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
restart;
E 7.8. P\303\251lda.
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Determinant(S0);
S1:=SubMatrix(S0,[1..2,4..6],[1..5]):
S1[1,5]:=x*A: S1[2,5]:=A: S1[3,5]:=x^2*B: S1[4,5]:=x*B: S1[5,5]:=B:
S1; Determinant(S1);
S2:=SubMatrix(S0,[1..1,4..5],[1..3]):
S2[1,3]:=A: S2[2,3]:=x*B: S2[3,3]:=B:
S2; Determinant(S2);
S3:=SubMatrix(S0,[4],[1]):
S3[1,1]:=B:
S3; Determinant(S3);
E 7.9. P\303\251lda.
A:=x^8+x^6-3*x^4-3*x^3+8*x^2+2*x-5; B:=3*x^6+5*x^4-4*x^2-9*x+21;
S0:=SylvesterMatrix(A,B,x);
Determinant(S0);
S1:=SubMatrix(S0,[1..5,7..13],[1..12]):
S1[1,12]:=x^4*A: S1[2,12]:=x^3*A: S1[3,12]:=x^2*A: S1[4,12]:=x*A: S1[5,12]:=A: S1[6,12]:=x^6*B: S1[7,12]:=x^5*B: S1[8,12]:=x^4*B: S1[9,12]:=x^3*B: S1[10,12]:=x^2*B: S1[11,12]:=x*B: S1[12,12]:=B:
S1; Determinant(S1);
S2:=SubMatrix(S0,[1..4,7..12],[1..10]):
S2[1,10]:=x^3*A: S2[2,10]:=x^2*A: S2[3,10]:=x*A: S2[4,10]:=A: S2[5,10]:=x^5*B: S2[6,10]:=x^4*B: S2[7,10]:=x^3*B: S2[8,10]:=x^2*B: S2[9,10]:=x*B: S2[10,10]:=B:
S2; Determinant(S2);
S3:=SubMatrix(S0,[1..3,7..11],[1..8]):
S3[1,8]:=x^2*A: S3[2,8]:=x*A: S3[3,8]:=A: S3[4,8]:=x^4*B: S3[5,8]:=x^3*B: S3[6,8]:=x^2*B: S3[7,8]:=x*B: S3[8,8]:=B:
S3; Determinant(S3);
S4:=SubMatrix(S0,[1..2,7..10],[1..6]):
S4[1,6]:=x*A: S4[2,6]:=A: S4[3,6]:=x^3*B: S4[4,6]:=x^2*B: S4[5,6]:=x*B: S4[6,6]:=B:
S4; Determinant(S4);
S5:=SubMatrix(S0,[1..1,7..9],[1..4]):
S5[1,4]:=A: S5[2,4]:=x^2*B: S5[3,4]:=x*B: S5[4,4]:=B:
S5; Determinant(S5);
S6:=SubMatrix(S0,[7..8],[1..2]):
S6[1,2]:=x*B: S6[2,2]:=B:
S6; Determinant(S6);
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E 7.16. P\303\251lda.
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`mod`:=mods;
A:=9*x^5+2*x^4*y*z-189*x^3*y^3*z+117*x^3*y*z^2+3*x^3-42*x^2*y^4*z^2+26*x^2*y^2*z^3+18*x^2-63*x*y^3*z+39*x*y*z^2+4*x*y*z+6;
B:=6*x^6-126*x^4*y^3*z+78*x^4*y*z^2+x^4*y+x^4*z+13*x^3-21*x^2*y^4*z-21*x^2*y^3*z^2+13*x^2*y^2*z^2+13*x^2*y*z^3-21*x*y^3*z+13*x*y*z^2+2*x*y+2*x*z+2;
A11:=A mod 11; B11:=B mod 11;
A11_2:=subs(z=2,A11) mod 11; B11_2:=subs(z=2,B11) mod 11;
A11_3_2:=subs(y=3,A11_2) mod 11; B11_3_2:=subs(y=3,B11_2) mod 11;
Gcd(A11_3_2,B11_3_2) mod 11;
Gcd(subs(y=5,A11_2)mod 11,subs(y=5,B11_2)mod 11) mod 11;
Gcd(subs(y=-4,A11_2)mod 11,subs(y=-4,B11_2)mod 11) mod 11;
Gcd(subs(y=-2,A11_2)mod 11,subs(y=-2,B11_2)mod 11) mod 11;
Gcd(subs(y=2,A11_2)mod 11,subs(y=2,B11_2)mod 11) mod 11;
with(CurveFitting);
PolynomialInterpolation([3,5,-4,-2,2],[x^3+x+2,x^3+4*x+2,x^3+5*x+2,x^3+x+2,x^3-x+2],y,form=Lagrange) mod 11; expand(%) mod 11;
PolynomialInterpolation([2,-5,-3,5],[x^3+2*x*y^3-3*x*y+2,x^3-5*x*y^3-5*x*y+2,x^3-3*x*y^3-4*x*y+2,x^3+5*x*y^3-5*x*y+2],z,form=Lagrange) mod 11; expand(%) mod 11;
chrem([3*x^3+3*x*y^3*z-5*x*y*z^2-5,3*x^3+2*x*y^3*z+6,3*x^3+5*x*y^3*z+5*x*y*z^2+6],[11,13,17]);
C:=%/igcd(coeffs(%));
simplify(A/C); simplify(B/C);
8. Faktoriz\303\241l\303\241s
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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