|  |  7.3.30 vdim (plural) 
See also
 ideal (plural);
 kbase (plural);
 std (plural).Syntax:vdim (ideal_expression)
 vdim (module_expression)Type:int
Purpose:computes the vector space dimension of the
factor-module that equals
ring (resp. free module) modulo the ideal (resp. submodule),
generated by the leading terms of the given generators.
If the factor-module is not of finite dimension, -1 is returned.
 
If the generators form a left Groebner basis,
this is the same as the vector space dimension of the
left factor module.
 
Note:In the non-commutative case, a ring modulo an ideal has a ring structure if and only if the ideal is two-sided.
Example:|  | ring R=0,(x,y,z),dp;
matrix d[3][3];
d[1,2]=-z;  d[1,3]=2x;  d[2,3]=-2y;
def RS=nc_algebra(1,d); //U(sl_2)
setring RS;
option(redSB); option(redTail);
ideal I=x3,y3,z3-z;
I=std(I);
I;
==> I[1]=z3-z
==> I[2]=y3
==> I[3]=x3
==> I[4]=y2z2-y2z
==> I[5]=x2z2+x2z
==> I[6]=x2y2z-2xyz2-2xyz+2z2+2z
vdim(I);
==> 21
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