hilb.hpp File Reference

Hilbert-series numerator via the Bigatti-Caboara-Robbiano recursion. More...

#include "hash.hpp"
#include "monoid.hpp"
#include "newdelete.hpp"
#include "ringelem.hpp"

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Classes
class	partition_table
struct	hilb_step
class	hilb_comp
	Computation of Hilbert functions. More...

Detailed Description

Hilbert-series numerator via the Bigatti-Caboara-Robbiano recursion.

Note

AI-generated documentation. Verify against the source before relying on it.

Declares hilb_comp, which computes the numerator of the Hilbert series for coker leadterms(M) (resp. coker I when the input is a MonomialIdeal) over the standard denominator prod (1 - t^{deg x_i}). The recursion picks a pivot monomial m and uses the short exact sequence 0 -> R/(I:m) -.m-> R/I -> R/(I + (m)) -> 0, giving H_{R/I} = t^{deg m} H_{R/(I:m)} + H_{R/(I + (m))}. The partition_table declared at the top runs the union-find that groups variables into connected components so the recursion splits on independent subproblems whenever possible.

The matrix entry point takes lead terms only — callers wanting the Hilbert series of an arbitrary ideal pass in a Groebner basis. Reading the Hilbert function or extracting the Hilbert polynomial from the numerator lives in top-level M2 code; this header exposes only the static hilbertNumerator family — three overloads (const Matrix*, const FreeModule*, const MonomialIdeal*) — and the per-instance value() / calc(nsteps) / is_done() / reset() / next_monideal() driver, plus coeff_of for sampling a single coefficient and stats() for printing the recursion counters (nsteps, depth, maxdepth, nideal, nrecurse).

See also

monideal.hpp

Definition in file hilb.hpp.