Find the subset of the standard basis which lies in a subring. If S
is the base ring of the standard basis, and
is the subring of
S defined above, create a matrix whose columns are those elements of
the standard basis whose lead monomials lie in
. If an integer
n is not specified, the default value for n is 1.
In other words, this command finds the subset of the standard basis corresponding to the above proposition. This command is in general very useful.
For example, suppose that the ring S is the same as above: the variables are "stabcd", and the monomial order is the product order "2 4". Then
% putstd j js % type js ; the entire standard basis ; c2-bd bc-ad b2-ac t3-d sd-tc sc-tb sb-ta st2-c s2t-b s3-a % elim j k % type k ; the subset not involving s,t ; c2-bd bc-ad b2-ac