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fix the method monomials_of_degree #35043

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merged 3 commits into from
Mar 13, 2023
Merged

fix the method monomials_of_degree #35043

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ff2d38d
fix the method monomials_of_degree
DavidAyotte Feb 7, 2023
a37eb29
fix and add doctests
DavidAyotte Feb 7, 2023
f119d2c
fix the ordering and add doctests
DavidAyotte Feb 7, 2023
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20 changes: 16 additions & 4 deletions src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -444,7 +444,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
1/2*x^3 + x*y + z^2 - 1/2*x + y + 25

.. SEEALSO::

:meth:`lagrange_polynomial<sage.rings.polynomial.polynomial_ring.PolynomialRing_field.lagrange_polynomial>`
"""
# get ring and number of variables
Expand Down Expand Up @@ -1379,16 +1379,28 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
sage: R.<x,y,z> = ZZ[]
sage: mons = R.monomials_of_degree(2)
sage: mons
[x^2, x*y, x*z, y^2, y*z, z^2]
[z^2, y*z, x*z, y^2, x*y, x^2]
sage: P = PolynomialRing(QQ, 3, 'x, y, z', order=TermOrder('wdeglex', [1, 2, 1]))
sage: P.monomials_of_degree(2)
[z^2, y, x*z, x^2]
sage: P = PolynomialRing(QQ, 3, 'x, y, z', order='lex')
sage: P.monomials_of_degree(3)
[z^3, y*z^2, y^2*z, y^3, x*z^2, x*y*z, x*y^2, x^2*z, x^2*y, x^3]
sage: P = PolynomialRing(QQ, 3, 'x, y, z', order='invlex')
sage: P.monomials_of_degree(3)
[x^3, x^2*y, x*y^2, y^3, x^2*z, x*y*z, y^2*z, x*z^2, y*z^2, z^3]

The number of such monomials equals `\binom{n+k-1}{k}`
where `n` is the number of variables and `k` the degree::

sage: len(mons) == binomial(3+2-1,2)
True
"""
from sage.combinat.integer_vector import IntegerVectors
return [self.monomial(*a) for a in IntegerVectors(degree, self.ngens())]
deg_of_gens = [x.degree() for x in self.gens()]
from sage.combinat.integer_vector_weighted import WeightedIntegerVectors
mons = [self.monomial(*a) for a in WeightedIntegerVectors(degree, deg_of_gens)]
mons.sort() # This could be implemented in WeightedIntegerVectors instead
return mons

def _macaulay_resultant_getS(self, mon_deg_tuple, dlist):
r"""
Expand Down