keep standard basis result matrix [n]

Find the subset of the standard basis which does not lie 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 do not lie in . If an integer n is not specified, the default value for n is 1.

The elements of the standard basis chosen are exactly the complement of those chosen by the elim command. 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
; c2-bd bc-ad b2-ac t3-d sd-tc sc-tb sb-ta st2-c s2t-b s3-a 

%  keep j k

%  type k  ; exactly the complement of the "elim" command.
; t3-d sd-tc sc-tb sb-ta st2-c s2t-b s3-a

Possible applications include finding the degree of a rational map, and finding the locus where a birational map is not one to one.