qring standard basis result ring

  Given a standard basis of an ideal, create a new ring where all operations in this new ring will be done modulo this ideal. A warning message is given if the first argument is not a standard basis. Creating a quotient ring where the base ring of the standard basis is already a quotient ring is legal.

All operations in Macaulay can be done over a quotient ring, including computing standard bases, syzygies, Hilbert functions, and all matrix arithmetic.

For example,

%  putstd j k

%  type k
; b3-acd ab-cd a2-b2 

%  qring j S

%  pring S
; ring S
; characteristic           : 31991
; number of variables      : 4
; variables                : abcd
; weights                  : 1 1 1 1 
; monomial order           : 4 c 
; top degree of a monomial : 512 
; quotient ring by ideal:
; a2-b2
; ab-cd
; b3-acd

%  poly f (a+b)^2

%  ; f is reduced w.r.t. the above standard basis:
%  type f
; 2b2+2cd

Caveat: Using the forcestd command, it is possible to create a quotient ring where the above ideal is not homogeneous. In this case, every computation command (Chapter 7) will most likely compute, and compute, and compute... These commands do not detect this possibility.