^2/6, x/2-1) returns [[6, 2] [-9, -11/2]], indicating that there are two intersections-one at (6,2) and the other at (-9,-5.5).\n\n"]
[null,"INTERSECT","Syntax: INTERSECT({list1}, ...{listN})\n\nReturns a list of the elements common to all the lists.\n\nExample: INTERSECT({1,2,3},{2,4,8}) returns {2}\n"]
[null,"interval2center","Syntax: interval2center(Interval or Real)\n\nReturns the center of the interval or the object.\n\nExample: interval2center(2..5) returns 7/2 \n\n\n"]
[null,"inv","Syntax: inv(Expr||Mtrx)\n\nReturns the inverse of an expression or matrix.\n\nExample: inv(9/5) returns 5/9 \n\n\n"]
[null,"inversion","Syntax: inversion(Point1, Realk, Point2)\n\nDraws the inversion of a point, with respect to another point, by a scale factor. \n\nExample: inversion(GA, 3, GB) draws point C on line AB such that AB*AC=3. In this case, point A is the center of the inversion and the scale factor is 3. Point B is the point whose inversion is created.\n\nIn general, the inversion of point A through center C, with scale factor k, maps A onto A’, such that A’ is on line CA and CA*CA’=k, where CA and CA’ denote the lengths of the corresponding segments. If k=1, then the lengths CA and CA’ are reciprocals.\n\n"]
[null,"INVERT","Syntax: INVERT([G], [x1, y1], [x2, y2])\nInverts the rectangle on G defined by the diagonal points (x1,y1) and (x2,y2). The effect is reverse video. \n\nThe following values are optional and their defaults are listed:\nx1, y1=top left corner of G\nx2, y2=bottom right corner of G\n\nIf only one x,y pair is specified, it refers to the top left corner of G.\n"]
[null,"INVERT_P","Syntax: INVERT_P([G], [x1, y1], [x2, y2])\nInverts the rectangle on G defined by the diagonal points (x1,y1) and (x2,y2). The effect is reverse video. \n\nThe following values are optional and their defaults are listed:\nx1, y1=top left corner of G\nx2, y2=bottom right corner of G\n\nIf only one (x,y) pair is specified, it refers to the top left corner of G.\n"]
[null,"invlaplace","Syntax: ilaplace(Expr,[Var],[IlapVar])\n\nReturns the inverse Laplace transform of Expr.\n\nExample: ilaplace(1/(x^2+1)^2) returns (-x/2)*cos(x)+(1/2)*sin(x)\n\n\n"]
[null,"invztrans","Syntax: invztrans(Expr,[Var],[InvZtransVar])\n\nInverse z transform of a rational fraction.\n\nExample: invztrans(1/(x^2+1)^2) returns (x*exp(x*(-i)*π/2)+x*exp(x*(i)*π/2)+4*Dirac(x)-2*exp(x*(-i)*π/2)-2*exp(x*(i)*π/2))/4 \n\n\n"]
[null,"IP","Syntax: IP(value)\n\nInteger part. Returns the Integer part of value. \n\nExample: IP(23.2) returns 23\n"]
[null,"iPart","Syntax: iPart(Real||LstReal)\n\nReturns the argument without its fractional part (type=DOM_FLOAT).\n\nExample: iPart(4.3) returns 4.0\n\n\n"]
[null,"iquo","Syntax: iquo(a, b)\n\nEuclidean quotient. Returns the integer quotient when the integer a is divided by the integer b.\n\nExample: iquo(63, 23) returns 2\n"]
[null,"iquorem","Syntax: iquorem(a, b)\n\nEuclidean quotient and remainder. Returns the integer quotient and remainder when the integer a is divided by the integer b.\n\nExample: iquorem(63, 23) returns [2, 17]\n"]
[null,"irem","Syntax: irem(a, b)\n\nEuclidean remainder. Returns the integer remainder when the integer a is divided by the integer b.\n\nExample: irem(63, 23) returns 17\n"]
[null,"is_collinear","Syntax: is_collinear(Point1, Point2, ..., Pointn)\nTakes a set of points as argument and tests whether or not they are collinear. Returns 1 if the points are collinear and 0 otherwise.\n\nExample:\nis_collinear(point(0,0), point(5,0), point(6,1)) returns 0.\n\n\n"]
[null,"is_concyclic","Syntax: is_concyclic(Point1, Point2, …, Pointn)\nTakes a set of points as argument and tests if they are all on the same circle. Returns 1 if the points are all on the same circle and 0 otherwise.\n\nExample:\n\nis_concyclic(point(-4,-2), point(-4,2), point(4,-2), point(4,2)) returns 1\n\n"]
[null,"is_conjugate","Syntax: is_conjugate(Crcle, Point1, Point2, [Point3]) or is_conjugate(Line1, Line2, Line3, {Line4])\n\nReturns 1 if the 3 (resp 4) arguments are conjugated toward a circle (resp 2 lines) and 0 otherwise.\n"]
[null,"is_coplanar","Syntax: is_coplanar(Point1, Point2, Point3, Point4)\n\nTests if 4 points are in the same plane. Returns 1 if true or 0 if false.\n"]
[null,"is_element","Syntax: is_element(Point, Object)\n\nTests if a point is on a geometric object. Returns 1 if it is and 0 otherwise\n\nExample:\nis_element(point((√(2)/2),(√(2)/2)),circle(0,1)) returns 1\n"]
[null,"is_equilateral","Syntax: is_equilateral(Point1, Point2, Point3)\n\nTakes three points and tests whether or not they are vertices of a single equilateral triangle. Returns 1 if they are and 0 otherwise..\n\nExample:\nis_equilateral(triangle(0,2,1+i*√3)) returns 1.\n"]
[null,"is_harmonic","Syntax: is_harmonic(Pnt or Cplx,Pnt or Cplx,Pnt or Cplx,Pnt or Cplx)\nReturns 1 if the 4 points are in a harmonic division and 0 otherwise.\n\n"]
[null,"is_harmonic_circle_bundle","Syntax: is_harmonic_circle_bundle(Lst(Crcle))\nReturns 1 if the circles build a bundle, 2 if they have the same center, 3 if they are the same and 0 otherwise.\n\n"]
[null,"is_harmonic_line_bundle"," \nSyntax: is_harmonic_line_bundle(Lst(Line))\n\nReturns 1 if the lines have a common point, 2 if they are parallels, 3 if they are the same and 0 otherwise.\n"]
[null,"is_isosceles","Syntax: is_isosceles(Point1, Point2, Point3)\n\nTakes three points and tests whether or not they are vertices of a single isosceles triangle. Returns 0 if they are not. If they are, returns the number order of the common point of the two sides of equal length (1, 2, or 3). Returns 4 if the three points form an equilateral triangle.\n\nExamples:\nis_isosceles(point(0,0), point(4,0), point(2,4)) returns 3\nis_isosceles(triangle(0,i,1+i)) returns 2\n\n\n"]
[null,"is_orthogonal","Syntax: is_orthogonal(Line1, Line2) or is_orthogonal(Circle1, Circle2\n\nTests whether or not two lines or two circles are orthogonal (perpendicular). In the case of two circles, tests whether or not the tangent lines at a point of intersection are orthogonal. Returns 1 if they are and 0 otherwise.\n\nExample:\nis_orthogonal(line(y=x),line(y=-x)) returns 1.\n"]
[null,"is_parallel","Syntax: is_parallel(Line1, Line2)\n\nTests whether or not two lines are parallel. Returns 1 if they are and 0 otherwise.\n\nExample:\nis_parallel(line(2x+3y=7),line(2x+3y=9) returns 1.\n\n\n"]
[null,"is_parallelogram","Syntax: is_parallelogram(Point1, Point2, Point3, Point4)\n\nTests whether or not a set of four points are vertices of a parallelogram. Returns 0 if they are not. If they are, then returns 1 if they form only a parallelogram, 2 if they form a rhombus, 3 if they form a rectangle, and 4 if they form a square.\n\nExample:\nis_parallelogram(point(0,0), point(2,4), point(0,8), point(-2,4)) returns 2.\n\n"]
[null,"is_perpendicular","Syntax: is_perpendicular(line1, Line2)\n\nSimilar to is_orthogonal. Tests whether or not two lines are perpendicular. Returns 1 if they are or 0 if they are not.\n\n\nExample: is_perpendicular(line(y=x),line(y=-x)) returns 1\n\n\n\n"]
[null,"is_rectangle","Syntax: is_rectangle(Point1, Point2, Point3, Point4)\n\nTests whether or not a set of four points are vertices of a rectangle. Returns 0 if they are not, 1 if they are, and 2 if they are vertices of a square.\n\nExamples:\nis_rectangle(point(0,0), point(4,2), point(2,6), point(-2,4)) returns 2.\n\nWith a set of only three points as argument, tests whether or not they are vertices of a right triangle. Returns 0 if they are not. If they are, returns the number order of the common point of the two perpendicular sides (1, 2, or 3).\n\nis_rectangle(point(0,0), point(4,2), point(2,6)) returns 2.\n\n\n"]
[null,"is_rhombus","Syntax: is_rhombus(Pnt or Cplx,Pnt or Cplx,Pnt or Cplx,Pnt or Cplx)\nReturns 1 or 2 if the 4 points (or the object) build a rhombus (2 for a square) and 0 otherwise.\n\n"]
[null,"is_square","Syntax: is_square(Point1, Point2, Point3, Point4)\n\nTests whether or not a set of four points are vertices of a square. Returns 1 if they are and 0 otherwise.\n\nExample:\nis_square(point(0,0), point(4,2), point(2,6), point(-2,4)) returns 1\n"]
[null,"ISKEYDOWN","Syntax: ISKEYDOWN(Key_ID)\nReturns true (non-zero) if the key whose Key_ID is provided is currently pressed, and false (0) if it is not.\n\n"]
[null,"ismith","Syntax: ismith(Mtrx(A))\n\nSmith normal form of a matrix with coefficients in Z : returns U,B,V such that U and V are invertible in Z, B is the diagonal, B[i,i] divide B[i+1,i+1] and B=U*A*V.\n\nExample: ismith([[1,2,3],[4,5,6],[7,8,9]]) returns [[1,0,0],[4,-1,0],[-1,2,-1]],[[1,0,0],[0,3,0],[0,0,0]],[[1,-2,1],[0,1,-2],[0,0,1]]\n\n\n"]
[null,"isobarycenter","Syntax: isobarycenter(Point1, Point2, …, Pointn)\n\nReturns the hypothetical center of mass of a set of points. Works like barycenter but assumes all points have equal weight.\n\nExample: isobarycenter(–3,3,3*√3*i) returns \npoint(3*√3*i/3), which is equivalent to (0,√3).\n\n\n"]
[null,"isopolygon","Syntax: isopolygon(Point1, Point2, Realn), where realn is an integer greater than 1.\n\nDraws a regular polygon given the first two vertices and the number of sides, where the number of sides is greater than 1. If the number of sides is 2, then the segment is drawn. You can provide CAS variable names for storing the coordinates of the calculated points in the order they were created. The orientation of the polygon is counterclockwise.\n\nExample\nisopolygon(GA, GB, 6) draws a regular hexagon whose first two vertices are the points A and B.\n\n\n"]
[null,"isosceles_triangle","Syntax: isosceles_triangle(Point1, Point2, Angle)\n\nDraws an isosceles triangle defined by two of its vertices and an angle. The vertices define one of the two sides equal in length and the angle defines the angle between the two sides of equal length. Like equilateral_triangle, you have the option of storing the coordinates of the third point into a CAS variable.\n\nExample:\nisosceles_triangle(GA, GB, angle(GC, GA, GB) defines an isosceles triangle such that one of the two sides of equal length is AB, and the angle between the two sides of equal length has a measure equal to that of ∡ACB.\n\n\n"]
[null,"isPrime","Syntax: isprime(a)\n\nPrime integer test. Returns true if the integer a is prime; otherwise, returns false.\n\nExample: isprime(1999) returns true\n\n"]
[null,"ITERATE","Syntax: ITERATE(expr, var, ivalue, #times)\nRepeatedly for #times evaluates expr in terms of var. The value for var is updated each time, starting with ivalue. \n ITERATE(X^2, X, 2, 3) returns 256.\n"]
[null,"ithprime","Syntax: ithprime(n)\n\nNth prime. For the integer n, returns the nth prime number less than 100,000-200,000.\n\nithprime(5) returns 11\n"]
[null,"jacobi_symbol","Syntax: jacobi_symbol(Intg,Intg)\n\nJacobi symbol.\n\nExample: jacobi_symbol(132,5) returns -1\n\n\n"]
[null,"jordan","Syntax: jordan(Mtrx)\n\nReturns the list made by the matrix of passage and the Jordan form of a matrix.\n\nExample: jordan([[0,2],[1,0]]) returns [[√2,-√2],[1,1]],[[√2,0],[0,-√2]]  \n\n\n"]
[null,"JordanBlock","Syntax: JordanBlock(Expr(a),Intg(n))\n\nReturns a matrix n*n with a on the diagonal, 1 above, and 0 everywhere else. \n\nExample: JordanBlock(7,3) returns [[7,1,0],[0,7,1],[0,0,7]]  \n\n\n"]
[null,"ker","Syntax: ker(Mtrx(M))\n\nKernel of a linear application of matrix M.\n\nExample: ker([[1,2],[3,6]]) returns [ 2, -1 ]\n"]
[null,"KILL","Syntax: KILL;\n\nStops the execution of the program.\n\n"]
[null,"l1norm","Syntax: l1norm(Vect)\n\nReturns the l1 norm of the vector=sum of the absolute value of its coordinates.\n\nExample: l1norm([3,-4,2]) returns 9 \n\n\n"]
[null,"l2norm","Syntax: l1norm(Vect)\n\nReturns the l1 norm of the vector=sum of the absolute value of its coordinates.\n\nExample: l1norm([3,-4,2]) returns 9 \n\n\n"]
[null,"lagrange","Syntax: lagrange((Listxk, Listyk) or lagrange(Matrix)\n\nReturns the polynomial of degree n-1 such that P(xk)=yk, for  k=0, 1, ..., n-1. \n\nExample: lagrange([1,3],[0,1]) returns (1/2)* (x-1)\n\n\n"]
[null,"laguerre","Syntax: laguerre(Integer)\n\nReturns the nth Laguerre polynomial.\n\nExample: laguerre(4) returns (1/24)*a^4+(-1/6)*a^3*x+5/12*a^3+1/4*a^2*x^2+(-3/2)*a^2*x+35/24*a^2+(-1/6)*a*x^3+7/4*a*x^2+(-13/3)*a*x+25/12*a+1/24*x^4+(-2/3)*x^3+3*x^2-4*x+1 \n\n\n"]
