How to create MAX integrate rule?

Alexander <vidybida@bitp.kiev.ua> writes:

> how to prepare a rule to integrate functions with MAX(.,.)?

Please try the following code, e.g, with demo("integrate_abs.dem");

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/* integrate_abs.dem */

print("Quick and dirty...")$

matchdeclare([%a%,%b%],true);
defrule(maxabs,max(%a%,%b%),(abs(%b%-%a%)+%b%+%a%)/2);

/* For simplicity, I assume here that ARG does not contain
indefinite integrals. */
split_integrals_at_0(arg):=
subst(
  lambda([exp,x,a,b],
    integrate(exp,x,0,b)-integrate(exp,x,0,a)),
  nounify(integrate),arg);

declare(integrate,linear);

assume(t>0);
assume(a>t);

integrate(max(t-x,0),x,0,a);
int:changevar(%,t-x=y,y,x);
apply1(%,maxabs);
split_integrals_at_0(%);

forget(a>t);
assume(a<t);

int;
apply1(%,maxabs);
split_integrals_at_0(%);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Wolfgang