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// Copyright 1996 Michael E. Stillman #ifndef _hilb_hh_ #define _hilb_hh_ // Computation of Hilbert functions via Bigatti's (et al) algorithm. #include "monideal.hpp" #include "matrix.hpp" #include "polyring.hpp" class RingElement; class Matrix; class MonomialIdeal; class partition_table // Partition a monomial ideal into several such that // the graph of variables occuring in each is connected. // Implemented using a union-find algorithm. { int n_vars; int n_sets; intarray adad; intarray aoccurs; int *dad; int *occurs; int merge_in(int x, int y); void merge_in(const int *m); int representative(int x); stash *mi_stash; // for all of the nodes in all of the monomial ideals public: partition_table(int nvars, stash *mi_stash0); ~partition_table() {} void reset(int nvars); void partition(MonomialIdeal *&I, VECTOR(MonomialIdeal *)& result); // Consumes I. }; struct hilb_step : public our_new_delete { hilb_step *up; hilb_step *down; int i; // Which monomial ideal is next ring_elem h0; // Hilbert function so far computed 'to the left' ring_elem h1; int first_sum; // First monomial ideal which corresponds to the 'sum' part VECTOR(MonomialIdeal *) monids; // The (partitoned) array of monomial ideals }; /** @ingroup hilb @brief Computation of Hilbert functions */ class hilb_comp : public MutableEngineObject { const PolynomialRing *S; // This is the base ring of the monomial ideal const PolynomialRing *R; // This is the output degree ring. const Monoid *M; // S->getMonoid() const Monoid *D; // R->getMonoid() == S->degree_monoid() stash *mi_stash; // for all of the nodes in all of the monomial ideals // Collected values from the matrix const Matrix *input_mat; // The input matrix ring_elem result_poincare; // The result poincare polynomial from components // 0..this_comp-1 int this_comp; int n_components; // If input_mat is not NULL, // this is the number of rows // The recursion stack is the following: hilb_step *current; // Statistics int nsteps; int depth; int maxdepth; int nideal; int nrecurse; // Some useful precomputed values ring_elem one; ring_elem minus_one; // Local variables that are allocated once and for all // extreme care is needed for their use! int *LOCAL_deg1; // An element of the degree monoid intarray LOCAL_vp; partition_table part_table; int step(); // Returns 0 when done void recurse(MonomialIdeal *&I, const int *pivot_vp); void do_ideal(MonomialIdeal *I); public: hilb_comp(const PolynomialRing *R, const Matrix *M); hilb_comp(const PolynomialRing *R, const MonomialIdeal *I); ~hilb_comp(); void reset(); void next_monideal(); int calc(int nsteps); int is_done() const; RingElement *value(); void stats() const; // static routines // If the coefficient in degree 'deg' is < 0, then // set an error, and return 0. The caller MUST check this. static int coeff_of(const RingElement *h, int deg); #if 0 // static int hilbertSeries(const Matrix *M, RingElement * &result); // // A return of 0 means that the result can be used. A non-zero return // // value means that the computation was interrupted, and so control should // // return to the user. #endif static RingElement /* or null */ *hilbertNumerator(const Matrix *M); /* This routine computes the numerator of the Hilbert series for coker leadterms(M), using the degrees of the rows of M. NULL is returned if the ring is