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sagemath · Jan 9, 2025 · 7a23525 · 7a23525
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diff --git a/src/sage/categories/kahler_algebras.py b/src/sage/categories/kahler_algebras.py
@@ -5,6 +5,15 @@
 
 - Shriya M
 """
+# ****************************************************************************
+#       Copyright (C) 2024 Shriya M <25shriya at gmail.com>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.categories.category_types import Category_over_base_ring
 from sage.categories.graded_algebras_with_basis import GradedAlgebrasWithBasis
@@ -15,15 +24,6 @@
 from sage.misc.cachefunc import cached_method
 
 
-# ****************************************************************************
-#       Copyright (C) 2024 Shriya M <25shriya at gmail.com>
-#
-# This program is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 2 of the License, or
-# (at your option) any later version.
-#                  https://www.gnu.org/licenses/
-# ****************************************************************************
 class KahlerAlgebras(Category_over_base_ring):
     r"""
     The category of graded algebras satisfying the Kähler package.
@@ -134,7 +134,7 @@ def lefschetz_element(self):
 
         def hodge_riemann_relations(self, k):
             r"""
-            Return the quadratic form for the corresponding ``k`` 
+            Return the quadratic form for the corresponding ``k``
             (`< \frac{r}{2}`) for the Kähler algebra, where `r` is the top degree.
 
             EXAMPLES::

diff --git a/src/sage/matroids/chow_ring.py b/src/sage/matroids/chow_ring.py
@@ -5,6 +5,15 @@
 
 - Shriya M
 """
+# ****************************************************************************
+#       Copyright (C) 2024 Shriya M <25shriya at gmail.com>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.matroids.chow_ring_ideal import ChowRingIdeal_nonaug, AugmentedChowRingIdeal_fy, AugmentedChowRingIdeal_atom_free
 from sage.rings.quotient_ring import QuotientRing_generic
@@ -284,31 +293,6 @@ def lefschetz_element(self):
                 6*A01234^3, 6*A01234^3, 2*A01234^3, 2*A01234^3, 6*A01234^3,
                 2*A01234^3, 6*A01234^3, 6*A01234^3, 2*A01234^3, 6*A01234^3,
                 6*A01234^3, 6*A01234^3, -20*A01234^3], 3: [0]}
-
-        TESTS::
-
-            sage: U46 = matroids.Uniform(4, 6)
-            sage: C = U46.chow_ring(QQ, False)
-            sage: w = C.lefschetz_element(); w
-            -2*A01 - 2*A02 - 2*A03 - 2*A04 - 2*A05 - 2*A12 - 2*A13 - 2*A14
-            - 2*A15 - 2*A23 - 2*A24 - 2*A25 - 2*A34 - 2*A35 - 2*A45 - 6*A012
-            - 6*A013 - 6*A014 - 6*A015 - 6*A023 - 6*A024 - 6*A025 - 6*A034
-            - 6*A035 - 6*A045 - 6*A123 - 6*A124 - 6*A125 - 6*A134 - 6*A135
-            - 6*A145 - 6*A234 - 6*A235 - 6*A245 - 6*A345 - 30*A012345
-            sage: basis_deg = {}
-            sage: for b in C.basis():
-            ....:     deg = b.homogeneous_degree()
-            ....:     if deg not in basis_deg:
-            ....:         basis_deg[deg] = []
-            ....:     basis_deg[deg].append(b)
-            sage: m = max(basis_deg); m
-            3
-            sage: len(basis_deg[1]) == len(basis_deg[2])
-            True
-            sage: matrix([(w*b).to_vector() for b in basis_deg[1]]).rank()
-            36
-            sage: len(basis_deg[2])
-            36
         """
         w = sum(len(F) * (len(self.matroid().groundset()) - len(F)) * gen
                 for F, gen in self.defining_ideal().flats_to_generator_dict().items())

diff --git a/src/sage/matroids/chow_ring_ideal.py b/src/sage/matroids/chow_ring_ideal.py
@@ -5,6 +5,15 @@
 
 - Shriya M
 """
+# ****************************************************************************
+#       Copyright (C) 2024 Shriya M <25shriya at gmail.com>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
 from sage.matroids.utilities import cmp_elements_key