Komputeralgebrai algoritmusok
J\303\241rai Antal
Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak.
3. Norm\303\241l form\303\241k, reprezent\303\241ci\303\263
5. K\303\255nai marad\303\251kol\303\241s
6. Newton-iter\303\241ci\303\263, Hensel-felemel\303\251s
7. Legnagyobb k\303\266z\303\266s oszt\303\263
8. Faktoriz\303\241l\303\241s
10. Gr\303\266bner-b\303\241zisok
E 10.3. P\303\251lda.
p:=-2*x^2*y*z+x^2*y^2+x^2*z^2+x^2*y+2*x*y^2*z^2-3*x*y*z^3-x*y+y*z+z^2+5;
sort(p,[x,y,z]);
op(1,p); lcoeff(%,[x,y,z],'t'); t;
collect(p,[x,y]);
pp:=collect(p,[x,y],`distributed`);
sort(pp,[x,y]);
op(1,p); lcoeff(%,[x,y],'t'); t;
with(Groebner);
LeadingTerm(p,tdeg(x,y,z)); %[1]*%[2];
LeadingMonomial(p,tdeg(x,y,z));
LeadingCoefficient(p,tdeg(x,y,z));
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A 10.1. Algoritmus.
reducers:=proc(p,Q,ord) local phmonom,qhmonom,q,R;
R:=[]; phmonom:=LeadingMonomial(p,ord);
for q in Q do
if q<>0 then
qhmonom:=LeadingMonomial(q,ord);
if divide(phmonom,qhmonom) then R:=[op(R),q]; fi;
fi;
od; R;
end;
Q:=[q1,q2]; QQ:=reducers(p,Q,tdeg(x,y,z));
reducer:=proc(p,Q,ord) Q[1] end;
reducer(p,QQ,tdeg(x,y,z));
myreduce:=proc(p,Q,ord) local QQ,q,pp,ppp,lpp,lq,t;
pp:=p; ppp:=0;
while pp<>0 do
QQ:=reducers(pp,Q,ord);
if QQ<>[] then
q:=reducer(p,QQ,ord);
t:=LeadingTerm(pp,ord); lpp:=t[1]*t[2];
t:=LeadingTerm(q,ord); lq:=t[1]*t[2];
pp:=expand(pp-lpp*q/lq);
else
LeadingTerm(pp,ord); lpp:=%[1]*%[2];
ppp:=ppp+lpp;
pp:=pp-lpp;
fi;
od; ppp;
end;
myreduce(p,Q,tdeg(x,y,z));
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E 10.8. P\303\251lda.
G:=[q1,q2,q3,x^2*y*z-z^3,x*z^3-x*z^2,y*z^3-z^3,x*y*z^2-x*z^2,x^2*z^2-z^4,
z^5-z^4];
myreduce(p1,G,tdeg(x,y,z)); myreduce(p2,G,tdeg(x,y,z));
myreduce(p1-p2,G,tdeg(x,y,z));
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11. Racion\303\241lis t\303\266rtf\303\274ggv\303\251nyek integr\303\241l\303\241sa
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