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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
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See
ideal;
option;
ring.
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