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Nelynx 04028fb3df add Matthias notes
2025-03-07 09:54:38 +01:00

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ring r = 0,(x,y),ds;
ideal f = x,xy+y6+y9;
kbase(std(f));
ring s = 0,(x,y),dp;
ideal f = x,xy+y6+y9
;
kbase(std(f));
ideal f = x,xy+y6+y8+y9;
kbase(std(f));
setring r;
f = imap(s,f);
f;
kbase(std(f));
quit;
LIB"AeCodPruebas.lib";
ring r = 0,(x,y),ds;
ideal f = x,y2,y3+x2y;
def Q = MalgrRing(ideal(0),2,f);
setring Q;
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
LIB"AeCodPruebas.lib";
TargetIdeal(ideal(x,y));
ring r = 0,(x,y),ds;
ideal f = x,y2,y3+x2y;
LIB"AeCodPruebas.lib";
TargetIdeal(f, ideal(x,y));
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
ring r = 0,(x,y),ds;
ideal f = x,y2,y3+x2y;
TargetIdeal(f, std(ideal(x,y)));
ring r = 0,(x,y),ds;
ideal f = x,y2,y3+x2y;
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
LIB"AeCodPruebas.lib";
TargetIdeal(f, std(ideal(x,y)));
TargetIdeal(f, std(maxideal(3)));
TargetIdeal(f, std(maxideal(5)));
LIB"AeCodPruebas.lib";
basering;
AeNormal(f);
LIB"AeCodPruebas.lib";
AeNormal(f);
;
LIB"AeCodPruebas.lib";
AeNormal(f);
LIB"AeCodPruebas.lib";
AeNormal(f);
;
LIB"AeCodPruebas.lib";
AeNormal(f);
ideal f = x+x4,y2,y3+x2y;
LIB"AeCodPruebas.lib";
ideal f = x+x4,y2,y3+x2y;
AeNormal(f,maxideal(3));
AeNormal(f,maxideal(4));
AeNormal(f);
LIB"AeCodPruebas.lib";
AeNormal(f);
AeNormal(f,maxideal(1));
AeNormal(f,maxideal(2));
AeNormal(f,maxideal(3));
AeNormal(f,maxideal(4));
AeNormal(f,maxideal(7));
AeNormal(f,maxideal(4));
AeNormal(f,maxideal(5));
f;
def Q = MalgrRing(ideal(0),2,f);
setring Q;
GF;
Gens;
setring r;
ideal w = x+x4,y2;
kbase(std(w));
setring Q;
GF;
basering;
GF;
reduce(x2, GF);
MalgrFormPoly(x2);
MalgrFormPoly(x2, maxideal(4));
MalgrFormPoly(x2, maxideal(2));
MalgrFormPoly(x2, maxideal(5));
MalgrFormPoly(x2, maxideal(6));
GF;
reduce(x2,GF);
x2;
X(3) - f[3];
X(3) - mappingf[3];
MalgrFormPoly(x2, maxideal(6));
LIB"AeCodPruebas.lib";
MalgrFormPoly(x2, maxideal(6));
LIB"AeCodPruebas.lib";
MalgrFormPoly(x2, maxideal(6));
MalgrFormPoly(x2, ideal(x,y)^4);
LIB"AeCodPruebas.lib";
MalgrFormPoly(x2, ideal(x,y)^4);
print(_);
MalgrFormPoly(x3, ideal(x,y)^4);
MalgrFormPoly(x3, ideal(x,y)^6);
MalgrFormPoly(x3, ideal(x,y)^7);
;
GF;
LIB"AeCodPruebas.lib";
ring r = 0,(x,y),ds;
ideal f = x,y2,y7+x2y;
AeNormal(f);
ideal f = x,y2,y5+x2y;
AeNormal(f);
ring r = 0,(t,x,y),ds;
ideal f = t,x,y3+t2y,(x+y)^4+t3y;
AeNormal(f);
ideal f = t,x,y4+t3y,(x+y)^3+t3y;
AeNormal(f);
ideal f = t,x,y5+t4y,(x+y)^4+t3y;
ideal f = t,x,y4+t3y,(x+y)^3+t2y;
AeNormal(f);
ideal f = t,x,y4+t3y,(x+y)^3+t2y;
AeNormal(f);
ideal f = t,x,y5+t4y,(x+y)^4+t3y;
AeNormal(f);
ideal f = t,x,y4+t3y,(x+y)^5+t4y;
AeNormal(f);
quit;
ring r = 0,(x,y),ds;
ideal f = x,y2,y3+x2y;
AeNormal(f);
LIB"AeCodPruebas.lib";
