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SubalgebraBases :: subringIntersection

subringIntersection -- Intersection of subrings

Synopsis

Description

Computes the intersection of subrings "S_1" and "S_2". These subrings must be subrings of the same ambient ring. The ambient ring is allowed to be a polynomial ring or the quotient of a polynomial ring.

i1 : R = QQ[x,y];
i2 : I = ideal(x^3 + x*y^2 + y^3);

o2 : Ideal of R
i3 : Q = R/I;
i4 : S1 = subring {x^2, x*y};
i5 : S2 = subring {x, y^2};
i6 : S = subringIntersection(S1, S2);
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i7 : gens S

o7 = | x2 x2y2+xy3 y4 xy3 y6 xy5 |

             1       6
o7 : Matrix Q  <--- Q
i8 : isSAGBI S
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o8 = true

If the generators of $S$ form a sagbi basis and the degree limit is high enough, then they are a generating set for the intersection.

See also

Ways to use subringIntersection :

For the programmer

The object subringIntersection is a method function with options.