9.79 Symbol

Symbols are one of the basic types manipulated by FriCAS. The Symbol domain provides ways to create symbols of many varieties.

The simplest way to create a symbol is to single quote an identifier.

X: Symbol := 'x

\[\]

x

_{Type: Symbol}

This gives the symbol even if x has been assigned a value. If x has not been assigned a value, then it is possible to omit the quote.

XX: Symbol := x

\[\]

x

_{Type: Symbol}

Declarations must be used when working with symbols, because otherwise the interpreter tries to place values in a more specialized type Variable.

A := 'a

\[\]

a

_{Type: Variable a}

B := b

\[\]

b

_{Type: Variable b}

The normal way of entering polynomials uses this fact.

x^2 + 1

\[\]

x2+1

_{Type: Polynomial Integer}

Another convenient way to create symbols is to convert a string. This is useful when the name is to be constructed by a program.

"Hello"::Symbol

\[\]

Hello

_{Type: Symbol}

Sometimes it is necessary to generate new unique symbols, for example, to name constants of integration. The expression new() generates a symbol starting with %.

new()$Symbol

\[\]

%A

_{Type: Symbol}

Successive calls to newnewSymbol produce different symbols.

new()$Symbol

\[\]

%B

_{Type: Symbol}

The expression new(“s”) produces a symbol starting with %s.

new("xyz")$Symbol

\[\]

%xyz0

_{Type: Symbol}

A symbol can be adorned in various ways. The most basic thing is applying a symbol to a list of subscripts.

X[i,j]

\[\]

xi,j

_{Type: Symbol}

Somewhat less pretty is to attach subscripts, superscripts or arguments.

U := subscript(u, [1,2,1,2])

\[\]

u1,2,1,2

_{Type: Symbol}

V := superscript(v, [n])

\[\]

vn

_{Type: Symbol}

P := argscript(p, [t])

\[\]

p(t)

_{Type: Symbol}

It is possible to test whether a symbol has scripts using the scripted?scripted?Symbol test.

scripted? U

\[\]

true

_{Type: Boolean}

scripted? X

\[\]

false

_{Type: Boolean}

If a symbol is not scripted, then it may be converted to a string.

string X

\[\]

“x”

_{Type: String}

The basic parts can always be extracted using the namenameSymbol and scriptsscriptsSymbol operations.

name U

\[\]

u

_{Type: Symbol}

scripts U

\[\]

[sub=[1,2,1,2],sup=[],presup=[],presub=[],args=[]]

_{Type: Record( sub: List OutputForm, sup: List OutputForm, presup: List} OutputForm, presub: List OutputForm, args: List OutputForm)

name X

\[\]

x

_{Type: Symbol}

scripts X

\[\]

[sub=[],sup=[],presup=[],presub=[],args=[]]

_{Type: Record( sub: List OutputForm, sup: List OutputForm, presup: List} OutputForm, presub: List OutputForm, args: List OutputForm)

The most general form is obtained using the scriptscriptSymbol operation. This operation takes an argument which is a list containing, in this order, lists of subscripts, superscripts, presuperscripts, presubscripts and arguments to a symbol.

M := script(Mammoth, [ [i,j],[k,l],[0,1],[2],[u,v,w] ])

\[\]

20,1Mammothi,jk,l(u,v,w)

_{Type: Symbol}

scripts M

\[\]

[sub=[i,j],sup=[k,l],presup=[0,1],presub=[2],args=[u,v,w]]

_{Type: Record( sub: List OutputForm, sup: List OutputForm, presup: List} OutputForm, presub: List OutputForm, args: List OutputForm)

If trailing lists of scripts are omitted, they are assumed to be empty.

N := script(Nut, [ [i,j],[k,l],[0,1] ])

\[\]

0,1Nuti,jk,l

_{Type: Symbol}

scripts N

\[\]

[sub=[i,j],sup=[k,l],presup=[0,1],presub=[],args=[]]

_{Type: Record( sub: List OutputForm, sup: List OutputForm, presup: List} OutputForm, presub: List OutputForm, args: List OutputForm)