[null,"laplace","Syntax: laplace(Expr,[Var],[LapVar])\n\nReturns the Laplace transform of Expr.\n\nExample: laplace(exp(x)*sin(x)) returns 1/(x^2-2*x+2) \n\n"]
[null,"laplacian","Syntax: laplacian(Expr(Xpr),LstVar)\n\nReturns the Laplacian of the expression Xpr with respect to the list of variables.\n\nExample: laplacian(exp(z)*cos(x*y),[x,y,z]) returns -x^2*cos(x*y)*exp(z)-y^2*cos(x*y)*exp(z)+cos(x*y)*exp(z)\n\n\n"]
[null,"lcm","Syntax: lcm(Intgr1, Intgr2) or lcm(Poly1, Poly2) or lcm(Rational1, Rational2)\n\nReturns the lowest common multiple of 2 polynomials of several variables or of 2 integers or of 2 rationals.\n\nExample: lcm(6,4) returns 12 \n\n\n"]
[null,"lcoeff","Syntax: lcoeff(Poly||Lst)\n\nReturns the coefficient of the term of highest degree of a polynomial (l=leading).\n\nExample: lcoeff(-2*x^3+x^2+7*x) returns -2\n\n\n"]
[null,"left","Sorry, but no on-line help is available for this item.\n\nTo browse through the entire help system, tap Tree. You can then use the cursor keys to navigate through the system and open help topics.\n\nIf you still cannot find the topic you are interested in, please consult the User Guide.\n\nTap OK to exit this page.\n"]
[null,"LEFT","Syntax: LEFT(string, n)\n\nReturns the first n characters of the string.\n\nExample: LEFT(\"MOMOGUMBO\",3) returns \"MOM\" \n"]
[null,"legendre","Syntax: legendre(Integer)\n\nReturns the nth Legendre polynomial.\n\nExample: legendre(4) returns (35/8)*x^4+(-15/4)*x^2+3/8\n\n\n"]
[null,"legendre_symbol","Syntax: legendre_symbol(Intg,Intg)\n\nLegendre symbol.\n\nExample: legendre_symbol(132,5) returns -1\n\n\n"]
[null,"length","Syntax: size(Lst or Str or Seq)\n\nReturns the size of a list, a string or a sequence.\n\nExample: size([1,2,3]) returns 3\n\n\n"]
[null,"lgcd","Syntax: lgcd(Seq or Lst )\n\nReturns the greatest common divisor of a list of polynomials or of integers.\n\nExamples: \nlgcd({45,75,20,15}) returns 5\nlgcd({x^2-2*x+1,x^3-1,x-1}) returns x-1\n\n\n"]
[null,"limit","Syntax: limit(Expr,Var,Val)\n\nLimit of an expression as a variable approaches a value. Returns the limit (2 sided or 1-sided) of the given expression as the given variable approaches a value.\n\nExample: limit((n*tan(x)-tan(n*x))/(sin(n*x)-n*sin(x)),x,0) returns 2\n\n\n"]
[null,"lin","Syntax: lin(Expr )\n\nLinearization of exponentials.\n\nExample: lin((exp(x)^3+exp(x))^2) returns exp(6*x)+2*exp(4*x)+exp(2*x)\n\n\n"]
[null,"line","Syntax: line(Point1, Point2) or line(a*x+b*y+c) or line(point1, slope=realm)\n\nDraws a line. The arguments can be two points, a linear expression of the form a*x+b*y+c, or a point and a slope.\n\nExamples:\n\nline(2+i, 3+2i) draws the line whose equation is y=x-1; that is, the line through the points (2,1) and (3,2).\nline(2x-3y-8) draws the line whose equation is 2x-3y=8\nline(3-2i,slope=1/2) draws the line whose equation is x-2y=7; that is, the line through (3, -2) with slope m=1/2\n\n"]
[null,"LINE","Syntax: LINE([G], x1, y1, x2, y2, [color])\n\nDraws a line on GROB G between points (x1,y1) and (x2,y2).\n \n"]
[null,"LINE_P","Syntax: LINE_P([G], x1, y1, x2, y2, [color])\n\nDraws a line on GROB G between points (x1,y1) and (x2,y2).\n \n"]
[null,"linear_interpolate","Syntax: linear_interpolate(Mtrx,xmin,xmax,xstep)\n\nMakes a regular sample from a polygonal line defined by a 2 row matrix.\n\nExample: linear_interpolate([[1,2,6,9],[3,4,6,7]],1,9,1) returns [[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0],[3.0,4.0,4.5,5.0,5.5,6.0,6.33333333333,6.66666666667,7.0]] \n\n\n"]
[null,"linear_regression","Syntax: linear_regression(Lst||Mtrx(A),[Lst])\n\nReturns the coefficients a and b of y=a*x+b \nIt is the best line approximation to the points where the coordinates are the rows of A (or the 2 lists).\n\nExample: linear_regression([[0.0,0.0],[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) returns 4.0,-2.0\n\n\n"]
[null,"LineHorz","Syntax: LineHorz(Expr(a))\n\nDraws the horizontal line y=a\n\n\n"]
[null,"LineTan","Syntax: LineTan(f(x), [Var], Value)\n\nDraws the tangent to y=f(x) at x=Value.\n\nExample: LineTan(x^2-x, 1) draws the line whose equation is y=x-1, which is tangent to the graph of y=x^2-x at x=1.\n\n\n"]
[null,"LineVert","Syntax: LineVert(Expr(a))\n\nDraws the vertical line x=a\n\n\n"]
[null,"linsolve","Syntax: linsolve(ListLinEq,ListVar)\n\nLinear equations system solver. Solves a set of linear equations for their common variable set.\n\nExample: linsolve([x+y+z=1,x-y=2,2*x-z=3],[x,y,z]) returns [3/2,-1/2,0]  \n\n\n"]
[null,"∏LIST","Syntax: ΠLIST(list)\n\nList Product. Calculates the product of all elements in list. \n\nExample: ΠLIST({2,3,4}) returns 24.\n"]
[null,"∆LIST","Syntax: ΔLIST(list)\n\nList Difference. Creates a new list composed of the first differences of list; that is, the differences between the sequential elements in list. The new list has one fewer elements than list.\n\nExample: ΔLIST({1, 2, 3, 5, 8}) returns {1, 1, 2, 3}\n"]
[null,"∑LIST","Syntax: ΣLIST(list)\n\nSum of a list. Returns the sum of all elements in list.\n\nExample: ΣLIST({2,3,4}) returns 9\n"]
[null,"list2mat","Syntax: list2mat(Lst(l),Intg(n))\n\nReturns the matrix with n columns and where terms are the list l completed eventually by 0.\n\nExample: list2mat([1,8,4,9],1) returns [[1],[8],[4],[9]]\n\n\n"]
[null,"LN","Ln: the Natural logarithm.\nSyntax: LN(Value)\n\nReturns the natural logarithm of Value. The natural logarithm is the logarithm to the base e, Euler's number.\n\nExample: LN(1) returns 0\n"]
[null,"lname","Syntax: lname(Expr )\n\nList of variables in the expression.\n\nExample: lname(exp(x)*2*sin(y)) returns [x,y]  \n\n\n"]
[null,"lncollect","Syntax: lncollect(Expr)\n\nCollect logarithms. Applies ln(a)+n*ln(b)=ln(a*b^n) where n is an integer.\n\nExample: lncollect(ln(x)+2*ln(y)) returns ln(x*y^2)\n\n\n"]
[null,"lnexpand","Syntax: lnexpand(Expr)\n\nExpands logarithms.\n\nExample: lnexpand(ln(3*x)) returns ln(3)+ln(x) \n\n\n"]
[null,"LNP1","Syntax: LNP1(value)\n\nNatural log plus 1. This is more accurate than the natural logarithm function when x is close to zero.\n\nExample: LNP1(.23) returns .207014169384\n"]
[null,"LOCAL","Syntax: LOCAL var_1[:=value][, more variables];\n\nDeclares a local variable.\nIf the declaration is in a function block, these variables will be local to the function.\nif the declaration is in the main program body, the variables are local to the program.\n"]
[null,"locus","Syntax: locus(Point,Element)\n\nGiven a first point and a second point that is an element of (a point on) a geometric object, draws the locus of the first point as the second point traverses its object.\n\n\n"]
[null,"LOG","General logarithm function\nSyntax: LOG(Value, [Base])\n\nReturns the logarithm of Value in Base. By default, Base=10.\n\nExample: LOG(8,2) returns 3 while LOG(8) returns 0.903089986992\n"]
[null,"log10","Syntax: log10(Expr)\n\nCommon logarithm (base 10).\n\nExample: log10(10) returns 1\n\n\n"]
[null,"logarithmic_regression","Syntax: logarithmic_regression(Lst||Mtrx(A),[Lst])\n\nReturns the coefficients a and b of y=a*ln(x)+b : it is the best logarithm that approximates the points where the coordinates are the rows of A (or the 2 lists).\n\nExample: logarithmic_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) returns 10.1506450002,-0.564824055818\n\n\n"]
[null,"logb","Syntax: logb(Real)\n\nLogarithm of base b.\n\nExample: logb(5,2) returns ln(5)/ln(2) which is approximately 2.32192809489 \n\n\n"]
[null,"logistic_regression","Syntax: logistic_regression(Lst(L),Real(x0),Real(y0)  )\n\nReturns y,y',C,y'max,xmax,R : y is a logistic function (sol of y'/y=a*y+b), such that y(x0)=y0 and where [y'(x0),y'(x0+1)...] is the best approximation of L.\n\nExample: logistic_regression([0.0,1.0,2.0,3.0,4.0],0.0,1.0) returns [-17.77/(1+exp(-0.496893925384*x+2.82232341488+3.14159265359*i)),-2.48542227469/(1+cosh(-0.496893925384*x+2.82232341488+3.14159265359*i))]\n\n\n"]
[null,"LQ","Syntax: LQ(matrix)\n\nLQ Factorization. Factors an m  n matrix into three matrices: {[[ m  n lowertrapezoidal]],[[ n  n orthogonal]], [[ m  m permutation]]}.\n\nExample: LQ([[1,2],[3,4]])\n"]
[null,"LSQ","Syntax: LSQ(matrix1, matrix2)\n\nLeast Squares. Displays the minimum norm least squares matrix (or vector).\n\nExample: LSQ([[1,2],[3,4]],[[5],[11]]) returns [[1],[2]]\n\n\n"]
[null,"LU","Syntax: LU(matrix)\n\nLU Decomposition. Factors a square matrix into three matrices: \n{[[lowertriangular]],[[uppertriangular]],[[permutation]]} \nThe uppertriangular has ones on its diagonal.\n\nExample: LU([[1,2],[3,4]])\n"]
[null,"lvar","Syntax: lvar(Expr)\n\nList of variables of an object (with rational dependence).\n\nExample: lvar(exp(x)*2*sin(y)) returns [exp(x),sin(y)]\n\n\n"]
[null,"magenta","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"MAKELIST","Syntax: MAKELIST(expression, variable, begin, end, [increment])\n\nMake List. Calculates a sequence of elements for a new list. Evaluates expression, incrementing variable from begin to end values, using increment steps (default 1). The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression.\n\nExample: MAKELIST(2*X-1, X, 1, 5, 1) returns {1, 3, 5, 7, 9}\n"]
[null,"MAKEMAT","Syntax: MAKEMAT(expression, n, [m])\n\nMake Matrix. Creates a matrix of dimension n × m, using expression to calculate each element. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J. With two arguments, this creates a vector of size n.\n\nExamples:\nMAKEMAT(0,3,3) returns [[0,0,0],[0,0,0],[0,0,0]]\nMAKEMAT(√2,2,3) returns [[√2,√2,√2],[√2,√2,√2]]\nMAKEMAT(I+J–1,2,3) returns [[1,2,3],[2,3,4]] \nMAKEMAT(√2,2) returns [√2,√2]\n"]
[null,"MANT","Syntax: MANT(value)\n\nMantissa. Returns the significant digits of value. \n\nExample: MANT(21.2E34) returns 2.12\n"]
[null,"map","Syntax: map(Lst(l),Fnc(f))\n\nApply the function f at the elements of the list l or at a polynomial of internal format.\n\nExample: map([1,2,3],x->x^3) returns [1,8,27] \n\n\n"]
[null,"mat2list","Syntax: mat2list(Mtrx)\n\nReturns the list of the terms of the matrix.\n\nExample: mat2list([[1,8],[4,9]]) returns [1,8,4,9]  \n\n\n"]
[null,"matpow","Syntax: matpow(Mtrx,Intg(n))\n\nCalculates the n power of a matrix by jordanization.\n\nExample: matpow([[1,2],[3,4]],n) returns [[(√33-3)*((√33+5)/2)^n*-6/(-12*√33)+(-(√33)-3)*((-(√33)+5)/2)^n*6/(-12*√33),(√33-3)*((√33+5)/2)^n*(-(√33)-3)/(-12*√33)+(-(√33)-3)*((-(√33)+5)/2)^n*(-(√33)+3)/(-12*√33)],[6*((√33+5)/2)^n*-6/(-12*√33)+6*((-(√33)+5)/2)^n*6/(-12*√33),6*((√33+5)/2)^n*(-(√33)-3)/(-12*√33)+6*((-(√33)+5)/2)^n*(-(√33)+3)/(-12*√33)]] \n\n\n"]
[null,"MAX","Syntax: MAX(value1,[value2],[..value16])\n\nMaximum. Returns the greatest of the values given, or the greatest value of a list.\n\nExample: MAX(210,25) returns 210 and MAX({1, 8, 2}) returns 8\n"]
[null,"maxnorm","Syntax: maxnorm(Vect or Mtrx)\n\nNorm with the maximum of a vector (or of a matrix): maxnorm([x1,x2,..,xn])=max(|x1|,..,|xn|)\n\nExample: maxnorm([1,2]) returns 2 \n\n\n"]
[null,"MAXREAL","Syntax: MAXREAL\nMaximum real number. The largest real number the HP Prime is capable of representing. The value of MAXREAL is 9.99999999999E499. Any number larger than this is represented as this number.\n"]
[null,"mean","Syntax: mean(Lst||Mtrx,[Lst])\n\nMean of a list with the second argument as weight, or of the columns of a matrix.\n\nExample: mean([1,2,3],[1,2,3]) returns 7/3 \n\n\n"]
[null,"median","Syntax: median(Lst||Mtrx,[Lst])\n\nReturns the median of a list with the second argument as the weight, or of the columns of a matrix.\n\nExample: median([1,2,3,5,10,4]) returns 3.0 \n\n\n"]
[null,"median_line","Syntax: median_line(Point1, Point2, Point3)\n\nGiven three points that define a triangle, creates the median of the triangle that passes through the first point and contains the midpoint of the segment defined by the other two points.\n\nExample:\nmedian_line(0, 8i, 4) draws the line whose equation is y=2x; that is, the line through (0,0) and (2,4), the midpoint of the segment whose endpoints are (0, 8) and (4, 0).\n\n"]
[null,"member","Syntax: member(Elem(e),(Lst(l) or Set(l)))\n\nTests if e is in the list or the set l (=0 or k+1 with l[k]=e)\n\nExample: member(1,[4,3,1,2]) returns 3\n\n\n"]
[null,"MID","Syntax: MID(string, position, [n])\n\nExtracts n characters from string starting at position. If n is not specified, then MID  extracts the remainder of the string from position.\n\nExample: \nMID(\"MOMOGUMBO\",3,5) returns \"MOGUM\"\nMID(\"PUDGE\",4) returns \"GE\"\n"]
