WSUtilityFunctions

jwsutils.spad line 1 [edit on github]

Julia Wolfram Symbolic utility functions using the MathLink Julia package.

fourierMatrix: PositiveInteger -> WSMatrix WSExpression

fourierMatrix(n) returns the n x n Fourier matrix.

gaussianMatrix: WSReal -> WSMatrix WSReal

gaussianMatrix(r) returns the Gaussian matrix with radius r. For example: example{gaussianMatrix “2.2”}

hankelMatrix: PositiveInteger -> WSMatrix WSInteger

hankelMatrix(n) returns the square Hankel matrix with integer coefficients.

hilbertMatrix: PositiveInteger -> WSMatrix WSRational

hilbertMatrix(n) returns the square Hilbert matrix.

identityMatrix: PositiveInteger -> WSMatrix WSInteger

identityMatrix(n) returns the identity matrix of size n.

jlWSDateString: () -> WSExpression

jlWSDateString() returns the WSExpression string of the local date and time. For example: example{toString dateTime()}

jlWSDateString: (WSExpression, WSExpression) -> WSExpression

jlWSDateString(expr, form) returns WSExpression string of the date from a WS date object with WS format form. For example: example{jlWSDateString(jWSExpr(“Now”), jWSExpr(“Entity[_”Language_”, _”French::367gk_”]”))}

jlWSDateString: WSExpression -> WSExpression

jlWSDateString(expr) returns the WSExpression string of the date from a WS date object. For example: example{jlWSDateString jWSExpr “Tomorrow”}

jlWSDocumentation: Symbol -> WSExpression

jlWSDocumentation(sym) prints WS informations about the symbol sym. For example: example{jlWSDocumentation sin}

jlWSExport: (String, WSExpression) -> WSExpression

jlWSExport(file.ext, obj) exports the object obj to the file file.ext. The extension ext will determine the saved format. A WS expression for example can be exported in an image file, it will be saved in the WS ‘StandardForm’ whereas in FriCAS it is outputted in WS ‘OutputForm': example{x:=jWSExpr(x);jlWSExport(“legendreP.png”, legendreP(7, x))}

jlWSExportString: (WSExpression, WSExpression) -> WSExpression

jlWSExportString(expr, jWSString(format)) returns the string representation of expr in the format form. Use toString or string to obtain the FriCAS String. For example: example{jWSExpr "Probability[x < 0, x \[Distributed] NormalDistribution[]]"} example{jWSExpr "Probability[x < 1, x \[Distributed] NormalDistribution[]]"} example{string jlWSExportString(%,jWSString “TeX”)}

jlWSImport: (String, WSExpression) -> WSExpression

jWSImport(expr, form) imports expr with format form.

jlWSImport: String -> WSExpression

jWSImport(expr) imports expr.

jlWSPlot: (WSExpression, WSExpression) -> WSExpression

jlWSPlot(expr, options) is the WS plot function. Since it should be run in a Wolfram notebook or any other supported graphical interfaces, the Wolfram Jupyter “plugin” for example, it is left to the user for testing purposes. The following uses the jlWSExport function: example{x:=jWSExpr(x);opt:=jWSList [x,-5,5]} example{jlWSExport(“sin.png”, jlWSPlot(sin(x),opt))}

jlWSRange: (WSInteger, WSInteger) -> WSList WSInteger

jlWSRange(n,m) returns a WSList that ranges from n to m.

jlWSRange: (WSInteger, WSInteger, WSInteger) -> WSList WSInteger

jlWSRange(n,m,d) returns a WSList that ranges from n to m with step d.

jlWSRange: WSInteger -> WSList WSInteger

jlWSRange(n) returns a WSList that ranges from 1 to n. For example: example{jlWSRange(10)@WSLIST(WSINT)}

jWSDateObject: () -> WSExpression

jWSDateObject() returns the WSExpression object of the local date and time.

jWSDateObject: (WSExpression, WSExpression) -> WSExpression

jWSDateObject(date,type) returns the WSExpression object of the date and type, for example “Month”.

jWSDateObject: WSExpression -> WSExpression

jWSDateObject(expr) returns the WSExpression object of the date from expr.

seedRandom: WSInteger -> WSExpression

seedRandom(n) reseeds the random number generator with n as seed. Returns the random generator state.

urand01Complex: (PositiveInteger, PositiveInteger) -> WSMatrix WSComplex

urand01Complex(rows,cols) returns a Julia WS matrix with uniformly distributed random complex elements in the unit square. Convenience function.

urand01Complex: PositiveInteger -> WSVector WSComplex

urand01Complex(n) returns a Julia WS vector with uniformly distributed random complex elements in the unit square. Convenience function.

urand01Real: (PositiveInteger, PositiveInteger) -> WSMatrix WSReal

urand01Real(rows,cols) returns a Julia WS matrix with uniformly distributed random elements in the range 0..1. Convenience function.

urand01Real: PositiveInteger -> WSVector WSReal

urand01Real(n) returns a Julia WS vector with uniformly distributed random elements in the range 0..1. Convenience function.

vandermondeMatrix: (WSList WSExpression, WSInteger) -> WSMatrix WSExpression

vandermondeMatrix(lvars, m) returns a Vandermonde matrix with nodes from lvars and m columns.

vandermondeMatrix: WSList WSExpression -> WSMatrix WSExpression

vandermondeMatrix(lvars) returns a Vandermonde matrix with nodes from lvars.

zeroMatrix: (PositiveInteger, PositiveInteger) -> WSMatrix WSInteger

zeroMatrix(m, n) returns a m-by-n zero matrix.