[GiNaC-devel] New in GiNaC: step function

[Vladimir Kisil]

CD> Yes, one would, for instance, have
CD> integral(x,-infty,infty, exp(I*k*x)/(x+I*epsilon)) = -2*Pi*I*step(k).
CD> This would give precisely the same right result also at k=0 if
CD> step(0)=1/2. For cases like this it seems that 1/2 is the best value.

Yes, this is an important case, which needs such a function.

CD> maybe the best thing to do would be to have step(0)=1/2 and not to do a
CD> simplification step(x)^2 -> step(x). 
CD> Can everybody live with that?

Since it is consistent no reasons to object.  

CD> After all, if desired, such a
CD> simplification could also be done by the user. (S)he could do
CD> .subs(step(wild())*step(wild())==step(wild()), subs_options::algebraic).

In heavy calculations it is important that some simplifications are made
automatically on intermediate cases. To this end we may have (in the
core GiNaC or user-defined) another function (say "jump") which have the
property jump^2(t) -> jump(t).

RC> > 	 I missed it. Should we add its power property like that:
RC> >
RC> >static ex csgn_power(const ex & arg, const ex & exp)
RC> >{
RC> >}
RC> 
RC> But that appears to be missing the possibiliby of fractional powers.

I am not sure what fractional powers of a negative values should be...

Best wishes,
Vladimir
--
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/