[null,"midpoint","Syntax: midpoint(Segment) or midpoint(Point1, Point2)\n\nReturns the midpoint of a segment. The argument can be either the name of a segment or two points that define a segment. In the latter case, the segment need not actually be drawn.\n\nExample: midpoint(0,6+6i) returns point(3,3)\n\n"]
[null,"MIN","Syntax: MIN(value1,[value2],[..value16])\n\nMinimum. Returns the lesser of the values given, or the lesser value of a list.\n\nExample: MIN(210,25) returns 25 and MIN({1, 8, 2}) returns 1\n"]
[null,"MINREAL","Syntax: MINREAL\nMinimum real number. The smallest real number that the HP Prime can represent. Its value is 1E-499. Any number smaller than this is represented as zero.\n"]
[null,"mkisom","Syntax: mkisom(Vect,(Sign(1) or -1))\n\nMatrix of an isometry given by its proper elements.\n\nExample: mkisom(π,1) returns [[-1,0],[0,-1]] in radian mode\n\n\n"]
[null,"MKSA","Syntax: MKSA(Value_Unit)\nConverts the measurement Value_Unit to its corresponding value and unit in Unit's MKSA equivalent. MKSA stands for the Meter-Kilogram-Second-Ampere system.\n\nExample: MKSA(32_yd) returns 29.2608_m.\n"]
[null,"MOD","Syntax: value1 MOD value2\n\nModulo. Returns the remainder of value1/value2.\n\nExample: 9 MOD 4 returns 1\n"]
[null,"modgcd","Syntax: modgcd(Poly,Poly)\n\nReturns the GCD of 2 polynomials, with the modular algorithm.\n\nExample: modgcd(x^4-1,(x-1)^2) returns x-1\n\n"]
[null,"MOUSE","Syntax: MOUSE[(index)]\n\nReturns the current pointer's location.\nreturns: two  lists of the form {#x, #y, #originalx, #originaly, #type}, one for each potential pointer. \nNote, if a pointer is unused, returns an empty list\n#type is:  #0: New, #1: Completed, #2: Drag, #3: Stretch, #4: Rotate, #5: LongClick\n\nMOUSE(x) returns the nth element that would be returned if MOUSE was called with no arguements or -1 if the associated pointer is not down.\n"]
[null,"mRow","Syntax: mRow(Expr(Xpr),Mtrx(A),Intg(n1))\n\nMultiplies the row n1 of the matrix A by Xpr.\n\nExample: mRow(12,[[1,2],[3,4],[5,6]],1) returns [[12,24],[3,4],[5,6]]\n\n\n"]
[null,"MSGBOX","Syntax: MSGBOX(expr,[OK_Cancel]) or MSGBOX(string,[OK_Cancel])\n\nDisplays a message box with either the value of expression or string. If OK_Cancel? is true, displays OK and CANCEL menu keys, otherwise only displays the OK menu key. Default value for OK_Cancel is false.\n\nReturns true (non-zero) if the user presses OK, false (0) if the user presses CANCEL.\n"]
[null,"mult_c_conjugate","Syntax: mult_c_conjugate(Expr)\n\nReturns the expression after multiplication by the complex conjugated quantity of the denominator (or of the numerator if no denominator).\n\nExample: mult_c_conjugate(1/(3+i*2)) returns 1*(3+(-i)*2)/((3+(i)*2)*(3+(-i)*2))\n\n\n"]
[null,"mult_conjugate","Syntax: mult_conjugate(Expr)\n\nReturns the expression after multiplication by the conjugated quantity of the denominator (or of the numerator if no denominator).\n\nExample: mult_conjugate(√3-√2) returns (√3-(√2))*(√3+√2)/(√3+√2) \n\n\n"]
[null,"nDeriv","Syntax: nDeriv(Expr(Xpr),Var(var),[Real(h)])\n\nReturns an approximation of the derivative number at a point:(Xpr(var+h)-Xpr(var-h))/(2*h) (by default h=0.001).\n\nExample: nDeriv(f(x),x,h) returns (f(x+h)-(f(x-h)))*0.5/h  \n\n\n"]
[null,"NEG","Syntax: -Value or -Expression\nUnary minus. \nChanges the sign of Value or Expression. Used to enter negative numbers.\n"]
[null,"nextprime","Syntax: nextprime(a)\n\nNext prime. Returns the next prime number greater than the integer a.\n\nnextprime(12) returns 13\n"]
[null,"normal","Syntax: normal(Expr)\n\nSimplify the expression.\n\nExample: normal(2*x*2) returns 4*x\n\n\n"]
[null,"NORMALD","Syntax: NORMALD([μ, σ,] x)\n\nNormal probability density function. Computes the probability density at the value x, given the mean, μ, and standard deviation, σ, of a normal distribution. With one argument, x, returns the probability density at x, assuming a mean of zero and standard deviation of 1.\n\nExample: NORMALD(0.5) returns 0.352065326765 and NORMALD(0, 2, 0.5) returns 0.193334058402\n\n"]
[null,"NORMALD_CDF","Syntax: NORMAL_CDF(μ, σ, x)\n\nCumulative normal distribution function. Returns the lower-tail probability of the normal probability density function for the value x, given the mean, μ, and standard deviation, σ, of a normal distribution. With one argument, x, returns the  lower-tail probability of the normal probability density function for the value x, assuming a mean of zero and standard deviation of 1.\n \nExample: NORMAL_CDF(0, 1, 2) returns 0.97724986805\n"]
[null,"NORMALD_ICDF","Syntax: NORMALD_ICDF(μ, ϭ, p)\n\nInverse cumulative normal distribution function. Returns the cumulative normal distribution value associated with the lower-tail probability, p, given the mean, μ, and standard deviation, ϭ, of a normal distribution. With one argument, p, assumes a mean of zero and a standard deviation of one.\n\nExample: NORMALD_ICDF(0, 1, 0.841344746069) returns 1\n"]
[null,"normalize","Syntax: normalize(Lst||Cplx)\n\nReturns the vector divided by its l2norm. It is also an option for plotfield.\n\nExample: normalize(3+4*i) returns (3+4*i)/5 \n\n\n"]
[null,"NOT","Syntax: NOT Value\nLogical NOT. \n\nReturns 1 if Value is zero; otherwise returns 0.\n\nExample NOT 3 returns 0\n\n"]
[null,"nSolve","Syntax: nSolve(Expr,Var||orVar=Guess)\n\nReturns a numerical solution of an equation or a system of equations.\n\nExamples:\n nSolve(cos(x)=x,x) returns 0.739085133215\nnSolve(cos(x)=x,x=1.3) returns 0.739085133215\n\n\n"]
[null,"NTHROOT","Syntax: Value1 √ Value2\nNTHROOT: the nth root function.\nThis Shift-key combination is the NTHROOT function. It returns the primary Value1 root of Value2. On the keyboard, the NTHROOT function is represented by n√ .\n\nExample: 3√ 8 returns 2\n"]
[null,"numer","Syntax: numer(a,b)\n\nSimplified Numerator. For the integers a and b, returns the numerator of the fraction a/b after simplification.\n\nExample: numer(10/12) returns 5\n"]
[null,"odd","Syntax: odd(Intg(n))\n\nReturns 1 if the integer is odd, otherwise returns 0.\n\nExample: odd(6) returns 0\n\n\n"]
[null,"odesolve","Syntax: odesolve(Expr,VectVar,VectInitCond,FinalVal,[tstep=Val,curve])\n\nOrdinary Differential Equation solver. Solves an ordinary differential equation given by Expr, with variables declared in VectrVar and initial conditions for those variables declared in VectrInit. For example, odesolve(f(t,y),[t,y],[t0,y0],t1) returns the approximate solution of y'=f(t,y) for the variables t and y with initial conditions t=t0 and y=y0.\n\nExample: odesolve(sin(t*y),[t,y],[0,1],2) returns [1.82241255674]  \n"]
[null,"open_polygon","Syntax: open_polygon(LstPnt||LstCplx)\n\nReturns and draws the polygonal line where its vertices are the element of l.\n\n\n\n"]
[null,"OR","Syntax: Value1 OR Value2\nLogical OR. \nReturns 1 if either Value1 or Value2 is non-zero, otherwise returns 0.\n\nExample: 3 OR 2 returns 1\n"]
[null,"order_size","Syntax: order_size(Expr)\n\nRemainder (O term) of a series expansion: limit(x^a*order_size(x),x=0)=0 if a>0 \n\n\n\n"]
[null,"ordinate","Syntax: ordinate(Poinnt) or ordinate(Vecctor)\n\nReturns the ordinate of a point or a vector.\n\nExample: ordinate(point(1+2*i)) returns 2  \n"]
[null,"orthocenter","Syntax: orthocenter(Triangle) or orthocenter(Point1, Point2, Point3)\n\nReturns the orthocenter of a triangle; that is, the intersection of the three altitudes of a triangle. The argument can be either the name of a triangle or three non-collinear points that define a triangle. In the latter case, the triangle does not need to be drawn.\n\nExample: orthocenter(0,4i,4) returns (0,0)\n\n\n"]
[null,"pa2b2","Syntax: pa2b2(Intg(n))\n\nReturns [a,b] such as a^2+b^2=n (for n prime and n=1 (mod 4))\n\nExample: pa2b2(17) returns [4,1] \n\n\n"]
[null,"pade","Syntax: pade(Expr(Xpr), Var(x), (Intg(n) || Poly(N)), Intg(p))\n\nPade approximation P/Q=Xpr mod x^(n+1) or mod N with degree(P)<p\n\nExample: pade(exp(x),x,10,6) returns (-x^5-30*x^4-420*x^3-3360*x^2-15120*x-30240)/(x^5-30*x^4+420*x^3-3360*x^2+15120*x-30240)  \n\n\n"]
[null,"parabola","Syntax: parabola(Point, Line) or parabola(Point, Realk) or parabola(Expr)\n\nDraws a parabola, given a focus point and a directrix line, or the vertex of the parabola and a real number that represents the focal length\n\nExamples:\nparabola(GA, GB) draws a parabola whose focus is point A and whose directrix is line B.\nparabola(GA, 1) draws a parabola whose vertex is point A and whose focal length is 1. \nparabola(x-y^2+y-2) draws the graph of the parabolic equation x=y^2-y+2\n\n\n\n"]
[null,"parallel","Syntax: parallel(Point, Line)\n\nDraws a line through a given point that is parallel to a given line.\n\nExamples:\nparallel(A, B) draws the line through point A that is parallel to line B.\nparallel(point(3–2*i), line(x+y–5)) draws the line through the point (3, –2) that is parallel to the line whose equation is x+y=5; that is, the line whose equation is y=–x+1.\n\n"]
[null,"parallelogram","Syntax: parallelogram(Point1, Point2, Point3)\n\nDraws a parallelogram given three of its vertices. The fourth point is calculated automatically but is not defined symbolically. As with most of the other polygon commands, you can store the fourth point’s coordinates into a CAS variable. The orientation of the parallelogram is counterclockwise from the first point.\n\nExample:\nparallelogram(0,6,9+5i) draws a parallelogram whose vertices are at (0, 0), (6, 0), (9, 5), and (3,5). The coordinates of the last point are calculated automatically.\n\n"]
[null,"parameq","Syntax: parameq(Obj)\n\nReturns a parametric equation for the geometric object Obj. The parametric equation is true for all complex numbers that represent points on Obj.\n\nExample: parameq(circle(0,1)) returns -exp(i*t) \n\n\n"]
[null,"partfrac","Syntax: partfrac(RatFrac or Opt)\nPerforms partial fraction decomposition on a fraction.\n\nExample: partfrac(x/(4-x^2)) returns (-1/2)/(x-2)-(1/2)/((x+2)\n\n"]
[null,"pcoeff","Syntax: pcoeff(Vect)\n\nReturns the polynomial coefficients having the roots specified in the vector Vect.\n\nExample: pcoeff([1,0,0,0,1]) returns poly1[1,-2,1,0,0,0]\n\n\n"]
[null,"perimeter","Syntax: perimeter(Polygon) or perimeter(Circle)\n\nReturns the perimeter of a polygon or the circumference of a circle.\n\nExamples:\nperimeter(0,1,i) returns √2+2\nIf GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as circle(GA, GB-GA), then perimeter(GC) returns 2π.\nIf GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as square(GA, GB-GA), then perimeter(GC) returns 4.\n\n"]
[null,"perimeterat","Syntax: perimeterat(Polygon, Pnt||Cplx(z0))\n\nDisplays at point(z0), with a legend, the perimeter of a circle or of a polygon (e.g. triangle, square, ...).\n\n\n\n\n"]
[null,"perimeteratraw","Syntax: perimeteratraw(Polygone, Pnt||Cplx(z0))\n\nDisplays at point(z0), the perimeter of a circle or of a polygon (e.g. triangle, square, ...).\n\n\n"]
[null,"PERM","Syntax: PERM(n, r)\n\nPermutations. Returns the number of permutations (with regard to order) of n things taken r at a time:  n!/(n-r)!\n\nExample: PERM(5,2) returns 20\n"]
[null,"perpen_bisector","Syntax:perpen_bisector(Segment) or perpen_bisector(Point1, Point2)\n\nDraws the perpendicular bisector of a segment. The segment is defined either by its name or by its two endpoints.\n\nExamples:\nperpen_bisector(GC) draws the perpendicular bisector of segment C.\nperpen_bisector(GA, GB) draws the perpendicular bisector of segment AB.\nperpen_bisector(3+2i, i) draws the perpendicular bisector of a segment whose endpoints have coordinates (3, 2) and (0, 1); that is, the line whose equation is y=x/3+1.\n\n"]
[null,"perpendicular","Syntax: perpendicular(Point, Line) or perpendicular(Point1, Point2, Point3)\n\nDraws a line through a given point that is perpendicular to a given line. The line may be defined by its name, two points, or an expression in x and y.\n\nExamples:\nperpendicular(GA, GD) draws a line perpendicular to line D through point A.\nperpendicular(3+2i, GB, GC) draws a line through the point whose coordinates are (3, 2) that is perpendicular to line BC.\nperpendicular(3+2i,line(x-y=1)) draws a line through the point whose coordinates are (3, 2) that is perpendicular to the line whose equation is x – y = 1; that is, the line whose equation is y=-x+5.\n\n\n"]
