subringIntersection -- Intersection of subrings

Synopsis

Usage:

result = subringIntersection(S1, S2)
Inputs:
- S1, an instance of the type Subring,
- S2, an instance of the type Subring,
- SAGBILimitType, a string, Either \"Fixed\" or \"Function\". Determined the stopping criterion for the sagbi computation. If \"Fixed\" then the Limit is used, otherwise if \"Function\" is selected then the maximum degree of the input generators is used as the degree limit.
Optional inputs:
- Strategy => a string, default value "Master", the update strategy at the beginning of each loop: \"DegreeByDegree\", \"Incremental\", and \"Master\". The strategy \"Master\" is a hybrid that combines the other two; starting with \"DegreeByDegree\" for low degrees and switching to \"Incremental\". (See: Strategy)
- SubductionMethod => a string, default value "Top", the method used for subduction either: \"Top\" or \"Engine\". (See: SubductionMethod)
- Limit => an integer, default value 20, a degree limit for the binomial S-pairs that are computed internally.
- PrintLevel => an integer, default value 0, When this is greater than zero, information is printed about the progress of the computation (See: PrintLevel).
- SAGBILimitType
Outputs:
- result, an instance of the type Subring,

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);
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i7 : gens S

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

             1       6
o7 : Matrix Q  <--- Q

i8 : isSAGBI S
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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.

Ways to use subringIntersection :

"subringIntersection(Subring,Subring)"

For the programmer

The object subringIntersection is a method function with options.

subringIntersection -- Intersection of subrings

Synopsis

Description

See also

Ways to use subringIntersection :

For the programmer