AeNormal(f);
LIB"AeCodPruebas.lib";
AeNormal(f);
ideal f = x+x4,y2,y3+x2y;
AeNormal(f);
AeNormal(f,maxideal(4));
ideal f = x+x4,y2,y3+x2y;
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
f;
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
f;
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(4));
AeNormal(f,maxideal(6));
AeNormal(f,maxideal(10));
AeNormal(f,maxideal(20));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
dimX
;
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
AeNormal(f,maxideal(10));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(10));
AeNormal(f,maxideal(20));
LIB"AeCodPruebas.lib";
AeNormal(f,maxideal(20));
f;
ideal g = x,xy+y^6+y^9;
AeNormal(g,maxideal(20));
AeNormal(g,maxideal(10));
AeNormal(g,maxideal(12));
AeNormal(f,maxideal(12));
AeNormal(f);
AeNormal(g);
AeNormal(g,maxideal(12));
AeNormal(g,maxideal(20));
AeNormal(g);
AeNormal(g,maxideal(50));
ring r = 0,(x,y),ds;
ring R = 0,(X,Y),ds;
setring r;
map Rr = R,x2,y3;
ideal J = maxideal(20);
setring R;
preimage(r,Rr,J);
setring r;
ideal J = maxideal(50);
setring R;
ideal J = maxideal(50);
preimage(r,Rr,J);
setring r;
ideal J = maxideal(100);
setring R;
preimage(r,Rr,J);
setring r;
map f = R,x2+y3,y5+x7;
J = maxideal(20);
setring R;
preimage(r,f,J);
LIB"AeCodPruebas.lib";
ring r = 0,(t,x,y),ds;
ideal f = t,x,y3+t2y,(x+y)^4+t3y;
AeNormal(f);
ideal f = t,x,y3+t2y,(x+y)^4+t3y;
f[4];
LIB"AeCodPruebas.lib";
ring r = 0,(t,x,y),ds;
ideal f = t,x,y3+t2y,y4+(t3+x3)*y;
AeNormal(f);
ideal f = t,x,y3+t2y,(x+y)^4+t3y;
f[4];
f[4] = f[4] -x4;
f;
AeNormal(f);
f[4]
;
f[4] = y3+(t3+x3)*y+xy3;
AeNormal(f);
f[4] = y3+(t3+x3)*y+xy3+x2y2;
AeNormal(f);
f[4] = y3+(t3+4x3)*y+4xy3+6x2y2;
AeNormal(f);
f;
f[4] = y4+(t3+4x3)*y+4xy3+6x2y2;
AeNormal(f);
f[4] = y4+(t3+x3)*y+xy3+x2y2;
AeNormal(f);
f[4] = y4+t3y+x3y+xy3+x2y2;
AeNormal(f);
f[4] = y4+t3y+xy3+x2y2;
AeNormal(f);f
;
f[4] = y4+t3y+xy3+x2y2+x3y;
AeNormal(f);f
;
AeNormal(f);
f[4] = y4+t3y+xy3+x2y2+x3y;
AeNormal(f);
f[4] = y4+t3y+xy3+x3y;
AeNormal(f);
f[4] = y4+t3y+xy3+x2y2+x3y;
AeNormal(f);
f[4] = y4+xy3+x2y2+x3y;
AeNormal(f);
f;
AeNormal(f);
f;
f[4] = y4+x3y;
AeNormal(f);
f[4] = y4+x3y+xy3;
AeNormal(f);
f[4] = y4+x2y2+xy3;
AeNormal(f);
f[4] = y4+x3y+x2y2;
AeNormal(f);f
f;
f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4;
size(AeNormal(f));
f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4+t4y;
size(AeNormal(f));
f = t,x,y4+t3y,(x+y)^5;
size(AeNormal(f));
f = t,x,y4+t3y,(x+y)^5+t4y;
size(AeNormal(f));
f[4];
f[4]=x5+t4y+x4y+x3y2+x2y3+xy4+y5;
size(AeNormal(f));
f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
size(AeNormal(f));
f[4]=t4y+x3y2+x2y3+xy4+y5;
size(AeNormal(f));
f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
size(AeNormal(f));
f[4]=t4y+x4y+x3y2+x2y3+y5;
size(AeNormal(f));
f[4]=x4y+x3y2+x2y3+y5;
