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);
 -- 0.00006749 seconds elapsed
 -- 0.000621794 seconds elapsed
 -- 0.000142992 seconds elapsed
 -- 0.000050761 seconds elapsed
 -- 0.000566374 seconds elapsed
 -- 0.000139741 seconds elapsed
 -- 0.00004436 seconds elapsed
 -- 0.000043461 seconds elapsed
 -- 0.000117412 seconds elapsed
 -- 0.000053621 seconds elapsed
 -- 0.000515825 seconds elapsed
 -- 0.00013127 seconds elapsed
 -- 0.000051501 seconds elapsed
 -- 0.000474073 seconds elapsed
 -- 0.000126941 seconds elapsed
 -- 0.000054051 seconds elapsed
 -- 0.000476176 seconds elapsed
 -- 0.00013093 seconds elapsed
 -- 0.00005321 seconds elapsed
 -- 0.000532385 seconds elapsed
 -- 0.000133392 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
 -- 0.00005624 seconds elapsed
 -- 0.000600175 seconds elapsed
 -- 0.000131241 seconds elapsed
 -- 0.000053112 seconds elapsed
 -- 0.000524944 seconds elapsed
 -- 0.00014523 seconds elapsed
 -- 0.00005135 seconds elapsed
 -- 0.000500195 seconds elapsed
 -- 0.000130521 seconds elapsed
 -- 0.000051601 seconds elapsed
 -- 0.000476844 seconds elapsed
 -- 0.000136591 seconds elapsed
 -- 0.000052691 seconds elapsed
 -- 0.000530225 seconds elapsed
 -- 0.000129801 seconds elapsed
 -- 0.0000504 seconds elapsed
 -- 0.000530456 seconds elapsed
 -- 0.00013097 seconds elapsed
 -- 0.000055081 seconds elapsed
 -- 0.000626854 seconds elapsed
 -- 0.000137521 seconds elapsed
 -- 0.000052651 seconds elapsed
 -- 0.000537605 seconds elapsed
 -- 0.000133551 seconds elapsed
 -- 0.00005447 seconds elapsed
 -- 0.000496655 seconds elapsed
 -- 0.000129862 seconds elapsed
 -- 0.000053481 seconds elapsed
 -- 0.000485755 seconds elapsed
 -- 0.00013971 seconds elapsed
 -- 0.000051041 seconds elapsed
 -- 0.000481755 seconds elapsed
 -- 0.000132821 seconds elapsed
 -- 0.00005242 seconds elapsed
 -- 0.000520536 seconds elapsed
 -- 0.000135932 seconds elapsed
 -- 0.0000531 seconds elapsed
 -- 0.000796176 seconds elapsed
 -- 0.000232362 seconds elapsed
 -- 0.000053921 seconds elapsed
 -- 0.000771947 seconds elapsed
 -- 0.000237542 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.