RingElement % Subring -- Remainder modulo a subring

Synopsis

Operator: %
Usage:

r = f % A
Inputs:
- f, a ring element, of the ambient ring of $A$ (endowed with some monomial order.)
- A, an instance of the type Subring,
Outputs:
- r, a ring element, the normal form of f modulo $A$

The result $r$ is zero if and only if $f$ belongs to $A$. This function should be considered experimental.

i1 : R = QQ[x1, x2, x3];

i2 : A = subring {x1+x2+x3, x1*x2+x1*x3+x2*x3, x1*x2*x3, (x1-x2)*(x1-x3)*(x2-x3)} --usual invariants of A_3

o2 = subring of R

o2 : Subring

i3 : f = x1 + x2 + 2*x3

o3 = x1 + x2 + 2x3

o3 : R

i4 : f % A

o4 = p
      2

o4 : QQ[p ..p ]
         0   6

i5 : g = x1^2*x2 + x2^2*x3 + x3^2*x1

       2       2          2
o5 = x1 x2 + x2 x3 + x1*x3

o5 : R

i6 : g % A

        2    2        2
o6 = p p  + p p  + p p
      0 1    0 2    1 2

o6 : QQ[p ..p ]
         0   6