Re: [Reduce-algebra-developers] On simplification

[Rainer S. <rai...@gm...>]

On Sun, 15 Dec 2013 at 15:46 +0100, Eberhard Schruefer proposed a change to 
addsq:

 > symbolic procedure addsq(u,v);
 >     % U and V are standard quotients.
 >     % Value is canonical sum of U and V.
 >     if null numr u then v
 >      else if null numr v then u
 >      else if denr u=1 and denr v=1 then addf(numr u,numr v) ./ 1
 >      else begin scalar x,y,z;
 >          if null !*exp then <<u := numr u ./ mkprod denr u;
 >                               v := numr v ./ mkprod denr v>>;
 >          if !*lcm then x := gcdf!*(denr u,denr v)
 >           else x := gcdf(denr u,denr v);
 >          z := canonsq(quotf(denr u,x) ./ quotf(denr v,x));
 >          y := addf(multf(denr z,numr u),multf(numr z,numr v));
 >          if null y then return nil ./ 1;
 >          z := multf(denr u,denr z);
 >          if (x := gcdf(y,x)) neq 1 then <<y := quotf(y,x);
 >                                           z := quotf(z,x)>>;
 >          if !*gcd then return if x=1 then y ./ z else canonsq(y ./ z);
 >          return if (x := gcdf(y,z))=1 then canonsq(y ./ z)
 >                  else canonsq(quotf(y,x) ./ quotf(z,x))
 >      end;
 > 
 > However, this slows down calculations a little bit.

I ran the test suite against this change.  The run times differ at most by 5% 
(specfn), in some cases the test runs a bit faster after making the change.

The only notable difference is in the assert test log: with the old code, the 
call

 addsq(simp 'x, numr simp 'x);

returns something whose structure is not a standard quotient, but with the new 
code it returns

 (1 . nil)

Ie. formally a s.q., but with zero denominator.

Any objection to including this change into the core system?

  Rainer