go_furuya@infoseek.jp wrote:
> hi
> Stavros and all
>
> at 2003 jun,we discussed gcd(m,n) concerning about Z homology.
> Carl Mactague said
>
>>in math'a [or Gcd(m,n) in yacas] and m and n aren't bound, then
>>GCD[m,n] simply remains unaltered wherever it appears. But in Maxima
>>(and perhaps this is really just a poor implementation of GCD and not
>>a critique of the Maxima evaluation scheme in general) you get
>>GCD(m,n) => 1!
Treated as polynomials in the indeterminates m,n the gcd of the two
polynomials m and n is correctly 1. That is, there is no
other polynomial other than 1 that exactly divides the polynomial n and
the polynomial m.
If you want to write a program with a different meaning, then I
suggest you change the name. If I understand what you want, then
integerGCD(m,n):= if integerp(m) and integerp(n) then gcd(m,n) else 'gcd(m,n).
or some such thing. Do you always print something? The rule tama looks
peculiar.
These sorts of barbs seem to arise quite often when I
>>use Maxima and they mess up all kinds of boundary conditions.
>
>
> What do you think this way?
> I use a rule evaled infinitly,but controled by maxapplydepth.
>
> (%i2) matchdeclare([m,n],true)$
> (%i13) defrule(tama,sgcd(m,n),if integerp(m) and integerp(n) then
> print(gcd(m,n)) else sgcd(m,n))$
> (%i4) maxapplydepth:2;
> (%o4) 2
> (%i5) apply1(sgcd(2,4),tama);
> 2
> (%o5) 2
> (%i6) apply1(sgcd(n1,n2),tama);
> (%o6) sgcd(n1, n2)
> (%i7) apply1(sin(sgcd(2,4)),tama);
> 2
> (%o7) SIN(2)
> (%i8) tgcd(_m,_n):=apply1(sgcd(_m,_n),tama)$
> (%i9) sin(tgcd(x,y));
> (%o9) SIN(sgcd(x, y))
> (%i10) sin(tgcd(5+3,6!));
> 8
> (%o10) SIN(8)
>
> I think that
> to control infinit loop with maxapplydepth makes us get ride
> of the barbs which Carl said about Maxima.
>
> gosei
>
>
>
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