[null,"PI","Syntax: π\nThe ratio of the circumference to the diameter of any circle. Internally represented as 3.14159265359.\n"]
[null,"PIECEWISE","Syntax (non-CAS, Textbook Entry disabled): PIECEWISE(test1, case1, ...[, testn], casen)\nSyntax (CAS, Textbook Entry disabled):piecewise(test1, case1, ...[, testn], casen)\nSyntax (Textbook Entry enabled):\n     {case1 if text1\n     ...\n     {casen [if textn]\n\nEvaluates cases one after another until one case is true. Returns the corresponding case.\n\nExample (Textbook Entry):\n\n     {“Even” if (324 MOD 2) == 0\n     {“Odd” if\n                                \n      returns “Even”\n\n\n"]
[null,"pivot","Syntax: pivot(Mtrx(A),Intg(nl),Intg(nc))\n\nReturns the matrix from A creating zeros in the column nc, by the method of Gauss-Jordan with the element A[nl,nc] as pivot.\n\nExample: pivot([[1,2],[3,4],[5,6]],0,1) returns [[1,2],[0,-2],[0,-4]] \n\n\n"]
[null,"PIXOFF","Syntax: PIXOFF([G], x, y)\n\nSets the color of the pixel of G with coordinates (x,y) to white.\n"]
[null,"PIXOFF_P","Syntax: PIXOFF_P([G], x, y)\n\nSets the color of the pixel of G with coordinates (x,y) to white.\n"]
[null,"PIXON","Syntax: PIXON([G], x, y, [color])\n\nSets the color of the pixel of GROB G with coordinates (x,y).\n"]
[null,"PIXON_P","Syntax: PIXON_P([G], x, y, [color])\n\nSets the color of the pixel of GROB G with coordinates (x,y).\n \n"]
[null,"plotcontour","Syntax: plotcontour(Expr(Xpr),[LstVar],[LstVal])\n\nDraws 11 contour-lines  z=z_min,,...z=z_max of the surface z=Xpr, where the contour-lines are defined by the 3rd argument.\n\n\n\n\n"]
[null,"plotfield","Syntax: plotfield(Expr,VectVar,[Opt])\n\nplotfield(f(t,y),[t,y]) draws the slope field of the differential equation y'=f(t,y)\n\n\n\n\n"]
[null,"plotfunc","Syntax: plotfunc(Expr)\n\nDraws the plot of a function, given an expression in the independent variable x. Note the use of lowercase x.\n\nExample: plotfunc(3*sin(x)) draws the graph of y=3*sin(x).\n\n"]
[null,"plotimplicit","Syntax: plotimplicit(Expr,Var1,Var2)\n\nplotimplicit(f(x,y),x,y) or plotimplicit(f(x,y),[x,y]) graph of f(x,y)=0\n\n\n"]
[null,"plotinequation","Syntax: plotinequation(Expr,[x=xrange,y=yrange],[xstep],[ystep])\n\nShows the graph of the solution of inequations with 2 variables.\n\n\n"]
[null,"plotlist","Syntax: plotlist(Lst(l)||Mtrx(M))\n\nDraws a polygonal line through the points of abscissa 0,...,n and ordinate l=[y0,...,yn] or the line through the points of abscissa in the first M column and the ordinates in the second column.\n\n\n\n\n"]
[null,"plotode","Syntax: plotode(Expr,VectVar,VectInitCond)\n\nplotode(f(t,y),[t,y],[t0,y0]) draws the solution of y'=f(t,y) and y(t0)=y0 or of the system [x'=g(t,x,y),y'=h(t,x,y)] with x(t0)=x0 and y(t0)=y0.\n\n\n\n\n"]
[null,"plotparam","Syntax: plotparam(Cplx||Lst,Var||Lst(Var))\n\nplotparam(a(x)+i*b(x),x=x0..x1) draws the curve X=a(x),Y=b(x) x=x0..x1 or plotparam([a(u,v),b(u,v),c(u,v)],[u=u0..u1,v=v0..v1]) draws the surface X=a(u,v),Y=b(u,v),Z=c(u,v) u=u0..u1 and v=v0..v1.\n\n\n"]
[null,"plotpolar","Syntax: plotpolar(Expr,Var,VarMin,VarMax)\n\nplotpolar(f(x),x,a,b) draws the polar curve r=fx) for x in [a,b]\n\n\n\n"]
[null,"plotseq","Syntax: plotseq(Expr(f(Var)),Var=[a,xm,xM],Intg(p))\n\nFor seeing the pth terms of the sequence u(0)=a,u(n)=f(u(n-1))\n\n\n\n\n"]
[null,"pmin","Syntax: pmin(Mtrx,[Var])\n\nReturns the minimal polynomial of a square matrix.\n\nExample: pmin([[1,0],[0,1]],x) returns x-1\n\n\n"]
[null,"point","Syntax: point(Real1, Real2) or point(Expr1, Expr2) or point(Complex)\n\nCreates a point, given the coordinates of the point. Each coordinate may be a value or an expression involving variables or measurements on other objects in the geometric construction. \n\nExamples:\npoint(3,4) creates a point whose coordinates are (3,4). This point may be selected and moved later.\npoint(abscissa(GA), ordinate(GB)) creates a point whose x-coordinate is the same as that of a point A and whose y-coordinate is the same as that of a point B. This point will change to reflect the movements of point A or point B.\n\n"]
[null,"point2d","Syntax: point2d(Var1, Var2, ..., Varn)\n\nRandomly re-distributes a set of points such that, for each point, x is in the interval [-5, 5] and y  is in the interval [-5, 5]. Any further movement of one of the points will randomly re-distribute all of the points.\n\n\n\n\n\n"]
[null,"POISSON","Syntax: POISSON(μ, k)\n\nPoisson probability mass function. Computes the probability of k occurrences of an event in a time interval, given μ expected (or mean) occurrences of the event in that interval. For this function, k is a non-negative integer and μ is a real number.\n\nExample: POISSON(4, 2) returns 0.14652511111\n"]
[null,"POISSON_CDF","Syntax: POISSON_CDF(μ, x)\n\nCumulative poisson distribution function. Returns the probability of x or fewer occurrences of an event in a given time interval, given μ expected (or mean) occurrences.\n\nPOISSON_CDF(4, 2) returns 0.238103305554\n"]
[null,"POISSON_ICDF","Syntax: POISSON_ICDF(μ, p)\n\nInverse cumulative poisson distribution function. Returns the value x such that the probability of x or fewer occurrences of an event in a time interval, with μ expected (or mean) occurrences of the event in the interval, is p.\n\nExample: POISSON_ICDF(4, 0.238103305554) returns 2\n"]
[null,"polar","Syntax: polar(Crcle,Pnt or Cplxe(A))\n\nReturns the line of the conjugated points of A with respect to the circle.\n\n\n"]
[null,"polar_coordinates","Syntax: polar_coordinates(Pnt or Cplx or LstRectCoord)\n\nReturns the list of the norm and of the argument of the affix of a point (for 2D) or of a complex number or of the the list of rectangular coordinates.\n\nExample: polar_coordinates(point(1+2*i)) returns [√5,atan(2)] \n\n\n"]
[null,"polar_point","Syntax: polar_point(Real(r),Real(t))\n\nReturns the point (for 2D) with the arguments r and t as polar coordinates.\n\n\n"]
[null,"pole","Syntax: pole(Crcle,Line)\n\nReturns the point having the line as polar with respect to the circle.\n\n\n"]
[null,"poly2symb","Syntax: poly2symb(Lst,Var)\n\nReturns a polynomial (orthe polynomial and its value) in Var (by default x), the polynomial being defined by the vector of coefficents in Vect .\n\nExamples: \npoly2symb([1,2,3],x) returns (x+2)*x+3 \npoly2symb([1,2,3],x=2) returns (x+2)*x+3=11\n\n"]
[null,"POLYCOEF","Syntax: POLYCOEF(vector or list)\nPolynomial coefficients. Returns the coefficients of the polynomial with the roots specified in vector.\nPOLYCOEF({-1, 1}) returns {1, 0, -1}\n"]
[null,"POLYEVAL","Syntax: POLYEVAL(vector or list , value)\nPolynomial evaluation. Evaluates a polynomial with the coefficients specified in vector, at value.\nPOLYEVAL({1, 0, -1}, 3) returns 8\n"]
[null,"polygon","Syntax: polygon(Point1, Point2, …, Pointn)\n\nDraws a polygon from a set of vertices.\n\nExample:\npolygon(GA, GB, GD) draws ΔABD\n\n\n"]
[null,"polygonplot","Syntax: polygonplot(Mtrx)\n\nDraws the polygons joining for j fixed and for k=0..nrows, the points (xk,yk) where xk=element row k column 0 and yk=element row k column j, when the xk are sorted (we obtain ncols-1 polygons).\n\n\n"]
[null,"polygonscatterplot","Syntax: polygonscatterplot(Mtrx)\n\nDraws the points (xk,yk) and the polygons joining for j fixed and for k=0..nrows, the points (xk,yk) where xk=element row k column 0 and yk=element row k column j ,when the xk are sorted (we obtain ncols-1 polygons).\n\n\n"]
[null,"polynomial_regression","Syntax: polynomial_regression(Lst||Mtrx(A),[Lst],Intg(n))\n\nReturns the coefficients (an,...a1,a0) of y=an*x^n+..a1x+a0): it is the best polynomial that approximates the points where the coordinates are the rows of A (or the 2 lists) (n is the 2nd argument).\n\nExample: polynomial_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]],3) returns [-0.0,1.0,-0.0,0.0]\n\n\n"]
[null,"POLYROOT","Syntax: POLYROOT(vector)\n\nPolynomial roots. Returns the roots for the polynomial whose coefficients are specified in vector.\n\nExample: POLYROOT([1, 0, -1]) returns {-1, 1}\n\n"]
[null,"POS","Syntax: POS(list, element)\n\nList Position. Returns the position of element within list. If there is more than one instance of the element, the position of the first occurrence is returned. A value of 0 is returned if there is no occurrence of the specified element.\n\nExample: POS({0, 1, 3, 5}, 1) returns 2\n"]
[null,"potential","Syntax: potential(Vect(V),VectVar)\n\nReturns U such as derive(U,Vector_of_variable)=V\n\nExample: potential([2*x*y+3,x^2-4*z,-4*y],[x,y,z]) returns 2*x^2*y/2+3*x-4*y*z\n\n\n"]
[null,"pow2exp","Syntax: pow2exp(Expr)\n\nConverts powers to exponentials. Essentially the inverse of exp2pow.\n\nExample: pow2exp(a^b) returns exp(b*ln(a))\n\n\n"]
[null,"power_regression","Syntax: power_regression(Lst|Mtrx(A),[Lst])\n\nReturns the coefficients (m,b) of y=b*x^m: it is the best monomial that approximates the points where the coordinates are the rows of A (or the 2 lists).\n\nExample: power_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) returns 2.0,1.0  \n\n\n"]
[null,"powerpc","Syntax: powerpc(Cercle,Pnt or Cplx)\n\nReturns the real number d^2-R^2 (d=distance between point and center, R=radius).\n\nExample: powerpc(circle(0,1+i),3+i) returns 8  \n\n\n"]
[null,"powexpand","Syntax: powexpand(Expr)\n\nExpresses a power in the form of a product. \n\nExample: powexpand(2^(x+y)) yields (2^x)*(2^y)\n"]
[null,"powmod","Syntax: powmod(a, n, p)\n\nPower and modulo. For the integers a, n, and p, returns a^n mod p.\n\nExample: powmod(5,2,13) returns 12\n\n"]
[null,"prepend","Syntax: prepend(Lst,Elem )\n\nPuts the element at the beginning of the list.\n\nExample: prepend([1,2],3) returns [3,1,2]   \n\n\n"]
[null,"preval","Syntax: preval(f(Var), Real1, Real2, [Var])\n\nReturns f(Real2)-f(Real1).\n\nExample: preval(x^2-2,2,3) returns 5\n\n\n"]
[null,"prevprime","Syntax: prevprime(a)\n\nPrevious prime. Returns the previous prime number before the integer a.\n\nExample: prevprime(11) returns 7\n"]
[null,"primpart","Syntax: primpart(Poly,[Var])\n\nReturns the polynomial P divided by the gcd of its coefficients.\n\nExample: primpart(2x^2+10x+6) returns x^2+5*x+3 \n\n\n"]
[null,"PRINT","Syntax: PRINT(expr) or PRINT(string) or PRINT( )\nPrints either the result of expr or string to the terminal.\n\nThe terminal is a program text output viewing mechanism which is displayed only when PRINT commands are executed. When visible, you can use the up/down keys to view the text, BKSP to erase the text and any other key to hide the terminal. You can show the terminal at anytime using the ON+T combination (press and HOLD the ON key, then press the T key, then release both keys). Pressing ON stops the interaction with the terminal.\n\nPRINT with no argument clears the terminal.\n"]
[null,"product","Syntax: product(Expr||Lst,[Var||Lst],[Intg(a)],[Intg(b)],[Intg(p)])\n\nMultiplicates the values of the expression when the variable goes from a to b with a step p (product expression,var,begin,end,step) by default p=1) or product of the elements of a list or product element by element of 2 lists or matrix.\n\nExample: product(n,n,1,10,2) returns 945\n\n\n"]
[null,"projection","Syntax: projection(Curve, Point)\n\nDraws the orthogonal projection of a point onto a curve.\n\nExample: projection(circle(x^2+y^2=4),point(6,6)) creates a point on the circle at (√2, √2)\n\n\n"]
[null,"proot","Syntax: proot(Vect||Poly)\n\nReturns all computed roots of a polynomial given by its coefficients (may not work if roots are not simple).\n\nExample: proot([1,0,-2]) returns [-1.41421356237,1.41421356237]\n\n\n"]
[null,"propfrac","Syntax: propfrac(Frac or RatFrac)\n\nSimplifies and writes the fraction (or rationnal fraction) A/B as Q+R/B with R<B (or deg(R)<deg(B))\n\nExample: propfrac(28/12) returns 2+1/3\n\n\n"]
[null,"Psi","Syntax: Psi(Real(a),Intg(n))\n\nPsi(a,n) returns the nth derivative of the digamma function at x=a (Psi(a,0)=Psi(a))\n\nExample: Psi(3,1) returns π^2/6-5/4\n\n\n"]
[null,"ptayl","Syntax: ptayl(Poly(P(var)),Real(a),[Var])\n\nReturns the Taylor polynomial Q such as P(x)=Q(x-a)\n\nExample: ptayl(x^2+2*x+1,1) returns x^2+4*x+4\n\n"]
[null,"purge","Syntax: purge(Var)\n\npurge(varname) unassigns the variable varname\n\n\n"]
[null,"PX→C","Syntax: PX→C(x, y)  or PX→C({x, y}) \n\nTransform pixel coordinates into cartesian coordinates. Returns a list.\n"]
