4.20.5 qring declaration

Syntax:

qring name = ideal_expression ;

Default:

none

Purpose:

declares a quotient ring as the basering modulo ideal_expression and sets it as current basering.

Operations based on standard bases (e.g. std,groebner, etc., reduce) and functions which require a standard basis (e.g. dim,hilb, etc.) operated with the residue classes; all others on the polynomial objects.

Example:

ring r=0,(x,y,z),dp; ideal i=xy; qring q=std(i); basering; ==> // coefficients: QQ considered as a field ==> // number of vars : 3 ==> // block 1 : ordering dp ==> // : names x y z ==> // block 2 : ordering C ==> // quotient ring from ideal ==> _[1]=xy // simplification is not immediate: (x+y)^2; ==> x2+2xy+y2 reduce(_,std(0)); ==> x2+y2 // polynomial and residue class: ring R=0,(x,y),dp; qring Q=std(y); poly p1=x; poly p2=x+y; // comparing polynomial objects: p1==p2; ==> 0 // comparing residue classes: reduce(p1,std(0))==reduce(p2,std(0)); ==> 1