JLWSUtilityFunctions

jwsutils.spad line 1 [edit on github]

Julia Wolfram Symbolic utility functions using the MathLink Julia package.

fourierMatrix: PositiveInteger -> JLWSMatrix JLWSExpression

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

gaussianMatrix: JLWSReal -> JLWSMatrix JLWSReal

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

hankelMatrix: PositiveInteger -> JLWSMatrix JLWSInteger

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

hilbertMatrix: PositiveInteger -> JLWSMatrix JLWSRational

hilbertMatrix(n) returns the square Hilbert matrix.

identityMatrix: PositiveInteger -> JLWSMatrix JLWSInteger

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

jlWSDateString: () -> JLWSExpression

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

jlWSDateString: (JLWSExpression, JLWSExpression) -> JLWSExpression

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

jlWSDateString: JLWSExpression -> JLWSExpression

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

jlWSExport: (String, JLWSExpression) -> JLWSExpression

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: (JLWSExpression, JLWSExpression) -> JLWSExpression

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, JLWSExpression) -> JLWSExpression

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

jlWSImport: String -> JLWSExpression

jWSImport(expr) imports expr.

jlWSInformation: Symbol -> JLWSExpression

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

jlWSPlot: (JLWSExpression, JLWSExpression) -> JLWSExpression

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: (JLWSInteger, JLWSInteger) -> JLWSList JLWSInteger

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

jlWSRange: (JLWSInteger, JLWSInteger, JLWSInteger) -> JLWSList JLWSInteger

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

jlWSRange: JLWSInteger -> JLWSList JLWSInteger

jlWSRange(n) returns a WS agg that ranges from 1 to n. For example: example{jlWSRange(10)@JWSLIST(JWSINT)}

jWSDateObject: () -> JLWSExpression

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

jWSDateObject: (JLWSExpression, JLWSExpression) -> JLWSExpression

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

jWSDateObject: JLWSExpression -> JLWSExpression

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

seedRandom: JLWSInteger -> JLWSExpression

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

urand01Complex: (PositiveInteger, PositiveInteger) -> JLWSMatrix JLWSComplex

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

urand01Complex: PositiveInteger -> JLWSVector JLWSComplex

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

urand01Real: (PositiveInteger, PositiveInteger) -> JLWSMatrix JLWSReal

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

urand01Real: PositiveInteger -> JLWSVector JLWSReal

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

vandermondeMatrix: (JLWSList JLWSExpression, JLWSInteger) -> JLWSMatrix JLWSExpression

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

vandermondeMatrix: JLWSList JLWSExpression -> JLWSMatrix JLWSExpression

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

zeroMatrix: (PositiveInteger, PositiveInteger) -> JLWSMatrix JLWSInteger

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