[null,"q2a","Syntax: q2a(QuadraForm,VectVar)\n\nq2a(q(x,y),[x,y]) returns the symmetric matrix associated with the quadratic form q\n\nExample: q2a(x^2+2*x*y+2*y^2,[x,y]) returns [[1,1],[1,2]] \n\n\n"]
[null,"QR","Syntax: QR(matrix)\n\nQR Factorization. Factors an mn matrix into three matrices:\n {[[mm orthogonal]],[[mn uppertrapezoidal]],[[nn permutation]]}.\n\nExample: QR([[1,2],[3,4]])\n"]
[null,"quadrilateral","Syntax: quadrilateral(Point1, Point2, Point3, Point4)\n\nDraws a quadrilateral from a set of four points.\n\nExample:\nquadrilateral(GA, GB, GC, GD) draws quadrilateral ABCD.\n\n\n"]
[null,"quantile","Syntax: quantile(Lst(l),Real(p))\n\nReturns the quantile of the elements of l corresponding to p (0<p<1)\n\nExample: quantile([0,1,3,4,2,5,6],0.25) returns [1.0] \n\n\n"]
[null,"quartile1","Syntax: quartile1(Lst||Mtrx,[Lst])\n\nReturns the 1st quartile of the elements (or of the columns) of the argument.\n\nExample: quartile1([1,2,3,5,10,4]) returns 2.0\n\n\n"]
[null,"quartile3","Syntax: quartile3(Lst||Mtrx,[Lst])\n\nReturns the 3rd quartile of the elements (or of the columns) of the argument\n\nExample: quartile3([1,2,3,5,10,4]) returns 5.0\n\n\n"]
[null,"quartiles","Syntax: quartiles(Lst||Mtrx,[Lst])\n\nReturns the min, 1st quartile, median, 3rd quartile, and max of the elements (or of the columns) of the argument.\n\nExample: quartiles([1,2,3,5,10,4]) returns [[1.0],[2.0],[3.0],[5.0],[10.0]] \n\n"]
[null,"quo","Syntax: quo((Vect or Poly),(Vect or Poly),[Var])\n\nReturns the Euclidean quotient of 2 polynomials\n\nExample: quo([1,2,3,4],[-1,2]) returns poly1[-1,-4,-11]\n\n\n"]
[null,"quorem","Syntax: quorem(Poly1, Poly2) or quorem(Vector1, Vector2)\n\nReturns the Euclidean quotient and remainder of the quotient of 2 polynomials in a vector. If the polynomials are expressed as vectors of their coefficients, then this command returns a similar vector of the quotient and a vector of the remainder.\n\nExamples: \nquorem(x^3+2*x^2+3*x+4,-x+2) returns [-x^2-4*x-11, 26]\nquorem([1,2,3,4],[-1,2]) returns [[-1, -4, -11] [26]]\n\n\n\n"]
[null,"QUOTE","Syntax: QUOTE(expression)\n\nReturns the expression unchanged and un-evaluated.\nThis function is mostly used with the STO▶ command in order to store a function in a function variable. For example if you want to store SIN(X) in F1.you cannot do SIN(X)►F1 as SIN(X) would be evaluated and a numerical result would be stored into F1. QUOTE(SIN(X))►F1 will store SIN(X) in F1.\n"]
[null,"radical_axis","Syntax: radical_axis(Crcle,Crcle)\n\nReturns the line of points with same powerpc with respect to the 2 circles.\n\n"]
[null,"radius","Syntax: radius(Circle)\n\nReturns the radius of a circle.\n\nExample: If GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as circle(GA, GB-GA), then radius(GC) returns 1.\n\n"]
[null,"randexp","Syntax: randexp(Real(a))\n\nReturns a random real according to the exponential distribution of parameter a>0\n\nExample: randexp(1) returns 1.17118631006\n\n\n"]
[null,"RANDINT","Syntax: RANDINT([a],[b],[c])\n\nRandom number. Returns a pseudo-random integer generated using a seed value, and updates the seed value.\n\nWith no argument, this function returns a random integer x from 0 to 1. With one argument, this returns a random integer x from 0 to a. With two arguments, this returns a random integer x from a to b. With three arguments, this returns a list of size a with each element being a random integer x from b to c.\n\nExample: RANDINT(3,1,6) returns { random1, random2, random3 }\n"]
[null,"RANDMAT","Syntax: RANDMAT (matrixname, rows, columns)\n\nCreates a random matrix with the specified number of rows and columns, and stores the result in matrixname. The entries will be integers ranging from –99 to 99.\n\nExample: RANDMAT(M1,2,2) returns [[n1,n2],[n3,n4]]\n"]
[null,"randMat","Syntax: ranm(Intg(n),[Intg(m)],[Interval or quote(DistribLaw)])\n\nReturns a list of size n or a n*m matrix that contains random integers in the range -99 through 99 with uniform distribution or contains random numbers according to the law in quote.\n\nExample: ranm(3) returns [-20,72,-86]\n\n"]
[null,"RANDNORM","Syntax: RANDNORM([μ],[σ]) or RANDNORM(n,μ,σ)\n\nReturn a random number from the normal distribution with the specified mean μ and standard deviation σ. Default values are 0 and 1.\n\nWith three arguments, returns  a list of size n with each element being a random number fron the normal distribution with the specified mean μ and standard deviation σ.\n\nExample: RANDNORM(3,0,1) returns { random1, random2, random3 }\n"]
[null,"randNorm","Syntax: randnorm(Real(mu),Real(sigma))\n\nReturns a random real with normal distribution N(mu,sigma)\n\nExample: randnorm(0,1) returns -0.860967215689\n\n"]
[null,"RANDOM","Syntax: RANDOM([a],[b],[c])\n\nRandom number. Returns a pseudo-random number generated using a seed value, and updates the seed value.\n\nWith no argument, this function returns a random number x with 0 ≤ x < 1. With one argument, this returns a random number x with 0 ≤ x < a. With two arguments, this returns a random number x with a ≤ x < b. With three arguments, this returns a list of size a with each element being a random number x with b ≤ x < c.\n\nExample: RANDOM(3,0,10) returns { random1, random2, random3 }\n"]
[null,"randperm","Syntax: randperm(Intg(n))\n\nReturns a random permutation of [0,1,2,..,n-1] \n\nExample: randperm(4) returns [2,1,3,0] \n\n"]
[null,"randPoly","Syntax: randpoly([Var],Intgr,[Dist])\n\nReturns a vector of coefficients of a polynomial of variable Var (or x), of degree Intgr and where the coefficients are random integers in the range -99 through 99 with uniform distribution or in an interval specified by Intrvl.\n\nExample: randpoly(t, 8, -1..1) returns a vector of 9 random integers, all of them between -1 and 1.\n\n"]
[null,"RANDSEED","Syntax: RANDSEED([value])\n\nSets the random number generator seed. With no input, uses current time value as seed.\n\nExample: RANDSEED(3.14)\n"]
[null,"RANK","Syntax: RANK(matrix)\n\nRank of a rectangular matrix.\n\nExample: RANK([[1,2],[3,4]]) returns 2\n"]
[null,"ratnormal","Syntax: ratnormal(Expr)\n\nRewrites Expr as an irreducible rational fraction\n\nExample: ratnormal((x^2-1)/(x^3-1)) returns (x+1)/(x^2+x+1) \n\n\n"]
[null,"RE","Syntax: RE(x+yi)\n\nReal Part. Returns the real part of a complex number.\n\nExample: RE(3+4i) returns 3\n"]
[null,"reciprocation","Syntax: reciprocation(Crcle,Lst(Pnt,Line))\n\nReturns the list where a point is replaced with its polar or a line is replaced with its pole, with respect to the circle C\n\n"]
[null,"RECT","Syntax: RECT([G], [x1, y1], [x2, y2], [edgecolor],[fillcolor])\nDraws a rectangle on G, with diagonal defined by points (x1,y1) and (x2,y2), using edgecolor for the perimeter and fillcolor for the inside.\n\nThe following values are optional and their defaults are listed:\nx1, y1=top left corner of G\nx2, y2=bottom right corner of G\nedgecolor=white\nfillcolor=edgecolor\n\nNote: To erase a GROB, execute RECT(G). To clear the screen execute RECT().\n"]
[null,"RECT_P","Syntax: RECT_P([G], [x1, y1], [x2, y2], [edgeColor],[fillColor])\nDraws a rectangle on G, with diagonal defined by points (x1,y1) and (x2,y2), using edgeColor for the perimeter and fillColor for the inside.\n\nThe following values are optional and their defaults are listed:\nx1, y1=top left corner of G\nx2, y2=bottom right corner of G\nedgeColor=white\nfillColor=edgeColor\n\nNote: To erase a GROB, execute RECT(G). To clear the screen, execute RECT().\n"]
[null,"rectangle","Syntax: rectangle(Point1, Point2, Point3) or rectangle(Point1, Point2, Realk)\n\nDraws a rectangle given two consecutive vertices and a point on the side opposite the side defined by the first two vertices or a scale factor for the sides perpendicular to the first side. As with many of the other polygon commands, you can specify optional CAS variable names for storing the coordinates of the other two vertices as points.\n\nExamples:\nrectangle(GA, GB, GE) draws a rectangle whose first two vertices are points A and B (one side is segment AB). Point E is on the line that contains the side of the rectangle opposite segment AB. \nrectangle(GA, GB, 3, p, q) draws a rectangle whose first two vertices are points A and B (one side is segment AB). The sides perpendicular to segment AB have length 3*AB. The third and fourth points are stored into the CAS variables p and q, respectively.\n\n\n"]
[null,"rectangular_coordinates","Syntax: rectangular_coordinates(LstPolCoord)\n\nReturns the list of the abscissa and of the ordinate of a point given by the list of its polar coordinates.\n\nExample: rectangular_coordinates([1,-1]) returns [cos(1),-sin(1)]\n"]
[null,"red","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"REDIM","Syntax: REDIM(matrixname, size)\nRedimensions the specified matrix or vector to size. For a matrix, size is a list of two integers {n1, n2}. For a vector, size is a list containing one integer {n}. Existing values in the matrix are preserved. Fill values will be zeros.\n"]
[null,"reduced_conic","Syntax: reduced_conic(Expr,[LstVar])\n\nReturns the origin and the matrix of a base in which the conic (given by its equation) is reduced, 0 or 1 (0 if the conic is degenerate), and the equation of the conic in this base and also its parametric equation\n\nExample: reduced_conic(x^2+2*x-2*y+1) returns [[-1,0],[[0,1],[-1,0]],1,y^2+2*x,[[-1+(-i)*(t*t/-2+(i)*t),t,-4,4,0.1]]] \n\n"]
[null,"ref","Syntax: ref(Mtrx(M))\n\nPerforms Gauss reduction of a matrix  AX=b (M=A|(-b))\n\nExample: ref([[3,1,-2],[3,2,2]]) returns [[1,1/3,-2/3],[0,1,4]] \n\n\n"]
[null,"reflection","Syntax: reflection(line, Object) or reflection(Point, Object)\n\nReflects a geometric object over a line or through a point. The latter is sometimes referred to as a half-turn.\n\nExamples: \nreflection(line(x=3),point(1,1)) reflects the point at (1, 1) over the vertical line x=3 to create a point at (5,1).\nreflection(1+I, 3-2i) reflects the point at (3, -2) through the point at (1, 1) to create a point at (-1, 4).\n\n\n\n"]
[null,"rem","Syntax: rem(Poly1, Poly2) or rem(Vector1, Vector2)\n\nReturns the Euclidean remainder of the quotient of 2 polynomials.  If the polynomials are expressed as vectors of their coefficients, then this command returns a similar vector of the remainder.\n\nExamples: \n \nrem(x^3+2*x^2+3*x+4,-x+2) returns 26\nrem([1,2,3,4],[-1,2]) returns [26]\n\n\n"]
[null,"remove","Syntax: remove(FncBool(f)||e,Lst(l))\n\nRemoves the occurences e of l or the elements e such that f(e)=true\n\nExample: remove(x->x>=5,[1,2,6,7]) returns [1,2] \n\n\n"]
[null,"reorder","Syntax: reorder(Expr,LstVar)\n\nReorders the variables in E according to the order of the 2nd argument \n\nExample: reorder(x^2+2*x+y^2,[y,x]) returns y^2+x^2+2*x  \n\n\n"]
[null,"REPEAT","Syntax: REPEAT command(s) UNTIL test;\n\nexecutes command(s) UNTIL the test is true.\n\nA:=5;\nREPEAT\n    PRINT(A); \n   A:= A-1;\nUNTIL A<1;\n\nwill print  5 4 3 2 1\n"]
[null,"REPLACE","Syntax: REPLACE(object,start,object)\n\nReplaces portion of a matrix, vector or string starting at start by object.\nFor a matrix, start is a list containing two numbers; for a vector or string it is a single number.\nNote: for strings, you can do: REPLACE(\"string\", \"sub_string\", \"replace_string\")\n"]
[null,"residue","Syntax: residue(Expr,Var(v),Cplx(a))\n\nReturns the residue in a of the expression Expr with v as variable\n\nExample: residue(1/z,z,0) returns 1\n\n\n"]
[null,"restart","Syntax: restart(NULL)\n\nPurges all the variables\n\n\n\n"]
[null,"resultant","Syntax: resultant(Poly,Poly,Var)\nReturns the inert form of the resultant for modular computation (irem/mod)\n\n"]
[null,"RETURN","Syntax: RETURN expression;\nExits from a function and returns the value of expression (optional).\n\nExample:\nEXPORT FACTORIAL(N)\nBEGIN\nIF N==1 THEN RETURN 1; ELSE RETURN N*FACTORIAL(N-1); END;\nEND;\n"]
[null,"REVERSE","Syntax: REVERSE(list)\n\nReverse list. Reverses the order of the elements in list and returns them in a new list. \n\nExample: REVERSE({2, 3, 4, 5}) returns {5, 4, 3, 2}.\n"]
[null,"revlist","Syntax: revlist(Lst(l))\n\nReturns the list l in reverse order\n\nExample: revlist([1,2,3]) returns [3,2,1]  \n\n\n"]
