9.79 SymbolΒΆ

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)