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 jlWSDateString()}

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 information about the symbol sym. Note that the WS language is preferable. Trivial implementation. For example: example{jlWSDocumentation sin} example{jlWSDocumentation ArcSin}

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 displayed 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 specified format. 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”)}

jlWSFileFormat: (String, WSExpression) -> WSExpression

jlWSFileFormat(src, list(form)) tries to determine the format of the source src from its content using the list of formats form. Returns WS None if no format is found. Can be used with jWSImport. For example: jlWSFileFormat("examples/customers-100.csv",jWSExpr "{_"CSV_",_"TSV_"}")

jlWSFileFormat: String -> WSExpression

jlWSFileFormat(src) tries to determine the format of the source src from its content. Can be used with jWSImport. For example: example{jlWSFileFormat(“examples/customers-100.csv”)}

jlWSImport: (WSExpression, WSExpression) -> WSExpression

jlWSImport(myfile, form) imports the file myfile with format form. For example: example{file:=jlWSImport(jWSString(“examples/customers-100.csv”), jWSString “CSV”);}

jlWSImport: WSExpression -> WSExpression

jlWSImport(src) imports the source src. For example: example{file:=jlWSImport jWSString “examples/customers-100.csv”;} example{jlWSDateString(file.2.11)}

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))}

jlWSSeedRandom!: WSInteger -> WSExpression

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

jlWSSnippet: (WSExpression, WSInteger) -> WSExpression

jlWSSnippet(expr, n) returns the first (or last) n snippets of the WSExpression expr. For example: example{jlWSSnippet(jlWSImport jWSString “http://www.fricas.org/”,-2)}

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.

jWSRange: (WSInteger, WSInteger) -> WSList WSInteger

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

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

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

jWSRange: WSInteger -> WSList WSInteger

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

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 an m-by-n zero matrix.