size(AeNormal(f));
f = t,x,y4+t3y,(x+y)^3,t2y;
size(AeNormal(f));
f = t,x,y4+t3y,(x+y)^3+t2y;
size(AeNormal(f));
f[4];
f[4] = t2y+x2t+xy2+y3;
size(AeNormal(f));
f[4] = t2y+x2y+xy2+y3;
size(AeNormal(f));
f[4] = t2y+3x2y+3xy2+y3;
size(AeNormal(f));
f[4] =3x2y+3xy2+y3;
size(AeNormal(f));
f[4] = t3y + 3x2y+3xy2+y3;
size(AeNormal(f));
f[4] = t5y + 3x2y+3xy2+y3;
size(AeNormal(f));
f[4] = t10y + 3x2y+3xy2+y3;
size(AeNormal(f));
f[4] = 3y + 3x2y+3xy2+y3;
size(AeNormal(f));
f;
size(AeNormal(f));
f[4] = + 3x2y+3xy2+y3;
size(AeNormal(f));
f[4] = y;
size(AeNormal(f));
size(AeNormal(f));
f = t,x,y3+t2y,(x+y)^4;
AeNormal(f);
f = t,x,y3+t2y,(x+y)^4+t3y;
AeNormal(f);
f[4];
f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4
;
AeNormal(f);
size(AeNormal(f));
f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4;
size(AeNormal(f));
f[4] = t3y+4x3y+6x2y2+4xy3+y4;
size(AeNormal(f));
f[4] = t3y+x3y+x2y2+xy3+y4;
size(AeNormal(f));
f[4] = x3y+x2y2+xy3+y4;
size(AeNormal(f));
f[4] = t3y+4x3y+6x2y2+4xy3+y4;
size(AeNormal(f));
f[4] = 4x3y+6x2y2+4xy3+y4;
size(AeNormal(f));
f[4] = x3y+x2y2+xy3+y4;
size(AeNormal(f));
f[4] = x2y2+xy3+y4;
size(AeNormal(f));
f[4] = x3y+x2y2+y4;
size(AeNormal(f));
f[3] = y4+t3y;
size(AeNormal(f));
f[4] = (x+y)^5+t4y;
size(AeNormal(f));
f[4];
f[4] = x4y+x3y2+x2y3+y5;
size(AeNormal(f));
f[4]^2;
f[4] = x4y+x3y2+x2y3+y5;
size(AeNormal(f));
f[4] = x4y+x3y2+y5;
size(AeNormal(f));
f[4] = x4y+2x3y2+y5;
size(AeNormal(f));
f[4] = x4y+3x3y2+y5;
size(AeNormal(f));
f[4] = 5x4y+3x3y2+y5;
size(AeNormal(f));
f;
f = t,x,(x+y)^4+t2y,y3+t2y;
AeNormal(f);
f:
;
f = t,x,(x+y)^4+t3y,y3+t2y;
AeNormal(f);
f = t,x,(x+y)^4+t2y,y3+t2y;
AeNormal(f);
f = t,x,(x+y)^5+t2y,y3+t2y;
AeNormal(f);
f = t,x,(x+y)^5+t2y,y4+t2y;
AeNormal(f);
f;
f = t,x,(x+y)^4+t3y,y3+t2y;
AeNormal(f);
f = t,x,(x+y)^4+t3y,y3;
AeNormal(f);
f = t,x,(x+y)^4+t3y,y3+t2y;
f = t,x,(x+y)^4+t3y,y3+t2y;
AeNormal(f);
f[3];
f = t,x,(x+y)^4+t3y,y3+t2y;
f[3];
f[3] = x4+x3y+x2y2+xy3+y4;
AeNormal(f);
f;
LIB"AeCodPruebas.lib";
ring r = 0,(t,x,y),ds;
map f = t,x,y3+t2y,y4+x3y;
ideal f = t,x,y3+t2y,y4+x3y;
size(AeNormal(f));
ideal f = t,x,y5+t4y,y6+x5y;
size(AeNormal(f));
ideal f = t,x,y5+t4y,y6+(x5+t4)*y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,xy3+x2y2+x3y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,y4+xy3+x3y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,y4+xy3-x3y;
size(AeNormal(f));
ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
ideal f = t,x,y3+t2y,y4+x2y2+x3y;
ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
ideal f = t,x,y3+t2y,y4+x2y2+x3y;
size(AeNormal(f));
ideal f = t,x,y4+t2y,y5+x2y2+x3y;
size(AeNormal(f));
ideal f = t,x,y4+t3y,y5+x4y+x3y2;
size(AeNormal(f));
ideal f = t,x,y4+t3y,y5+x4y+x3y2+x2y3;
size(AeNormal(f));
quit;
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