80.1 Functions and Variables for opsubst

Function: opsubst
    opsubst (f,g,e)
    opsubst (g=f,e)
    opsubst ([g1=f1,g2=f2,..., gn=fn],e) ¶

The function opsubst is similar to the function subst, except that opsubst only makes substitutions for the operators in an expression. In general, When f is an operator in the expression e, substitute g for f in the expression e.

To determine the operator, opsubst sets inflag to true. This means opsubst substitutes for the internal, not the displayed, operator in the expression.

Examples:

(%i1) load ("opsubst")$

(%i2) opsubst(f,g,g(g(x)));
(%o2)                     f(f(x))
(%i3) opsubst(f,g,g(g));
(%o3)                       f(g)
(%i4) opsubst(f,g[x],g[x](z));
(%o4)                       f(z)
(%i5) opsubst(g[x],f, f(z));
(%o5)                      g (z)
                            x
(%i6) opsubst(tan, sin, sin(sin));
(%o6)                     tan(sin)
(%i7) opsubst([f=g,g=h],f(x));
(%o7)                       h(x)

Internally, Maxima does not use the unary negation, division, or the subtraction operators; thus:

(%i8) opsubst("+","-",a-b);
(%o8)                     a - b
(%i9) opsubst("f","-",-a);
(%o9)                      - a
(%i10) opsubst("^^","/",a/b);
                             a
(%o10)                       -
                             b

The internal representation of -a*b is *(-1,a,b); thus

(%i11) opsubst("[","*", -a*b);
(%o11)                  [- 1, a, b]

When either operator isn’t a Maxima symbol, generally some other function will signal an error:

(%i12) opsubst(a+b,f, f(x));

Improper name or value in functional position:
b + a
 -- an error.  Quitting.  To debug this try debugmode(true);

However, subscripted operators are allowed:

(%i13) opsubst(g[5],f, f(x));
(%o13)                     g (x)
                            5

To use this function write first load("opsubst").

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