Get groundset from morphism domain

Author: gmou3

src/sage/matroids/constructor.py

@@ -538,17 +538,42 @@ def Matroid(groundset=None, data=None, **kwds):
         input::
 
             sage: M = matroids.catalog.Fano()
-            sage: A = M.representation(order=True, labels=True); A
-            (Generic morphism:
-               From: Free module generated by {'a', 'b', 'c', 'd', 'e', 'f', 'g'} over
-                     Finite Field of size 2
-               To:   Free module generated by {0, 1, 2} over Finite Field of size 2,
-             ['a', 'b', 'c', 'd', 'e', 'f', 'g'])
+            sage: A = M.representation(order=True); A
+            Generic morphism:
+              From: Free module generated by {'a', 'b', 'c', 'd', 'e', 'f', 'g'} over
+                    Finite Field of size 2
+              To:   Free module generated by {0, 1, 2} over Finite Field of size 2
+            sage: A._unicode_art_matrix()
+              a b c d e f g
+            0⎛1 0 0 0 1 1 1⎞
+            1⎜0 1 0 1 0 1 1⎟
+            2⎝0 0 1 1 1 0 1⎠
             sage: N = Matroid(A); N
             Binary matroid of rank 3 on 7 elements, type (3, 0)
             sage: N.groundset()
             frozenset({'a', 'b', 'c', 'd', 'e', 'f', 'g'})
-            sage: M.is_isomorphic(N)
+            sage: M == N
+            True
+
+        The keywords `morphism` and `reduced_morphism` are also available::
+
+            sage: M = matroids.catalog.RelaxedNonFano("abcdefg")
+            sage: A = M.representation(order=True, reduced=True); A
+            Generic morphism:
+              From: Free module generated by {'d', 'e', 'f', 'g'} over
+                    Finite Field in w of size 2^2
+              To:   Free module generated by {'a', 'b', 'c'} over
+                    Finite Field in w of size 2^2
+            sage: A._unicode_art_matrix()
+              d e f g
+            a⎛1 1 0 1⎞
+            b⎜1 0 1 1⎟
+            c⎝0 1 w 1⎠
+            sage: N = Matroid(reduced_morphism=A); N
+            Quaternary matroid of rank 3 on 7 elements
+            sage: N.groundset()
+            frozenset({'a', 'b', 'c', 'd', 'e', 'f', 'g'})
+            sage: M == N
             True
 
     #.  Rank function:
@@ -731,8 +756,8 @@ def Matroid(groundset=None, data=None, **kwds):
     if data is None:
         for k in ['bases', 'independent_sets', 'circuits',
                   'nonspanning_circuits', 'flats', 'graph', 'matrix',
-                  'reduced_matrix', 'morphism', 'rank_function', 'revlex',
-                  'circuit_closures', 'matroid']:
+                  'reduced_matrix', 'morphism', 'reduced_morphism',
+                  'rank_function', 'revlex', 'circuit_closures', 'matroid']:
             if k in kwds:
                 data = kwds.pop(k)
                 key = k
@@ -752,7 +777,9 @@ def Matroid(groundset=None, data=None, **kwds):
             key = 'graph'
         elif is_Matrix(data):
             key = 'matrix'
-        elif isinstance(data, sage.modules.with_basis.morphism.ModuleMorphism) or isinstance(data, tuple):
+        elif isinstance(data, sage.modules.with_basis.morphism.ModuleMorphism) or (
+             isinstance(data, tuple) and
+             isinstance(data[0], sage.modules.with_basis.morphism.ModuleMorphism)):
             key = 'morphism'
         elif isinstance(data, sage.matroids.matroid.Matroid):
             key = 'matroid'
@@ -876,15 +903,17 @@ def Matroid(groundset=None, data=None, **kwds):
             M = GraphicMatroid(G, groundset=groundset)
 
     # Matrices:
-    elif key in ['matrix', 'reduced_matrix', 'morphism']:
+    elif key in ['matrix', 'reduced_matrix', 'morphism', 'reduced_morphism']:
         A = data
-        is_reduced = (key == 'reduced_matrix')
-        if key == 'morphism':
+        is_reduced = (key == 'reduced_matrix' or key == 'reduced_morphism')
+        if key == 'morphism' or key == 'reduced_morphism':
             if isinstance(data, tuple):
                 A = data[0]
-                groundset = data[1]
-            if isinstance(A, sage.modules.with_basis.morphism.ModuleMorphism):
-                A = A.matrix()
+            if groundset is None:
+                groundset = list(A.domain().basis().keys())
+                if is_reduced:
+                    groundset = list(A.codomain().basis().keys()) + groundset
+            A = A.matrix()
 
         # Fix the representation
         if not is_Matrix(A):