Source code for sage_acsv.backends.macaulay2

"""Interface to macaulay2."""

from sage.categories.homset import Hom
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.rational_field import QQ

from sage_acsv.settings import ACSVSettings


def _construct_m2_morphisms(ideal):
    R = ideal.gens()[0].parent()
    n = len(R.gens())
    RM2 = PolynomialRing(QQ, n, [f"x{i}" for i in range(n)])
    vs = list(RM2.gens())
    mor = Hom(R, RM2)(vs)
    inv = mor.inverse()
    return mor, inv




def compute_primary_decomposition(ideal):
    """Return the primary decomposition of an ideal, computed via
    Macaulay2.

    INPUT:

    * ``ideal`` - A polynomial ideal

    EXAMPLES::

        sage: # optional -- macaulay2
        sage: from sage_acsv.backends.macaulay2 import *
        sage: R = PolynomialRing(QQ, 'x,y')
        sage: x,y = R.gens()
        sage: id = R.ideal([y*x*(x-y)])
        sage: list(compute_primary_decomposition(id))
        [Ideal (y) of Multivariate Polynomial Ring in x, y over Rational Field,
         Ideal (x) of Multivariate Polynomial Ring in x, y over Rational Field,
         Ideal (x - y) of Multivariate Polynomial Ring in x, y over Rational Field]
    """
    mor, inv = _construct_m2_morphisms(ideal)
    ideal = ideal.apply_morphism(mor)
    m2 = ACSVSettings.get_macaulay2()
    return iter(J.sage().apply_morphism(inv) for J in m2.decompose(ideal))





def compute_groebner_basis(ideal):
    """Return a Groebner basis of an ideal, computed via Macaulay2.

    INPUT:

    * ``ideal`` - A polynomial ideal

    EXAMPLES::

        sage: # optional -- macaulay2
        sage: from sage_acsv.backends.macaulay2 import *
        sage: R = PolynomialRing(QQ, 'x,y')
        sage: x,y = R.gens()
        sage: id = R.ideal([y*y-x,x-4])
        sage: compute_groebner_basis(id)
        [x - 4, y^2 - 4]
    """
    mor, inv = _construct_m2_morphisms(ideal)
    ideal = ideal.apply_morphism(mor)
    m2 = ACSVSettings.get_macaulay2()
    # This is really roundabout but for some reason returning the generators
    # from M2 to sage puts them in the wrong ring
    return m2.ideal(m2.gb(ideal).generators()).sage().apply_morphism(inv).gens()





def compute_radical(ideal):
    """Return the radical of an ideal, computed via Macaulay2.

    INPUT:

    * ``ideal`` - A polynomial ideal

    EXAMPLES::

        sage: # optional -- macaulay2
        sage: from sage_acsv.backends.macaulay2 import *
        sage: R = PolynomialRing(QQ, 'x,y')
        sage: x,y = R.gens()
        sage: id = R.ideal([y*y,(x-5)**2])
        sage: compute_radical(id)
        Ideal (y, x - 5) of Multivariate Polynomial Ring in x, y over Rational Field
    """
    mor, inv = _construct_m2_morphisms(ideal)
    ideal = ideal.apply_morphism(mor)
    m2 = ACSVSettings.get_macaulay2()
    return m2.radical(ideal).sage().apply_morphism(inv)