[null,"RGB","Syntax: RGB(R, G, B, [A])\n\nReturns an integer number that can be used as the color parameter for a  drawing function. Based on Red, Green and Blue components values (0 to 255).\n\nIf Alpha is greater than 128, returns the color flagged as transparent. There is no alpha channel blending on Prime.\n"]
[null,"rhombus","Syntax: rhombus(Pnt(A)||Cplx,Pnt(B)||Cplx,Angle(a)||Pnt(P)||Lst(P,a)),[Var(C)],[Var(D)])\n\nReturns and draws the rhombus ABCD such that the angle (AB,AD)=a or such that in the plane ABP the angle(AB,AD)=angle(AB,AP)\n\n\n"]
[null,"RIGHT","Syntax: RIGHT(string, n)\n\nReturns the last n characters of the string.\n\nExample: RIGHT(\"MOMOGUMBO\",5) returns \"GUMBO\" \n"]
[null,"right","Sorry, but no on-line help is available for this item.\n\nTo browse through the entire help system, tap Tree. You can then use the cursor keys to navigate through the system and open help topics.\n\nIf you still cannot find the topic you are interested in, please consult the User Guide.\n\nTap OK to exit this page.\n"]
[null,"right_triangle","Syntax: right_triangle(Point1, Point2, Realk)\n\nDraws a right triangle given two points and a scale factor. One leg of the right triangle is defined by the two points, the vertex of the right angle is at the first point, and the scale factor multiplies the length of the first leg to determine the length of the second leg.\n\nExample: right_triangle(GA, GB, 1) draws an isosceles right triangles with its right angle at point A, and with both legs equal in length to segment AB.\n\n\n"]
[null,"romberg","Syntax: romberg(Expr(f(x)),Var(x),Real(a),Real(b))\n\nUses Romberg's method to return the approximate value of the integral of the expression over the interval a to b\n\nExample: romberg(exp(x^2),x,0,1) returns 1.46265174591   \n\n"]
[null,"ROTATE","Syntax: ROTATE(string, n)\nIf n is not negative, takes the first  n characters of string and put them on the right of string. If n is negative, takes the last  n characters and put them on the left of  string. If ABS(n)>dim(string), returns string.\nROTATE(\"12345\",2) returns \"34512\"\nROTATE(\"12345\",-1) returns \"51234\"\nROTATE(\"12345\",6) returns \"12345\"\n"]
[null,"rotation","Syntax: rotate(Point, Angle, Object)\n\nRotates a geometric object, about a given center point, through a given angle.\n\nExample: rotate(GA, angle(GB, GC, GD),GK) rotates the geometric object labeled K, about point A, through an angle equal to ∡CBD.\n\n"]
[null,"ROUND","Syntax: ROUND(value, [places])\n\nRounds value to system display settings. If optional places is given, rounds value to places decimal places. If places is negative, rounds to significant digits instead.\n\nROUND(7.8676,2) returns 7.87\n"]
[null,"row","Syntax: row(Mtrx(A),Intg(n)||Interval(n1..n2))\n\nReturns the row n or the sequence of the rows n1..n2 of the matrix A \n\nExample: row([[1,2,3],[4,5,6],[7,8,9]],1) returns [4,5,6] \n\n\n"]
[null,"rowAdd","Syntax: rowAdd(Mtrx(A),Intg(n1),Intg(n2))\n\nReturns the matrix obtained from matrix A when the n2th row is replaced by the sum of the n1th and n2th rows\n\nExample: rowAdd([[1,2],[3,4],[5,6]],1,2) returns [[1,2],[3,4],[8,10]]  \n\n"]
[null,"rowDim","Syntax: rowDim(Mtrx)\n\nReturns the number of rows of a matrix\n\nExample: rowDim([[1,2,3],[4,5,6]]) returns 2 \n\n\n"]
[null,"ROWNORM","Syntax: ROWNORM(matrix)\nRow Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row.\n\nExample: ROWNORM([[1,2],[3,4]]) returns 7\n"]
[null,"rowSwap","Syntax: rowSwap(Mtrx(A),Intg(n1),Intg(n2))\n\nReturns the matrix obtained from A by swapping the  n1th row and the n2th row\n\nExample: rowSwap([[1,2],[3,4],[5,6]],1,2) returns [[1,2],[5,6],[3,4]]  \n\n\n"]
[null,"RREF","Syntax: RREF(matrix)\n\nReduced-Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon form.\n\nExample: RREF([[1,-2,1],[3,4,-1]]) returns [[1,0,.2],[0,1,-.4]]\n"]
[null,"rsolve","Syntax: rsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal))\n\nGives the value of a recurrent sequence or of a system of recurrent sequences\n\nExample: rsolve(u(n+1)=2*u(n)+n,u(n),u(0)=1 returns [-n+2*2^n-1]  \n\n\n"]
[null,"R→B","Syntax: R→B(Real [, bits [,base]])\n\nTransform a real number into an integer. Optionally specifies bits and base.\n-64<Bits<65\n0<=Base<=4\n0: system, 1: bin, 2: oct, 3: dec, 4: hex\n"]
[null,"SCALE","Syntax: SCALE(matrixname, value, rownumber)\nMultiplies the specified row_number of the specified matrix by value.\n\n"]
[null,"SCALEADD","Syntax: SCALEADD(matrixname, value, row1, row2) \n\nMultiplies the specified row1 of the matrix name by value, then adds this result to the second specified row2 of the matrix matrixname.\n"]
[null,"SCHUR","Syntax: SCHUR(matrix)\n\nSchur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the result is {[[orthogonal]],[[upper-quasi triangular]]}.\n If Complex mode is on and the matrix is complex, then the result is \n{[[unitary]],[[upper-triangular]]}.\n\nExample: SCHUR([[1,2],[3,4]])\n"]
[null,"SEC","Syntax: SEC(value)\n\nSecant. The Secant function; that is, 1/cos(x).\n\nExample: SEC(0) returns 1 in degree mode\n"]
[null,"segment","Syntax: segment(Point1, Point2)\n\nDraws a segment defined by its endpoints.\n\nExamples:\nsegment(1+2i, 4) draws the segment defined by the points whose coordinates are (1, 2) and (4, 0).\nsegment(GA, GB) draws segment AB.\n\n\n\n"]
[null,"select","Syntax: select(FncBool(f),Lst(l))\n\nSelects the elements e of l such that f(e)=true\n\nExample: select(x->x>=5,[1,2,6,7]) returns [6,7]  \n\n"]
[null,"seq","Syntax: seq(Expr(Xpr),Intg(n)||Var(var),[Intg(a)],[Intg(b)],[Intg(p)])\n\nReturns the sequence (if 2 or 3 arguments) or the list (if 4 or 5 arguments) obtained when var goes from a to b (step p) in Xpr, or when Xpr is repeated n times.\n\nExample: seq(2^k,k=0..8) returns 1,2,4,8,16,32,64,128,256  \n\n"]
[null,"seqsolve","Syntax: seqsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal))\n\nGives the value of a recurrent sequence (u_{n+1}=f(u_n) or u_{n+2}=f(u_{n+1},u_n)...) or of a system of recurrent sequences\n\nExample: seqsolve(2x+n,[x,n],1) returns -n-1+2*2^n \n\n"]
[null,"series","Syntax: series(Expr,Equal(var=limit_point),[Order],[Dir(1,0,-1)])\n\nReturns the series expansion of an expression in the vicinity of a given equality variable. With the optional third and fourth arguments you can specify the order and direction of the series expansion. If no order is specified the series returned is\nfifth order. If no direction is specified, the series is bidirectional.\n\nExample: series((x^4+x+2)/(x^2+1),x=0,5) returns 2+x-2x^2-x^3+3x^4+x^5+x^6*order_size(x)\n\n\n"]
[null,"SETBASE","Syntax: SETBASE(#integer[, base])\n\nSets the base used for display of this integer.\nIf base is not specified the calculator default is used.\n0<=Base<=4\n0: system, 1: bin, 2: oct, 3: dec, 4: hex\n"]
[null,"SETBITS","Syntax: SETBITS(#integer[, bits])\n\nSets the number of bits used for calculations with this integer to bits.\nIf bits is not specified the calculator default is used.\n-64<Bits<65\n"]
[null,"shift_phase","Syntax: shift_phase(Expr)\n\nReturns the expressions where the phase of the evaluated trigonometric expressions is increased by π/2\n\nExample: shift_phase(sin(x)) returns -cos((π+2*x)/2) \n\n"]
[null,"Si","Syntax: Si(Expr)\n\nSine integral int(sin(t)/t,t=0..x)\n\nExample: Si(1.0) returns 0.946083070367\n\n\n"]
[null,"SIGN","Syntax: SIGN(value) or SIGN(x+yi)\n\nSign. Returns the sign of value. If positive, the result is 1; if negative, -1. If zero, the result is zero. For complex inputs returns the unit vector.\n\nExample: SIGN (2) returns 1\n"]
[null,"signature","Syntax: signature(Permut)\n\nReturns the signature of a permutation\n\nExample: signature([2,1,4,5,3]) returns -1\n\n"]
[null,"similarity","Syntax: similarity(Point, Realk, Angle, Object)\n\nDilates and rotates a geometric object about the same center point.\n\nExample: similarity(0, 3, angle(0,1,i),point(2,0)) dilates the point at (2,0) by a scale factor of 3 (a point at (6,0)), then rotates the result 90° counterclockwise to create a point at (0, 6)\n\n\n"]
[null,"simplify","Syntax: simplify(Expr)\n\nSimplifies an expression.\n\nExample: simplify(4*atan(1/5)-atan(1/239)) yields (1/4)*π\n\n"]
[null,"simult","Syntax: simult(Mtrx(A),Mtrx(B))\n\nReturns the matrix where the column of index k is solution of A*X=column of index k of B (=B[0..nr-1,k..k] with nr=number of rows of B)\n\nExample: simult([[3,1],[3,2]],[[-2],[2]]) returns [[-2],[4]]  \n\n"]
[null,"SIN","SIN: the sine function.\nSyntax: SIN(Value)\n\nReturns the sine of Value. Value is interpreted as either degrees or radians, depending on the setting of Angle Measure in Home Modes or Symbolic Setup.\n\nExample: in radians mode, SIN(π/2) returns 1\n"]
[null,"sin2costan","Syntax: sin2costan(Expr)\n\nRewrites Expr so that sin(x) is replaced by cos(x)*tan(x) \n\nExample: sin2costan(sin(x)) returns tan(x)*cos(x)  \n\n"]
[null,"sincos","Syntax: sincos(Expr)\n\nReturns an expression with the complex exponentials rewritten in terms of sine and cosine.\n\nExample: sincos(exp(-i*x)) returns cos(x)-i*sin(x) \n\n"]
[null,"single_inter","Syntax: single_inter(Curve,Curve,[Pnt(A)||LstPnt(L)])\n\nGives one of the intersections of 2 curves or surfaces (or the intersection near A or not in L)\n\n"]
[null,"SINH","Syntax: SINH(value)\n\nHyperbolic sine.\n\nExample: SINH(1) returns 1.17520119364\n"]
[null,"SIZE","Syntax: SIZE(list)\n\nList Size. Returns the number of elements in list.\n\nExample: SIZE({0, 1, 2, 3}) returns 4\n"]
[null,"slope","Syntax: slope(Line||Pnt||Cplx,[Pnt||Cplx])\n\nReturns the slope of the line defined in the argument\n\nExample: slope(line(1,2i)) returns -2\n\n"]
[null,"slopeat","Syntax: slopeat(Segment, Point) or slopeat(Line, Point) or slopeat(Ray, Point)\n\nDisplays, with a legend, the value of the slope of the segment, ray, or line (Line may be a tangent, bisector, etc.) at the location Point in Plot view.\n\nExample: slopeat(line(point(0,1), point(3,2)),point(-10,4)) places \"sline(point(0,1),point(3,2)=1/3\" at the point (-10,4) in Plot view\n\n"]
[null,"slopeatraw","Syntax: slopeatraw(Line, Pnt||Cplx(z0))\n\nslopeatraw(d,z0) displays the value of the slope of the line or segment d at point(z0) \n\n\n"]
[null,"solve","Syntax: solve(Expr,[Var] )\n\nSolves a polynomial equation or a set of polynomial equations.\n\nExample: solve(x^2-3=1) returns {-2,2}  \n\n"]
[null,"SORT","Syntax: SORT(list)\n\nSort list. Sorts the elements of list in ascending order.\n\nExample: SORT({2, 9, 5, 3}) returns {2, 3, 5, 9}.\n"]
[null,"SPECNORM","Syntax: SPECNORM(matrix)\n\nSpectral Norm of matrix.\n\nExample: SPECNORM([[1,2],[3,4]]) returns 5.46498570422\n"]
[null,"SPECRAD","Syntax: SPECRAD(matrix)\n\nSpectral radius of matrix.\n\nExample: SPECRAD([[1,2],[3,4]]) returns 5.37228132327\n"]
[null,"spline","Syntax: spline(Lst(lx),Lst(ly),Var(x),Intg(d))\n\nReturns the natural spline through the points given by lx and ly, variable x, degree d\n\nExample: spline([0,1,2],[1,3,0],x,3) returns [-5*x^3/4+13*x/4+1,5*(x-1)^3/4+-15*(x-1)^2/4+(x-1)/-2+3] \n\n"]
[null,"sqrfree","Syntax: sqrfree(Expr)\n\nReturns a polynomial factorized as a product of powers of coprime factors where each factor has roots of multiplicity 1\n\nExample: sqrfree(x^4-2*x^2+1) returns (x^2-1)^2\n\n"]
[null,"sqrt","Syntax: √(Expr)\n\nReturns the square root of Expr\n\nExample: √50 returns 5*√2 \n\n"]
[null,"square","Syntax: square(Point1, Point2)\n\nDraws a square, given two consecutive vertices as points.\n\nExample: square(0, 3+2i, p, q) draws a square with vertices at (0, 0), (3, 2), (1, 5), and (-2, 3). The last two vertices are computed automatically and are saved into the CAS variables p and q.\n\n\n"]
[null,"STARTAPP","Syntax: STARTAPP(\"AppName\")\nStarts the app AppName. The App's START function will run if present. The App’s default view will be started. Note that the START function is always executed when the user presses the START menu key in the App Library. Also works for apps saved in the App Library.\n"]
