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3.26 twostd

Syntax:
twostd( ideal_expression);
Type:
ideal or module
Purpose:
returns a left Groebner basis of the two-sided ideal, generated by the input, treated as a set of two-sided generators.

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); 
// this is algebra U(sl_2)
int N=2;
poly f=1;
for(int n=0;n<=N;n++)
{ 
  f=f*(z+N-2*n);
}
f;
==> z3-4z
ideal i=x^(N+1),y^(N+1),f;
option(redSB);
option(redTail);
ideal I=std(i);
I;
==> I[1]=z3-4z
==> I[2]=yz2-2yz
==> I[3]=xz2+2xz
==> I[4]=2xyz-z2-2z
==> I[5]=y3
==> I[6]=x3
ideal J=twostd(i);
J;
==> J[1]=z3-4z
==> J[2]=yz2-2yz
==> J[3]=xz2+2xz
==> J[4]=y2z-2y2
==> J[5]=2xyz-z2-2z
==> J[6]=x2z+2x2
==> J[7]=y3
==> J[8]=xy2-yz
==> J[9]=x2y-xz-2x
==> J[10]=x3

Remark:
There are algebras with no two-sided ideals except 0 and the whole algebra (like Weyl algebras).


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