Re: gcd

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Aug 09, 2019 at 12:05:51PM +0900, macsyma wrote:
> > PARI is not well suited to compute gcd of multivariate polynomials.
> 
> Even with the following simple method, the correct result can be obtained, 
> so I posted in the hope that some modification will make gcd() work well.
> 
> while(Q=P%(R=Q),P=R);liftpol(R/pollead(R))
> %4 = x^35+((-2814705810*c7^5-12865509020*c7^4-2956013550*c7^3+6832839580*c7^2-3002993630*c7-7609289760)*c5^3+(-11072532380*c7^5-12027706250*c7^4-2118210780*c7^3-1424986990*c7^2-3002993630*c7+1673794090)*c5^2+(-1236699170*c7^5-11980726170*c7^4-11980726170*c7^3-1236699170*c7^2-2932502040)*c5+(-9449209994*c7^5-18890856012*c7^4-9081390038*c7^3-7779009056*c7^2-15991519880*c7-9462010960))

Well, you can also obtain this result with my method:

p7=c7^6+c7^5+c7^4+c7^3+c7^2+c7+1;
p5=c5^4+c5^3+c5^2+c5+1;
P7=subst(p7,c7,t);
P5=subst(p5,c5,t);
[R,C7,C5,k]=polcompositum(P7,P5,3);
PP=subst(liftall(P),c5,C5)*Mod(1,R);
QQ=subst(liftall(Q),c7,C7)*Mod(1,R);
R=gcd(PP/content(PP),QQ/content(QQ));
liftall(subst(liftall(R),t,(k*c7+c5)*Mod(1,p7)*Mod(1,p5)))/pollead(R)

%10 =
x^35+((-2814705810*c7^5-12865509020*c7^4-2956013550*c7^3+6832839580*c7^2-3002993630*c7-7609289760)*c5^3+(-11072532380*c7^5-12027706250*c7^4-2118210780*c7^3-1424986990*c7^2-3002993630*c7+1673794090)*c5^2+(-1236699170*c7^5-11980726170*c7^4-11980726170*c7^3-1236699170*c7^2-2932502040)*c5+(-9449209994*c7^5-18890856012*c7^4-9081390038*c7^3-7779009056*c7^2-15991519880*c7-9462010960))

Cheers,
Bill.