# Question:How do I substitute a combination of functions by variable, for any input?

## Question:How do I substitute a combination of functions by variable, for any input?

Maple 2020

I want to do the substitution f(t) - ff(t) = epsilon for any variable t in Maple:

expand(myerror);
2 f(x - 2 h)   f(x)   3 f(x + 3 h)   2 ff(x - 2 h)   ff(x)
- ------------ - ---- + ------------ + ------------- + -----
15 h       6 h        10 h           15 h         6 h

3 ff(x + 3 h)
- -------------
10 h

NULL;
myfunc := t -> f(t) - ff(t) = epsilon;
myfunc := proc (t) options operator, arrow, function_assign;

f(t)-ff(t) = epsilon end proc

algsubs(myfunc(t), myerror);
2               1        3
- -- f(x - 2 h) - - f(x) + -- f(x + 3 h)
15              6        10
----------------------------------------
h

2                1         3
- -- ff(x - 2 h) - - ff(x) + -- ff(x + 3 h)
15               6         10
- -------------------------------------------
h

NULL;
subs(f(-h*n + x) = 1, ff(-h*n + x) = 0, f(x) = 1, ff(x) = 0, f(h*m + x) = 1, ff(h*m + x) = 0, myerror)*epsilon;
4 epsilon
---------
15 h

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