result = isFullIntersection(S)
Checks if the algorithm for computing the intersection of two subrings in the function intersect produced a subalgebra basis for the intersection.







This test is onesided: if the function isFullIntersection returns false, then the generators of the given subring may still generate the intersection as a subalgebra basis.







If the function isFullIntersection returns false then, there are a few different possibilities: First, the composite subring $S$ may have a finite subalgebra basis that could be found by setting the option SAGBILimitType to its default value of Fixed or by using a higher Limit option in intersect. Second, $S$ may not have a finite subalgebra basis but the intersection does have a finite subalgebra basis. In this case, the output may be a generating set for the full intersection, but cannot be verified by the algorithm. Third, the intersection of the input algebras may not have a finite subalgebra basis, and so the composite subring does not have a finite subalgebra basis. In this case, the computed generators may be a generating set (but not a subalgebra basis) for the intersection but the algorithm cannot guarantee it.
The object isFullIntersection is a method function.