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3.23 std

Syntax:
std ( ideal_expression)
std ( module_expression)
std ( ideal_expression, poly_expression )
std ( module_expression, vector_expression )
Type:
ideal or module
Purpose:
returns a Groebner basis of an ideal or module with respect to the monomial ordering of the basering. A Groebner basis is a set of generators such that the leading terms generate the leading ideal, resp. module.

Use an optional second argument of type poly, resp. vector, to construct the Groebner basis from an already computed one (given as the first argument) and one additional generator (the second argument).

Note:
To view the progress of long running computations, use option(prot)

Example:
 
ring R=0,(x,y,z),dp;
matrix d[3][3];
d[1,2]=-z;  d[1,3]=2x;  d[2,3]=-2y;
ncalgebra(1,d); //U(sl_2)
ideal I=x2,y2,z2-1;
I=std(I);
I;
==> I[1]=z2-1
==> I[2]=yz-y
==> I[3]=xz+x
==> I[4]=y2
==> I[5]=2xy-z-1
==> I[6]=x2
kill R;
//------------------------------------------
ring Rq3=(0,Q),(x,y,z),dp; //U'_q(so_3)
minpoly=Q^2-Q+1; // at the 3rd root of unity
matrix C[3][3];
matrix D[3][3];
C[1,2]=Q2;    C[1,3]=1/Q2;  C[2,3]=Q2;
D[1,2]=-Q*z;  D[1,3]=1/Q*y; D[2,3]=-Q*x; 
ncalgebra(C,D);
ideal J=x2,y2,z2;
J=std(J);
J;
==> J[1]=z
==> J[2]=y
==> J[3]=x

See ideal; option; ring.


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