next | previous | forward | backward | up | top | index | toc | 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);
 -- 0.000129459 seconds elapsed
 -- 0.00127862 seconds elapsed
 -- 0.000349077 seconds elapsed
 -- 0.000128234 seconds elapsed
 -- 0.00112814 seconds elapsed
 -- 0.000336286 seconds elapsed
 -- 0.000107371 seconds elapsed
 -- 0.000108037 seconds elapsed
 -- 0.000309058 seconds elapsed
 -- 0.000124714 seconds elapsed
 -- 0.00106852 seconds elapsed
 -- 0.000318384 seconds elapsed
 -- 0.000122238 seconds elapsed
 -- 0.00102346 seconds elapsed
 -- 0.000310488 seconds elapsed
 -- 0.000135615 seconds elapsed
 -- 0.00101562 seconds elapsed
 -- 0.000314684 seconds elapsed
 -- 0.000131369 seconds elapsed
 -- 0.00108258 seconds elapsed
 -- 0.000325955 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
 -- 0.000133994 seconds elapsed
 -- 0.00121068 seconds elapsed
 -- 0.000317274 seconds elapsed
 -- 0.000130934 seconds elapsed
 -- 0.0011084 seconds elapsed
 -- 0.000320694 seconds elapsed
 -- 0.000129754 seconds elapsed
 -- 0.0010445 seconds elapsed
 -- 0.000313548 seconds elapsed
 -- 0.000129364 seconds elapsed
 -- 0.00104335 seconds elapsed
 -- 0.000311813 seconds elapsed
 -- 0.000171694 seconds elapsed
 -- 0.000988981 seconds elapsed
 -- 0.000313869 seconds elapsed
 -- 0.000120688 seconds elapsed
 -- 0.00108935 seconds elapsed
 -- 0.000318144 seconds elapsed
 -- 0.000132169 seconds elapsed
 -- 0.00122366 seconds elapsed
 -- 0.000327255 seconds elapsed
 -- 0.000122608 seconds elapsed
 -- 0.00111799 seconds elapsed
 -- 0.000319869 seconds elapsed
 -- 0.000125409 seconds elapsed
 -- 0.00104295 seconds elapsed
 -- 0.00032393 seconds elapsed
 -- 0.000123283 seconds elapsed
 -- 0.0010128 seconds elapsed
 -- 0.000310358 seconds elapsed
 -- 0.000121903 seconds elapsed
 -- 0.00102192 seconds elapsed
 -- 0.000313363 seconds elapsed
 -- 0.00014393 seconds elapsed
 -- 0.00106668 seconds elapsed
 -- 0.000313088 seconds elapsed
 -- 0.000124363 seconds elapsed
 -- 0.00151343 seconds elapsed
 -- 0.000526402 seconds elapsed
 -- 0.000125394 seconds elapsed
 -- 0.00149745 seconds elapsed
 -- 0.000520005 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.