gh-39044: provide default argument for monomial_coefficients
    
This is a followup to #38767, where we put polynomials into the category
of modules with basis.  Back then, we missed the fact that
`monomial_coefficients` should take an optional argument `copy`, which
we fix here.

Fixes #39037
    
URL: #39044
Reported by: Martin Rubey
Reviewer(s): Marc Mezzarobba

Author: Release Manager

src/sage/algebras/commutative_dga.py

@@ -1559,7 +1559,7 @@ def homogeneous_parts(self):
                     res[deg] = term
             return {i: res[i] for i in sorted(res.keys())}
 
-        def monomial_coefficients(self):
+        def monomial_coefficients(self, copy=True):
             r"""
             A dictionary that determines the element.
 
@@ -1578,7 +1578,7 @@ def monomial_coefficients(self):
                 sage: sorted(elt.dict().items())
                 [((0, 1, 1, 0), -5), ((1, 1, 0, 0), 1), ((1, 2, 3, 1), 7)]
             """
-            return self.lift().monomial_coefficients()
+            return self.lift().monomial_coefficients(copy=copy)
 
         dict = monomial_coefficients
 

src/sage/algebras/splitting_algebra.py

@@ -102,7 +102,7 @@ def is_unit(self):
 
         return super().is_unit()
 
-    def monomial_coefficients(self):
+    def monomial_coefficients(self, copy=True):
         r"""
         Return the dictionary of ``self`` according to its lift to the cover.
 
@@ -119,7 +119,7 @@ def monomial_coefficients(self):
             sage: f.dict()
             {0: 42, 1: 1}
         """
-        return self.lift().monomial_coefficients()
+        return self.lift().monomial_coefficients(copy=copy)
 
     dict = monomial_coefficients
 

src/sage/categories/modules_with_basis.py

@@ -1860,6 +1860,18 @@ def leading_item(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.leading_item()                                                  # needs sage.combinat sage.modules
                 ([3], -5)
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_item()
+                ((0, 4, 0), 1)
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_item()
+                ((1, 2, 0), 3)
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_item()
+                ((0, 1, 3), 2)
             """
             k = self.leading_support(*args, **kwds)
             return k, self[k]
@@ -1890,6 +1902,18 @@ def leading_monomial(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.leading_monomial()                                              # needs sage.combinat sage.modules
                 s[3]
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_monomial()
+                y^4
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_monomial()
+                x*y^2
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_monomial()
+                y*z^3
             """
             return self.parent().monomial(self.leading_support(*args, **kwds))
 
@@ -1919,6 +1943,18 @@ def leading_coefficient(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.leading_coefficient()                                           # needs sage.combinat sage.modules
                 -5
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_coefficient()
+                1
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_coefficient()
+                3
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_coefficient()
+                2
             """
             return self.leading_item(*args, **kwds)[1]
 
@@ -1948,6 +1984,18 @@ def leading_term(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.leading_term()                                                  # needs sage.combinat sage.modules
                 -5*s[3]
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_term()
+                y^4
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_term()
+                3*x*y^2
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).leading_term()
+                2*y*z^3
             """
             return self.parent().term(*self.leading_item(*args, **kwds))
 
@@ -2005,6 +2053,18 @@ def trailing_item(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.trailing_item()                                                 # needs sage.combinat sage.modules
                 ([1], 2)
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_item()
+                ((1, 1, 1), 4)
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_item()
+                ((0, 1, 3), 2)
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_item()
+                ((1, 2, 0), 3)
             """
             k = self.trailing_support(*args, **kwds)
             return k, self[k]
@@ -2035,6 +2095,18 @@ def trailing_monomial(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.trailing_monomial()                                             # needs sage.combinat sage.modules
                 s[1]
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_monomial()
+                x*y*z
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_monomial()
+                y*z^3
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_monomial()
+                x*y^2
             """
             return self.parent().monomial(self.trailing_support(*args, **kwds))
 
@@ -2064,6 +2136,18 @@ def trailing_coefficient(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.trailing_coefficient()                                          # needs sage.combinat sage.modules
                 2
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_coefficient()
+                4
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_coefficient()
+                2
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_coefficient()
+                3
             """
             return self.trailing_item(*args, **kwds)[1]
 
@@ -2093,6 +2177,18 @@ def trailing_term(self, *args, **kwds):
                 sage: f = 2*s[1] + 3*s[2,1] - 5*s[3]                                    # needs sage.combinat sage.modules
                 sage: f.trailing_term()                                                 # needs sage.combinat sage.modules
                 2*s[1]
+
+            The term ordering of polynomial rings is taken into account::
+
+                sage: R.<x,y,z> = QQ[]
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_term()
+                4*x*y*z
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='lex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_term()
+                2*y*z^3
+                sage: R.<x,y,z> = PolynomialRing(QQ, order='invlex')
+                sage: (3*x*y^2 + 2*y*z^3 + y^4 + 4*x*y*z).trailing_term()
+                3*x*y^2
             """
             return self.parent().term(*self.trailing_item(*args, **kwds))
 

src/sage/rings/derivation.py

@@ -996,7 +996,7 @@ def list(self):
         parent = self.parent()
         return [self(x) for x in parent.dual_basis()]
 
-    def monomial_coefficients(self):
+    def monomial_coefficients(self, copy=None):
         r"""
         Return dictionary of nonzero coordinates (on the canonical
         basis) of this derivation.

src/sage/rings/multi_power_series_ring_element.py

@@ -1099,7 +1099,7 @@ def __mod__(self, other):
             return self.change_ring(Zmod(other))
         raise NotImplementedError("Mod on multivariate power series ring elements not defined except modulo an integer.")
 
-    def monomial_coefficients(self):
+    def monomial_coefficients(self, copy=None):
         """
         Return underlying dictionary with keys the exponents and values the
         coefficients of this power series.