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TestIdeals :: descendIdeal

descendIdeal -- finds the maximal F-pure Cartier submodule of an ideal viewed as a Cartier module

Synopsis

Description

This command computes the maximal $F$-pure Cartier submodule of an ideal $J$ under the dual-$e$-iterated Frobenius induced by $f_1^{t_1}\ldots f_n^{t_n}$.

The function returns a sequence, where the first entry is the descended ideal, and the second entry is the number of times frobeniusRoot was applied (i.e., the HSL number).

i1 : R = ZZ/7[x,y,z];
i2 : f = y^2 - x^3;
i3 : descendIdeal(1, {5}, {f}, ideal 1_R) --this computes the non-F-pure ideal of (R, f^{5/6})

o3 = (ideal 1, 0)

o3 : Sequence
i4 : descendIdeal(2, {41}, {f}, ideal 1_R) --this computes the non-F-pure ideal of (R, f^{41/48})

o4 = (ideal (y, x), 1)

o4 : Sequence

The same two examples could also be accomplished via calls of FPureModule, as illustrated below; however, the descendIdeal construction gives the user more direct control.

i5 : first FPureModule(5/6, f, CanonicalIdeal => ideal 1_R, GeneratorList => {1_R})

o5 = ideal 1

o5 : Ideal of R
i6 : first FPureModule(41/48, f, CanonicalIdeal => ideal 1_R, GeneratorList => {1_R})

o6 = ideal (y, x)

o6 : Ideal of R

The option FrobeniusRootStrategy is passed to internal frobeniusRoot calls.

See also

Ways to use descendIdeal :

For the programmer

The object descendIdeal is a method function with options.