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4.18.5 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;
==> // characteristic : 0
==> // 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
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