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Symbol examples
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Symbols are one of the basic types manipulated by Axiom.  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:
o )show Symbol