[null,"STARTVIEW","Syntax: STARTVIEW(ViewNumber[,Redraw])\n\nStarts a view of the current app. Redraw, is optional; if Redraw, is true (non 0), it will force a refresh for the view.\n\nThe view numbers are as follows:\n0=Symbolic\n1=Plot\n2=Numeric\n3=Symbolic Setup\n4=Plot Setup\n5=Numeric Setup\n6=App Info\n7=Views key\n\n\nIf the current app has views defined under the Views menu, then the following view numbers are used:\n8=First special view (Split Screen Plot Detail)\n9=Second special view (Split Screen Plot Table)\n10=Third special view (Autoscale)\n11=Fourth special view (Decimal)\n12=Fifth special view (Integer)\n13=Sixth special view (Trig)\n\n\nIf ViewNumber is negative, the following global views are used:\n-1=HomeScreen\n-2=Modes\n-3=Memory Manager\n-4=App Library\n-5=Matrix Catalog\n-6=List Catalog\n-7=Program Catalog\n-8=Note Catalog\n"]
[null,"stddev","Syntax: stddev(Lst||Mtrx,[Lst])\n\nReturns the standard deviation of the elements in a list or of the list of standard deviations \n\nExample: stddev([1,2,3]) returns (√6)/3 \n"]
[null,"stddevp","Syntax: stddevp(Lst||Mtrx,[Lst])\n\nReturns the population standard eviation of the elements of a list with the second argument as weight.\n\nExample: stddevp([1,2,3]) returns 1\n\n"]
[null,"STEP","Syntax: FOR var FROM start TO (or DOWNTO) finish [STEP increment] DO command(s) END;\n\nSets variable var to start; then, for as long as this variable’s value is less than or equal to (or more than for a DOWNTO) finish, executes  command(s) and adds (or substract for DOWNTO) 1 (or increment) to var. \n\nFOR A FROM 1 TO 10 STEP 2\n  DO \n    PRINT(A); \nEND;\n\nwill print  1 3 5 7 9\n"]
[null,"sto","Syntax: sto(arg1,Var)\n\nStores the first argument in the variable given as second argument\n\nExample: sto(\"hello\",b)\n"]
[null,"STRING","Syntax: STRING(expression)\n\nEvaluates expression and returns the result as a string.\n"]
[null,"STRINGFROMID","Syntax: STRINGFROMID(integer)\n\nReturns the built-in string associated with the ID of the current language.\n"]
[null,"STUDENT","Syntax: STUDENT(n, x)\n\nStudent’s t probability density function. Computes the probability density of the Student’s-t distribution at x, given n degrees of freedom.\n\nExample: STUDENT(3, 5.2) returns 0.00366574413491\n"]
[null,"STUDENT_CDF","Syntax: STUDENT_CDF(n, x)\n\nCumulative Student’s t distribution function. Returns the lower-tail probability of the Student’s t probability density function at x, given n degrees of freedom.\n\nExample: STUDENT_CDF(3, -3.2) returns 0.0246659214813\n"]
[null,"STUDENT_ICDF","Syntax: STUDENT_ICDF(n, p)\n\nInverse cumulative Student’s t distribution function. Returns the value x such that the Student’s-t lower-tail probability of x, with n degrees of freedom, is p.\n\nExample: STUDENT_ICDF(3, 0.0246659214813) returns -3.2\n"]
[null,"sturmab","Syntax: sturmab(Poly,Var,Cplx1, Cplx2)\n\nReturns the number of sign changes of a polynomial in the interval (Cplx1, Cplx2] or the number of complex roots in (Cplx1, Cplx2] if Cplx1 or Cplx2 is non-real.\n\nExample: sturmab(x^3-1,x,-2,5) returns 1 \n\n"]
[null,"sturmseq","Syntax: sturmseq(Poly,[Var])\n\nReturns the Sturm sequence corresponding to a polynomial or to a rational fraction\n\nExample: sturmseq(x^3-1,x) returns [1,[[1,0,0,-1],[3,0,0],9],1]  \n\n"]
[null,"SUB","Syntax: SUB(object, start, end)\n\nExtracts a portion, of a list or matrix.\n\nFor a matrix, start and end are two lists of two numbers ({row, col}) specifying the top left and bottom right of the portion to extract.\nFor a vector or list, start and end are two numbers specifying the indexes of the first and last objects of the portion to extract.\n\n"]
[null,"SUBGROB","Syntax: SUBGROB(srcG, [x1, y1], [x2, y2], trgtG)\nSets graphic trgtG to be a copy of the area of srcG between points (x1,y1) and (x2,y2). If both (x1, y1) and (x2, y2) are not specified, then the entire graphic srcG is used. If (x1, y1) is not specified, then the top left corner of srcG is used; if (x2, y2) is not specified, then the bottom right corner of srcG is used.\n\ntrgtGRB can be any of the graphic variables except G0.\n\nSUBGROB(G1, G4) will copy G1 in G4.\n"]
[null,"SUBGROB_P","Syntax: SUBGROB_P(srcG, [x1, y1], [x2, y2], trgtG)\nSets graphic trgtG to be a copy of the area of srcG between points (x1,y1) and (x2,y2). If both (x1, y1) and (x2, y2) are not specified, then the entire graphic srcG is used. If (x1, y1) is not specified, then the top left corner of srcG is used; if (x2, y2) is not specified, then the bottom right corner of srcG is used.\n\ntrgtGRB can be any of the graphic variables except G0.\n\nSUBGROB(G1, G4) will copy G1 in G4.\n"]
[null,"subMat","Syntax: subMat(Mtrx(A),Intg(n1),Intg(n2),Intg(n3),Intg(n4))\n\nExtracts a sub matrix with first element=A[n1,n2] and last element=A[n3,n4]\n\nExample: subMat([[1,2],[3,4],[5,6]],1,0,2,1) returns [[3,4],[5,6]] \n\n"]
[null,"subst","Syntax: subst(Expr,Var=value)\n\nSubstitutes a value for a variable in an expression.\n\nExample: subst(x/(4-x^2),x=3) returns -3/5\n\n\n"]
[null,"sum","Syntax: sum(Expr,Var,Real1, Real2,[Step])\n\nReturns the discrete sum of Expr with respect to the variable Var from Real1 to Real2. You can also use the summation template in the Template menu.\n\nExample: sum(n^2,n,1,5) returns 55\n\n"]
[null,"sum_riemann","Syntax: sum_riemann(Expr,List(Var1,Var2))\n\nReturns, in the neighbourhood of n=∞, an equivalent of the sum of Expr(Var1,Var2) for Var2 from Var2=1 to Var2=Var1 when the sum is looked at as a Riemann sum associated with a continuous function defined on [0,1]\n\nExample: sum_riemann(1/(n+k),[n,k]) returns ln(2)\n\n\n"]
[null,"suppress","Syntax: suppress(Vect(l),Intg(n))\n\nReturns l without the element of index n \n\nExample: suppress([0,1,2,3],2) returns [0,1,3] \n"]
[null,"surd","Syntax: surd(Expr,Intg(n))\n\nReturns Expr to the power of 1/n\n\nExample: surd(8,3) returns 8^(1/3)\n\n\n"]
[null,"SVD","Syntax: SVD(matrix)\n\nSingular Value Decomposition. Factors an m  n matrix into two matrices and a vector: {[[m  m square orthogonal]],[[n  n square orthogonal]], [real]}.\n\nExample: SVD([[1,2],[3,4]])\n"]
[null,"SVL","Syntax: SVL(matrix)\n\nSingular Values. Returns a vector containing the singular values of matrix.\n\nExample: SVL([[1,2],[3,4]])\n"]
[null,"SWAPCOL","Syntax: SWAPCOL(matrixname, column1, column2)\nSwap Columns. Exchanges column1 and column2 in the specified matrix  matrixname.\n"]
[null,"SWAPROW","Syntax: SWAPROW(matrixname, row1, row2)\n\nSwap Rows. Exchanges row1 and row2 in the specified matrix matrixname.\n\n"]
[null,"sylvester","Syntax: sylvester(Poly,Poly,Var)\n\nReturns the Sylvester matrix of two polynomials\n\nExample: sylvester(x^2-1,x^3-1,x) returns [[1,0,-1,0,0],[0,1,0,-1,0],[0,0,1,0,-1],[1,0,0,-1,0],[0,1,0,0,-1]] \n\n"]
[null,"symb2poly","Syntax: symb2poly(Expr,[Var]) or symb2poly(Expr, ListVar)\n\nReturns the coefficients of a polynomial Expr with respect tothe variable Var or if the second argument is a list returns the internal format of the polynomial. Essentaiilly the inverse of poly2symb().\n\nExample: symb2poly( (x+2)*x+3) returns [1,2,3]\n"]
[null,"table","Syntax: table(SeqEqual(index=value))\n\nDefines an array where the index are strings or real numbers\n\n"]
[null,"tail","Syntax: tail(Lst or Seq or Str)\n\nReturns the list (or sequence or string) without its first element\n\nExample: tail([3,2,4,1,0]) returns [2,4,1,0] \n\n"]
[null,"TAN","TAN: the tangent function.\nSyntax: TAN(Value)\n\nReturns the tangent of Value. Value is interpreted as either degrees or radians, depending on the setting of Angle Measure in Home Modes or Symbolic Setup.\n\nExample: in radians mode, TAN(0) returns 0\n"]
[null,"tan2cossin2","Syntax: tan2cossin2(Expr)\n\nRewrites Expr with tan(x) replaced by (1-cos(2*x))/sin(2*x) \n\nExample: tan2cossin2(tan(x)) returns (1-cos(2*x))/sin(2*x) \n\n"]
[null,"tan2sincos","Syntax: tan2sincos(Expr)\n\nRewrites Expr with tan(x) using sin(x)/cos(x) \n\nExample: tan2sincos(tan(x)) returns sin(x)/cos(x)\n\n"]
[null,"tan2sincos2","Syntax: tan2sincos2(Expr)\n\nRewrites Expr with tan(x) replaced by sin(2*x)/(1+cos(2*x))\n\nExample: tan2sincos2(tan(x)) returns sin(2*x)/(1+cos(2*x)) \n\n"]
[null,"tangent","Syntax: tangent(Curve, Point)\n\nDraws the tangent(s) to a given curve through a given point. The point does not have to be a point on the curve.\n\nExamples:\ntangent(plotfunc(x^2), point(1,1)) draws the tangent to the graph y=x^2 through the point (1,1); that is, the line whose equation is y=2*x-1.\ntangent(plotfunc(x^2), GA) draws the tangent to the graph of y=x^2 through point A. Point A can then be moved and the tangent will move with it.\ntangent(circle(GB, GC-GB), GA) draws one or more tangent lines through point A to the circle whose center is at point B and whose radius is defined by segment BC.\n\n"]
[null,"TANH","Syntax: TANH(value)\n\nHyperbolic tangent.\n\nExample: TANH(1) returns .761594155956\n"]
[null,"taylor","Syntax: taylor(Expr,[Var=Value],[Order])\n\nReturns the Taylor series expansion of an expression at a point or at infinity (by default, at x=0 and with relative order=5).\n\nExample: taylor(sin(x)/x,x=0) returns 1-(1/6)*x^2+(1/120)*x^4+x^6*order_size(x)\n\n\n"]
[null,"tchebyshev1","Syntax: tchebyshev1(Integer))\n\nReturns the nth Tchebyshev polynomial of the first kind.\n\nExample: tchebyshev1(3) returns 4*x^3-3*x\n\n"]
[null,"tchebyshev2","Syntax: tchebyshev2(Integer)\n\nReturns the nth Tchebyshev polynomial of the second kind.\n\nExample: tchebyshev2(3) returns 8*x^3-4*x \n\n\n"]
[null,"tcollect","Syntax: tcollect(Expr)\n\nCollects trigonometric expressions.\n\nExample: tcollect(sin(x)+cos(x)) returns √2*cos(x-1/4*π)\n\n"]
[null,"texpand","Syntax: texpand(Expr)\n\nExpands a transcendental expression; that is, an expression containing trigonometric, logarithmic, or exponential functions. texpand develops the expression in terms of sin(), cos(), ln(), and exp().\n\nExample: texpand(sin(2*x)+exp(x+y)) returns 2*cos(x)*sin(x)+exp(x)*exp(y)\n\n\n"]
[null,"TEXTOUT","Syntax: TEXTOUT(text, [G], x, y, [font], [textColor], [width], [backgroundColor])\nDraws text on graphic G at position (x, y) using font. Paints the background before drawing the text using color backgroundColor. If width is specified, does not draw text more than width pixels wide. If backgroundColor is not specified, the background is not erased.\n\nThe sizes for font are:\n\n0=current font (default)\n1=font_10\n2=font_12 (Small)\n3=font_14 (Medium)\n4=font_16 (Large)\n5=font_18\n6=font_20\n7=font_22\n\n"]
[null,"TEXTOUT_P","Syntax: TEXTOUT_P(text, [G], x, y, [font], [textColor], [width], [backgroundColor])\nDraws text on graphic G at position (x, y) using font. Paints the background before drawing the text using color backgroundColor. If width is specified, does not draw text more than width pixels wide. If backgroundColor is not specified, the background is not erased.\n\nThe sizes for font are:\n\n0=current font (default)\n1=font_10\n2=font_12 (Small)\n3=font_14 (Medium)\n4=font_16 (Large)\n5=font_18\n6=font_20\n7=font_22\n"]
[null,"THEN","Starts an \"IF...THEN...END\" or \"IF...THEN...ELSE...END\" branch structure.\n\nSyntax: IF test THEN command(s) [ELSE commands] END;\nEvaluates test. If test is true (non 0), executes command(s); otherwise, executes the comands in the ELSE clause nothing happens.\n\nIF A<1 \n  THEN PRINT(\"A IS SMALLER THAN 1\"); \n  ELSE PRINT(\"A IS LARGER THAN 1\"); \nEND;\n"]
[null,"tlin","Syntax: tlin(Expr)\n\nReturns a trigonometric expression with the products and integer powers linearized\n\nExample: tlin(sin(x)^3) returns (3/4)*sin(x)-(1/4)*sin(3*x)\n\n"]
[null,"TO","Syntax: FOR var FROM start TO (or DOWNTO) finish [STEP increment] DO command(s) END;\n\nSets variable var to start; then, for as long as this variable’s value is less than or equal to (or more than for a DOWNTO) finish, executes  command(s) and adds (or substract for DOWNTO) 1 (or increment) to var. \n\nFOR A FROM 1 TO 10 STEP 2\n  DO \n    PRINT(A); \nEND;\n\nwill print  1 3 5 7 9\n"]
[null,"TRACE","Syntax: TRACE(matrix)\n\nTrace of a square matrix. Finds the trace of a square matrix, equal to the sum of the diagonal elements ( also equal to the sum of the eigenvalues).\n\nExample: TRACE([[1,2],[3,4]]) returns 5\n"]
[null,"trace","Syntax: trace(Point)\n\nBegins tracing the specified point.\n\n\n"]
[null,"translation","Syntax: translation(Vector, Object)\n\nTranslates a geometric object along a given vector. The vector is given as the difference of two points (head-tail).\n\nExamples:\ntranslation(0-i, GA) translates object A down one unit.\ntranslation(GB-GA, GC) translates object C along the vector AB.\n\n"]
