Maxima Function
tellsimp (pattern, replacement)
is similar to tellsimpafter but places
new information before old so that it is applied before the built-in
simplification rules.
tellsimp is used when it is important to modify
the expression before the simplifier works on it, for instance if the
simplifier "knows" something about the expression, but what it returns
is not to your liking.
If the simplifier "knows" something about the
main operator of the expression, but is simply not doing enough for
you, you probably want to use tellsimpafter.
The pattern may not be a sum, product, single variable, or number.
rules is the list of rules defined by
defrule, defmatch, tellsimp, and tellsimpafter.
Examples:
(%i1) matchdeclare (x, freeof (%i)); (%o1) done (%i2) %iargs: false$ (%i3) tellsimp (sin(%i*x), %i*sinh(x)); (%o3) [sinrule1, simp-%sin] (%i4) trigexpand (sin (%i*y + x)); (%o4) sin(x) cos(%i y) + %i cos(x) sinh(y) (%i5) %iargs:true$ (%i6) errcatch(0^0); 0 0 has been generated (%o6) [] (%i7) ev (tellsimp (0^0, 1), simp: false); (%o7) [^rule1, simpexpt] (%i8) 0^0; (%o8) 1 (%i9) remrule ("^", %th(2)[1]); (%o9) ^ (%i10) tellsimp (sin(x)^2, 1 - cos(x)^2); (%o10) [^rule2, simpexpt] (%i11) (1 + sin(x))^2; 2 (%o11) (sin(x) + 1) (%i12) expand (%); 2 (%o12) 2 sin(x) - cos (x) + 2 (%i13) sin(x)^2; 2 (%o13) 1 - cos (x) (%i14) kill (rules); (%o14) done (%i15) matchdeclare (a, true); (%o15) done (%i16) tellsimp (sin(a)^2, 1 - cos(a)^2); (%o16) [^rule3, simpexpt] (%i17) sin(y)^2; 2 (%o17) 1 - cos (y)