64.1 Functions and Variables for opsubst

Function: opsubst (f, g, e) ¶

Function: opsubst (g = f, e) ¶

Function: 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.

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

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