[null,"transpose","Syntax: tran(Mtrx)\n\nTransposes a matrix (without conjugation)\n\nExample: tran([[1,2,3],[1,3,6],[2,5,7]]) returns [[1,1,2],[2,3,5],[3,6,7]] \n\n"]
[null,"triangle","Syntax: triangle(Point1, Point2, Point3)\n\nDraws a triangle, given its three vertices.\n\nExample: triangle(GA, GB, GC) draws ΔABC.\n\n"]
[null,"TRIANGLE","Syntax: TRIANGLE([G], x1, y1, x2, y2, x3, y3, c1, [c2, c3], [Alpha], [\"ZString\", z1, z2, z3]) or TRIANGLE([G], {x1, y1, [c1], [z1]}, {x2, y2, [c2], [z2]},{x3, y3, [c3], [z3]}, [\"ZString\"]) or TRIANGLE([G], [[x/y coordinate matrix]], [[color matrix]], {[[z matrix]], [zcode], [[[projection matrix]]], [zstring]) or TRIANGLE([G])\n\nDraws a triangle between specified cartesian coordinates in the graphic using the specified color and transparency (0 ≤ Alpha ≤ 255). If 3 colors are specified, blends the colors in between the vertexes.\n\nThe next form of TRIANGLE allows display of multiple triangles at a time.\nThis is mostly used if you have a set of vertices and want to display them all at once.\n\nThe first 2 matrices indicate the x/y coordinates and colors of each points. TRIANGLE will draw 1 quadrilateral for each set of 4 adjacent vertices and blends the colors associated with the 4 points.\nIf a z and projection matrix are provided, for each point, this matrix is multiplied by the [x,y,z,1] vector to create the display x,y coordinates.\nIf zcode is a list that contains 3 real numbers { ex, ey, ez } then x,y are further modified by doing x=ez/z*x-ex and y=ez/z*y-ey creating a perspective projection.\nIf zstring is provided, z clipping will happen using the z value (see below).\nIf zcode=\"N\" or is a list that starts with \"N\", then each z is normalized to be between 0 and 255.\n\nAbout ZString\nTRIANGLE([G]) returns a string adapted for z clipping.\n\nTo use Z clipping, call TRIANGLE to create a Z clipping string (initialized at 255 for each pixels). You can then call TRIANGLE with appropriate z (0-255) values for each of the triangle vertexes and TRIANGLE will not draw pixels further than the already drawn pixels. ZString is automatically updated as appropriate.\n\nExamples: TRIANGLE(0,0,5,5,5,-5,#FFh,#FF00h,#FF0000h,128)\n\n"]
[null,"TRIANGLE_P","Syntax: TRIANGLE_P([G], x1, y1, x2, y2, x3, y3, c1, [c2, c3], [Alpha], [\"ZString\", z1, z2, z3]) or TRIANGLE_P([G], {x1, y1, [c1], [z1]}, {x2, y2, [c2], [z2]},{x3, y3, [c3], [z3]}, [\"ZString\"]) or TRIANGLE_P([G], [[x/y coordinate matrix]], [[color matrix]], {[[z matrix]], [zcode], [[[projection matrix]]], [zstring]) or TRIANGLE_P([G])\n\nDraws a triangle between specified pixel coordinates in the graphic using the specified color and transparency (0 ≤ Alpha ≤ 255). If 3 colors are specified, blends the colors in between the vertexes.\n\nThe next form of TRIANGLE allows display of multiple triangles at a time.\nThis is mostly used if you have a set of vertices and want to display them all at once.\n\nThe first 2 matrices indicate the x/y coordinates and colors of each points. TRIANGLE_P will draw 1 quadrilateral for each set of 4 adjacent vertices and blends the colors associated with the 4 points.\nIf a z and projection matrix are provided, for each point, this matrix is multiplied by the [x,y,z,1] vector to create the display x,y coordinates.\nIf zcode is a list that contains 3 real numbers { ex, ey, ez } then x,y are further modified by doing x=ez/z*x-ex and y=ez/z*y-ey creating a perspective projection.\nIf zstring is provided, z clipping will happen using the z value (see below).\nIf zcode=\"N\" or is a list that starts with \"N\", then each z is normalized to be between 0 and 255.\n\nAbout ZString\nTRIANGLE_P([G]) returns a string adapted for z clipping.\n\nTo use Z clipping, call TRIANGLE_P to create a Z clipping string (initialized at 255 for each pixels). You can then call TRIANGLE_P with appropriate z (0-255) values for each of the triangle vertexes and TRIANGLE_P will not draw pixels further than the already drawn pixels. ZString is automatically updated as appropriate.\n\nExamples: TRIANGLE_P(0,20,150,50,100,100,#FFh,#FF00h,#FF0000h,128)\n\n"]
[null,"trig2exp","Syntax: trig2exp(Expr)\n\nReplaces trigonometric functions in Expr with complex exponentials( without linearization).\n\nExample: trig2exp(sin(x)) returns (exp(i*x)-(1/exp(i*x)))/(2*i)\n\n"]
[null,"trigcos","Syntax: trigcos(Expr)\n\nSimplifies the argument Expr using the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging cosine)\n\nExample: trigcos(sin(x)^4+sin(x)^2) returns cos(x)^4-3*cos(x)^2+2\n\n"]
[null,"trigexpand","Syntax: trigexpand(Expr)\n\nExpands trigonometric functions.\n\nExample: trigexpand(sin(3*x)) returns (4*cos(x)^2-1)*sin(x)\n\n\n"]
[null,"trigsin","Syntax: trigsin(Expr)\n\nSimplifies the argument Expr using the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging sine)\n\nExample: trigsin(cos(x)^4+sin(x)^2) returns sin(x)^4-sin(x)^2+1\n\n"]
[null,"trigtan","Syntax: trigtan(Expr)\n\nSimplifies the argument Expr using the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging tangent) \n\nExample: trigtan(cos(x)^4+sin(x)^2) returns (tan(x)^4+tan(x)^2+1)/(tan(x)^4+2*tan(x)^2+1)\n\n"]
[null,"TRN","Syntax: TRN(matrix)\n\nTranspose. Transposes matrix. If Complex mode is on and the matrix contains complex elements, then TRN finds the conjugate transpose.\n\nExample: TRN([[1,2],[3,4]]) returns [[1,3],[2,4]] \n"]
[null,"trunc","Syntax: trunc(Real, [Integer]) or trunc(List, [Integer])\n\nTruncates a value to n decimal places (by default n=0).Accepts complex numbers.\n\nExamples: \ntrunc(4.3) returns 4\ntrunc({3.25, 8.71, 9.01},1) returns {3.2, 8.7, 9.}\n\n"]
[null,"TRUNCATE","Syntax: TRUNCATE(value, [places])\n\nTruncates value to system display settings. If optional places is given, truncates value to places decimal places. If places is negative, truncates to significant digits instead.\n\nExample: TRUNCATE(2.3678,2) returns 2.36\n"]
[null,"tsimplify","Syntax: tsimplify(Expr)\n\nReturns an expression with transcendentals rewritten as complex exponentials\n\nExample: tsimplify(exp(2*x)+exp(x)) returns exp(x)^2+exp(x)\n\n"]
[null,"type","Syntax: type(Expr)\n\nReturns n in [1..12] that defines the type of the argument\n\nExample: type(\"abc\") returns DOM_STRING\n\n"]
[null,"TYPE","Syntax: TYPE(object)\nReturns the type of the object:\n0: Real\n1: Integer\n2: String\n3: Complex\n4: Matrix\n5: Error\n6: List\n8: Function\n9: Unit\n14.?: cas object. the fractional part is the cas type\n"]
[null,"UFACTOR","Syntax: UFACTOR(Value_Unit1, 1_Unit2)\nUnit factor conversion. \nConverts a measurement using a compound unit into a measurement expressed in constituent units. \n\nExample: a Coulomb—a measure of electric charge—is a compound unit derived from the SI base units of Ampere and second: 1 C = 1 A * 1 s.  Using UFACTOR, you can express a measurement in Coulombs as a product of Amperes and time.\n\nUFACTOR(100_C,1_A)) returns 100_A*s\nUFACTOR(100_C, 1_min) returns 1.66666666667_min*A\n\n\n"]
[null,"unapply","Syntax: unapply(Expr,Var)\n\nReturns a function defined by an expression.\n\nExample: unapply(2*x^2,x) returns  (x)->2*x^2\n"]
[null,"UNCHECK","Syntax: UNCHECK(n)\nUnchecks (deselects) the corresponding symbolic definition field in the current app. The integer n must be between 0 and 9 for most apps. For Statistics 1-Var and Statistics 2-Var apps, n must be between 1 and 5.\n\nFor example, UNCHECK(3)  would uncheck F3 if the current app is Function.\n"]
[null,"UNTIL","Syntax: REPEAT command(s) UNTIL test;\n\nexecutes command(s) UNTIL the test is true.\n\nA:=5;\nREPEAT\n    PRINT(A); \n   A:= A-1;\nUNTIL A<1;\n\nwill print  5 4 3 2 1\n"]
[null,"USIMPLIFY","Syntax: USIMPLIFY(Value_Unitsexpr)\nUnit simplification.\nSimplifies Value in a complex unit expression Unitsexpr to an equivalent value in a simpler unit expression.  \n\nExample: a Joule is defined as 1 kg*m^2/s^2. \n\nUSIMPLIFY(5_kg*m2/s2) returns 5_J\n"]
[null,"valuation","Syntax: valuation(Poly(P))\n\nReturns the valuation (degree of the term of lowest degree) of the polynomial P .\n\nExample: valuation(x^4+x^3) returns 3\n"]
[null,"vandermonde","Syntax: vandermonde(Vect(V))\n\nReturns the Vandermonde matrix=[V^0,V^1,..] \n\nExample: vandermonde([1,2,3]) returns [[1,1,1],[1,2,4],[1,3,9]]\n"]
[null,"variance","Syntax: variance(Lst||Mtrx,[Lst])\n\nReturns the variance of a list with the second argument as the weight, or the list of variance of the columns of a matrix.\n\nExample: variance([3,4,2]) returns 2/3\n"]
[null,"vector","Syntax: vector(Pnt,Pnt || Pnt,Vect)\n\nDefines a vector(origin is 0 if 1 arg) with two points or two components or two affix (for 2D) or with a point and a vector or with a point (its extrmity and its origin is [0,0,0]).\n"]
[null,"vertices","Syntax: vertices(Polygon or Polyedr(P))\n\nReturns the list of the vertices of the polygon or polyhedron P.\n\n"]
[null,"vertices_abca","Syntax: vertices_abca(Polygon or Polyedr(P))\n\nReturns the closed list [A,B,...A] of the vertices of the polygon or polyhedron P.\n"]
[null,"VIEW","Syntax: VIEW \"text\", Function()\nVIEW. Allows a programmer to customize the Views menu. Causes \"text\" to apear when VIEW key is pressed and Function to be executed when the OK menu key (or ENTER key) is pressed.\n"]
[null,"vpotential","Syntax: vpotential(Vect(V),LstVar)\n\nReturns U such as curl(U)=V\n\nExample: vpotential([2*x*y+3,x^2-4*z,-2*y*z],[x,y,z]) returns [0,-2*x*y*z,-x^3/3+4*x*z+3*y] \n\n"]
[null,"WAIT","Syntax: WAIT(n)\nHalts program execution for the specified number of seconds.\nIf n is omitted or 0, halts execution until the user presses a key and returns the keycode (or -1 after 1 minute).\n\nIf n is -1, halts executions until the user presses a key or there is a mouse event.\nIf a key is pressed, the keycode is returned.\nAfter a 1 minute timeout, returns -1\n\nIf a mouse event happends, a list of the form { type, [x, y], [dx, dy] } is returned. Normally x/y is the event position unless otherwise indicated.\nType can be:\n0: Mouse Down\n1: Mouse Move\n2: Mouse Up (x/y is not provided)\n3: Mouse Click (note, if a click is detected, there is no MouseUp)\n5: Mouse Stretch. x/y is the delta since the last event. dx/dy is the delta since the ORIGINAL mouse down...\n6: Mouse Rotate, x is original angle, y is new angle in 32nd of a circle.\n7: Mouse Long Click, This means that the mouse stayed down for 1 second...\n\n\nExample:\nWAIT(5) halts program execution for 5 seconds.\n"]
[null,"when","Syntax: when(Cond,Expr1,Expr2)\n\nIf condition (even symbolic) returns expr1 else returns expr2 (? is the infixed version of when).\n\n"]
[null,"WHILE","Syntax: WHILE test DO command(s) END;\n\nexecutes command(s) WHILE the test is true.\n\nA:=5;\nWHILE A>1 DO \n    PRINT(A); \n   A:= A-1;\nEND;\n\nwill print  5 4 3 2 1\n"]
[null,"white","Syntax: white(Opt)\n\nOption of the display command to display with color.\n\n"]
[null,"XOR","Syntax: Value1 XOR Value2\nExclusive OR. \nReturns 1 if either Value1 or Value2 is non-zero but not both; otherwise, returns 0.\n\nExample: 3 XOR 2 returns 0\n"]
[null,"XPON","Syntax: XPON(value)\n\nExponent. Returns the exponent of value. \n\nExample: XPON(123.4) returns 2\n"]
[null,"yellow","Syntax: ('display')=[color]\n\nFor example, suppose you have drawn a circle in the Geometry app. In Symbolic view, the circle's definition might be GC:=circle(GA,GB-GA). If you wanted that circle to be, say, red, you could modify that definition to read:\n\nExample: GC:=circle(GA,GB-GA, ('display')=red)\n\n\n\n\n"]
[null,"zeros","Syntax: zeros(Expr,[Var])\n\nReturns the zeros (reals or complex according to the CAS settings) of the expression Expr for the variable Var (or the matrix where the lines are the solutions of the system : Expr1=0,Expr2=0...).\n\nExample: zeros(x^2+4) returns [] in real mode and [-2*i,2*i] in complex mode \n"]
[null,"Zeta","Syntax: Zeta(Real(a))\n\nReturns if a>1 sum(1/n^a,n,1,∞)\n\nExample: Zeta(2) returns π^2/6  \n\n"]
[null,"zip","Syntax: zip(Fnc2d(f),Lst(l1),Lst(l2),[Val(default)])\n\nReturns a list whose j-th entry is f(l1[j],l2[j]): without default value its length is the minimum of the lengths of the two input lists and else the shorter list is padded with the default value.\n\nExample: zip('+',[a,b,c,d], [1,2,3,4]) returns [a+1,b+2,c+3,d+4]\n"]
[null,"ztrans","Syntax: ztrans(Expr,[Var],[ZtransVar])\n\nZ transform of a sequence.\n\nExample: ztrans(a^x)\n"]