Method polynomial_construction for multivalued laurent polynomial is no monomial_factorization

and alias is created for univariate ones.

Author: enriqueartal

src/sage/groups/finitely_presented.py

@@ -1798,7 +1798,7 @@ def characteristic_varieties(self, ring=QQ, matrix_ideal=None, groebner=False):
         S = R.polynomial_ring()
         ideal = [S(elt) for elt in ideal]
         for j in range(1, A.ncols()):
-            L = [p.polynomial_construction()[0] for p in A.minors(j)]
+            L = [p.monomial_factorization()[0] for p in A.minors(j)]
             J = R.ideal(L + ideal)
             res.append(J)
         if not groebner or not R.base_ring().is_field():

src/sage/rings/polynomial/laurent_polynomial.pyx

@@ -1557,6 +1557,8 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
         Return the polynomial and the shift in power used to construct the
         Laurent polynomial `t^n u`.
 
+        ``monomial_factorization`` is an alias for ``polynomial_construction``
+
         OUTPUT:
 
         A tuple ``(u, n)`` where ``u`` is the underlying polynomial and ``n``
@@ -1568,9 +1570,13 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
             sage: f = 1/x + x^2 + 3*x^4
             sage: f.polynomial_construction()
             (3*x^5 + x^3 + 1, -1)
+            sage: f.polynomial_construction() == f.monomial_factorization()
+            True
         """
         return (self.__u, self.__n)
 
+    monomial_factorization = polynomial_construction
+
     def is_constant(self):
         """
         Return whether this Laurent polynomial is constant.

src/sage/rings/polynomial/laurent_polynomial_mpair.pyx

@@ -1520,7 +1520,7 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial):
 
         return R({m[i]: c for m, c in self.dict().iteritems()})
 
-    def polynomial_construction(self):
+    def monomial_factorization(self):
         """
         Factor ``self`` into a polynomial and a monomial.
 
@@ -1533,28 +1533,21 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial):
 
             sage: R.<x, y> = LaurentPolynomialRing(QQ)
             sage: f = y / x + x^2 / y + 3 * x^4 * y^-2
-            sage: f.polynomial_construction()
+            sage: f.monomial_factorization()
             (3*x^5 + x^3*y + y^3, 1/(x*y^2))
             sage: f = y * x + x^2 / y + 3 * x^4 * y^-2
-            sage: f.polynomial_construction()
+            sage: f.monomial_factorization()
              (3*x^3 + y^3 + x*y, x/y^2)
-            sage: x.polynomial_construction()
+            sage: x.monomial_factorization()
             (1, x)
-            sage: (y^-1).polynomial_construction()
+            sage: (y^-1).monomial_factorization()
             (1, 1/y)
         """
         self._normalize()
         ring = self._parent._R
         g = ring.gens()
         mon = ring.prod(g[i] ** j for i, j in enumerate(self._mon))
-        return (self._poly, mon)        # R = self.parent()
-        # n = R.ngens()
-        # S = R.polynomial_ring()
-        # if not self:
-        #     return (self, R(1))
-        # minimo = tuple(min(a[1].degree(v) for a in self) for v in R.gens())
-        # mon = R({minimo: 1})
-        # return (S(mon ** -1 * self), mon)
+        return (self._poly, mon)
 
     def factor(self):
         """