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SAGBILimitType -- Flag for calculating degree limit in intersections

Description

There are two possible values for SAGBILimitType: Fixed or Function. Determines the stopping criterion for the subalgebra basis computation performed by the function intersect(Subring,Subring). This function creates a subring $S$, called the composite subring, from the input algebras and attempts to compute a subalgebra basis for $S$. The Limit of this subalgebra basis computation is controlled by the two options SAGBILimitType and Limit.

If SAGBILimitType is set to Fixed, then the Limit of the subalgebra basis computation is set to the value of the option Limit. Otherwise, if SAGBILimitType is set to Function, then the Limit of the subalgebra basis computation is set to the product of the degrees of the maximum degree generators of the input algebras.

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 : gens (S3 = intersect(S1, S2, SAGBILimitType => "Fixed", Limit => 5))
-- Warning! Result is not a full intersection.  Try increasing Limit.

o6 = | x2 x2y2+xy3 |

             1      2
o6 : Matrix Q  <-- Q
 
i7 : gens (S4 = intersect(S1, S2, SAGBILimitType => "Fixed", Limit => 10))

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

             1      6
o7 : Matrix Q  <-- Q
 
i8 : gens (S5 = intersect(S1, S2, SAGBILimitType => "Function"))
-- Warning! Result is not a full intersection.  Try increasing Limit.

o8 = | x2 x2y2+xy3 |

             1      2
o8 : Matrix Q  <-- Q

By default, the option SAGBILimitType is set to Fixed, and the default Limit is $20$. For more information see intersect(Subring,Subring).

See also

Functions with optional argument named SAGBILimitType:

For the programmer

The object SAGBILimitType is a symbol.