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
2
x + 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()$Symbol
%A
Type: Symbol
Successive calls to new produce different symbols.
new()$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]
x
i,j
Type: Symbol
Somewhat less pretty is to attach subscripts, superscripts or arguments.
U := subscript(u, [1,2,1,2])
u
1,2,1,2
Type: Symbol
V := superscript(v, [n])
n
v
Type: Symbol
P := argscript(p, [t])
p(t)
Type: Symbol
It is possible to test whether a symbol has scripts using the scripted? 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 name and scripts 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 script 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] ])
0,1 k,l
Mammoth (u,v,w)
2 i,j
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] ])
0,1 k,l
Nut
i,j
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)
See Also: