Komputeralgebrai algoritmusok
J\303\241rai Antal
Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak.
1. T\303\266rt\303\251net
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
restart;
A 8.1. Algoritmus.
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SquareFree:=proc(a,x) local i,out,b,c,y,z,w;
i:=1; out:=1; b:=diff(a,x);
c:=gcd(a,b); w:=quo(a,c,x);
while c<>1 do
y:=gcd(w,c);
z:=quo(w,y,x);
out:=out*z^i;
i:=i+1;
w:=y; c:=quo(c,y,x);
od; out:=out*w^i; end;
E 8.14. P\303\251lda.
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a:=x^63+1;
a1:=Gcd(a,x^2-x) mod 2; a:=Quo(a,a1,x) mod 2;
a2:=Gcd(a,x^4-x) mod 2; a:=Quo(a,a2,x) mod 2;
a3:=Gcd(a,x^8-x) mod 2; a:=Quo(a,a3,x) mod 2;
a4:=Gcd(a,x^16-x) mod 2; a:=Quo(a,a4,x) mod 2;
a5:=Gcd(a,x^32-x) mod 2; a:=Quo(a,a5,x) mod 2;
a6:=Gcd(a,x^64-x) mod 2; a:=Quo(a,a6,x) mod 2;
A 8.8. Algoritmus.
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PartialFactorDD:=proc(a,x,p) local aa,L,aaa,w,i;
i:=1; w:=x; aa:=a; L:=[];
while i<=degree(aa)/2 do
w:=Rem(w^p,aa,x) mod p;
aaa:=Gcd(aa,w-x) mod p;
L:=[op(L),aaa];
if aaa<>1 then
aa:=Quo(aa,aaa,x) mod p:
w:=Rem(w,aa,x) mod p;
fi; i:=i+1;
od; L:=[op(L),aa]; end;
10. Gr\303\266bner-b\303\241zisok
11. Racion\303\241lis t\303\266rtf\303\274ggv\303\251nyek integr\303\241l\303\241sa
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