IntersectedSubring -- The type of all subrings arising from intersection

Description

IntersectedSubring is a type of Subring produced by intersecting two subrings using the function intersect. The function intersect is the constructor for IntersectedSubring. Applying the function isFullIntersection to an instance $S$ of IntersectedSubring checks whether the generators of $S$ are guaranteed to generate the intersection of the original subrings.

i1 : R = QQ[x,y];

i2 : S1 = subring{x^3,y};

i3 : S2 = subring{x^2,y^2};

i4 : S = intersect(S1,S2)

o4 = QQ[p_0..p_1], subring of R

o4 : IntersectedSubring

i5 : S#"originalSubrings"

o5 = {QQ[p_0..p_1], subring of R, QQ[p_0..p_1], subring of R}

o5 : List

The originalSubrings field lists the two subrings which were used to generate the intersection.

Functions and methods returning an intersected subring :

intersect(Subring,Subring) -- Intersection of subrings

Methods that use an intersected subring :

isFullIntersection(IntersectedSubring) -- see isFullIntersection -- check correctness of intersection computation
originalSubringGens(IntersectedSubring) -- see originalSubringGens -- generators of the original subrings

For the programmer

The object IntersectedSubring is a type, with ancestor classes Subring < HashTable < Thing.

IntersectedSubring -- The type of all subrings arising from intersection

Description

See also

Functions and methods returning an intersected subring :

Methods that use an intersected subring :

For the programmer