next | previous | forward | backward | up | top | index | toc | Macaulay2 website
SubalgebraBases :: RingElement % Subring

RingElement % Subring -- Remainder modulo a subring

Synopsis

Description

The result is zero if and only if the input belongs to the subring. If a sagbi basis is known for the subring then subduction is used to compute the normal forms. If no sagbi basis is known then an extrisic method is used, similar to groebnerMembershipTest.

i1 : R = QQ[x1, x2, x3];
i2 : S = 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 with 4 generators

o2 : Subring
i3 : f = x1 + x2 + 2*x3

o3 = x1 + x2 + 2x3

o3 : R
i4 : f % S

o4 = x3

o4 : R
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 % S

o6 = 0

o6 : R

See also

Ways to use this method: