inpart standard basis result matrix [variable list]

Find the minimally generated monomial ideal or submodule of initial forms of a standard basis, where some of the variables are considered as constants. In terms of the notation above, the result matrix is set with a minimal set of generators for the submodule . For example,

%  putstd j js

%  type js
; d2-3 c2+1 

%  inpart js jin 
; warning: no standard basis. Using initial terms of matrix

%  type jin    ; this is "1", since there were elements constant w.r.t. s,t.
; d2 c2 

%  keep js js1
; warning: no standard basis. Using initial terms of matrix

%  type js1
; d2-3 c2+1 

%  inpart js1 jin1
; warning: no standard basis. Using initial terms of matrix

%  type jin1
; d2 c2

Possible applications include finding the initial monomial ideal of an ideal or submodule over a quotient field, and finding the initial monomial ideal of an inhomogeneous ideal or submodule via homogenization.