monideal-minprimes.hpp File Reference

MinimalPrimes — minimal primes of a MonomialIdeal via a two-phase state machine. More...

#include "monideal.hpp"

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Classes
class	MinimalPrimes

Detailed Description

MinimalPrimes — minimal primes of a MonomialIdeal via a two-phase state machine.

Note

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Declares MinimalPrimes, the cousin of AssociatedPrimes specialised to the minimal-codimension primes only. The constructor radicalises the input (minimal primes of I agree with minimal primes of rad(I), and working with the radical eliminates higher-power monomials cheaply), sets min_codim to an impossibly large nvars + 1, and leaves an empty accumulator primes. The state field runs the same two-stage shape as AssociatedPrimes: do_codim finds the minimum codimension cheaply, do_primes enumerates the minimal-codimension primes; callers who only need codimension() can stop after the first phase. Generators are stored as squarefree monomials in the accumulator primes, with the Q worklist of Bag*s carrying in-progress candidates between recursive steps; the combinatorial recursion is the standard monomial split-on-x_i that drives monomial primary decomposition.

The public surface offers two enumeration algorithms — min_primes(maxcodim, count) (the Nmi_node-tree walk via ass_prime_generator) and alg1_min_primes(maxcodim, count) (the alg1_grab_prime / alg1_min_prime_generator exponent- vector recursion) — plus associated_primes(count), max_indep_sets(count), and static convenience overloads MinimalPrimes::codimension / ::min_primes / ::max_indep_sets that build a transient instance and call the matching member.

See also

monideal.hpp

assprime.hpp

Definition in file monideal-minprimes.hpp.