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.
The object descendIdeal is a method function with options.