next | previous | forward | backward | up | top | index | toc | packages | Macaulay2 website
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);
 -- 0.000070081 seconds elapsed
 -- 0.000615576 seconds elapsed
 -- 0.000158743 seconds elapsed
 -- 0.000063933 seconds elapsed
 -- 0.000556213 seconds elapsed
 -- 0.000154317 seconds elapsed
 -- 0.000045446 seconds elapsed
 -- 0.000044789 seconds elapsed
 -- 0.000116285 seconds elapsed
 -- 0.000061694 seconds elapsed
 -- 0.000524442 seconds elapsed
 -- 0.000141327 seconds elapsed
 -- 0.000062896 seconds elapsed
 -- 0.000492679 seconds elapsed
 -- 0.000139265 seconds elapsed
 -- 0.00006279 seconds elapsed
 -- 0.000524016 seconds elapsed
 -- 0.000147153 seconds elapsed
 -- 0.000062399 seconds elapsed
 -- 0.000551404 seconds elapsed
 -- 0.000147932 seconds elapsed
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
i7 : gens S

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

             1       6
o7 : Matrix Q  <--- Q
i8 : isSAGBI S
 -- 0.000073243 seconds elapsed
 -- 0.00060486 seconds elapsed
 -- 0.000142735 seconds elapsed
 -- 0.000063047 seconds elapsed
 -- 0.000540477 seconds elapsed
 -- 0.000144883 seconds elapsed
 -- 0.000101943 seconds elapsed
 -- 0.00054239 seconds elapsed
 -- 0.000185817 seconds elapsed
 -- 0.000069957 seconds elapsed
 -- 0.000512633 seconds elapsed
 -- 0.00014844 seconds elapsed
 -- 0.000062296 seconds elapsed
 -- 0.000489507 seconds elapsed
 -- 0.000143718 seconds elapsed
 -- 0.000063047 seconds elapsed
 -- 0.000528553 seconds elapsed
 -- 0.000164635 seconds elapsed
 -- 0.000074847 seconds elapsed
 -- 0.000613351 seconds elapsed
 -- 0.000150172 seconds elapsed
 -- 0.000069629 seconds elapsed
 -- 0.000557432 seconds elapsed
 -- 0.000152635 seconds elapsed
 -- 0.000064137 seconds elapsed
 -- 0.00053065 seconds elapsed
 -- 0.000151419 seconds elapsed
 -- 0.000065844 seconds elapsed
 -- 0.000520193 seconds elapsed
 -- 0.000151278 seconds elapsed
 -- 0.000069784 seconds elapsed
 -- 0.000510371 seconds elapsed
 -- 0.000150959 seconds elapsed
 -- 0.000064738 seconds elapsed
 -- 0.000543953 seconds elapsed
 -- 0.000149017 seconds elapsed
 -- 0.000076054 seconds elapsed
 -- 0.000788674 seconds elapsed
 -- 0.000239477 seconds elapsed
 -- 0.000062259 seconds elapsed
 -- 0.000801246 seconds elapsed
 -- 0.000250559 seconds elapsed
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction

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.