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D.4.9.7 ffmodStd
Procedure from library ffmodstd.lib (see ffmodstd_lib).
- Usage:
- ffmodStd(I [, d]); I ideal, d int
- Return:
- Groebner basis of I over an algebraic function field
- Note:
- An optional parameter d>0, a positive integer, can be provided for the procedure.
It refers to a number of evaluation points to used.
Example:
| | LIB "ffmodstd.lib";
ring Ra=(0,a),(x,y,z),dp;
ideal I = (a^2+2)*x^2*y+a*y*z^2, x*z^2+(a+1)*x^2-a*y^2;
ffmodStd(I);
==> _[1]=xz2+(a+1)*x2+(-a)*y2
==> _[2]=(a2+2)*x2y+(a)*yz2
==> _[3]=(a2+2)*yz4+(a4+4a2+4)*xy3+(a4+a3+2a2+2a)*y3+(a3+2a2+a)*yz2
ideal J = x^2*y+y*z^2, x*z^2+x^2-y^2;
ffmodStd(J);
==> _[1]=xz2+x2-y2
==> _[2]=x2y+yz2
==> _[3]=yz4+xy3+y3+yz2
ring R1=(0,a,b),(x,y,z),dp;
ideal I = x^2*y^3*z+2*a*x*y*z^2+7*y^3,
x^2*y^4*z+(a-7b)*x^2*y*z^2-x*y^2*z^2+2*x^2*y*z-12*x+by,
(a2+b-2)*y^5*z+(a+5b)*x^2*y^2*z-b*x*y^3*z-x*y^3+y^4+2*a2*y^2*z,
a*x^2*y^2*z-x*y^3*z+3a*x*y*z^3+(-a+4)*y^3*z^2+4*z^2-bx;
ffmodStd(I);
==> _[1]=12*x+(-b)*y
==> _[2]=48*z2+(-b2)*y
==> _[3]=y2z
==> _[4]=y3
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See also:
nfmodStd.
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