SeriesParallelReductionNode.core, SpecialLeafNode.rep_matrix: New; Ma…

…trix_cmr_chr_sparse.three_sum: Add doc (#13)

src/sage/matrix/matrix_cmr_sparse.pyx

@@ -465,10 +465,31 @@ cdef class Matrix_cmr_chr_sparse(Matrix_cmr_sparse):
 
     def three_sum(first_mat, second_mat, first_col_index1, first_col_index2, second_col_index1, second_col_index2):
         r"""
-        Return the 3-sum matrix constructed from the given matrices ``first_mat`` and ``second_mat``, with 'first_col_index1'
-        and 'first_col_index2' being the indices of the column vectors of the matrix, which are identical except for one row
-        having a 0 in one column and the other a non-zero entry in that row. The method assumes the nonzero entry is one. The same assumptions
-        are made for 'second_mat' and its input index variables.
+        Return the 3-sum matrix constructed from the given matrices ``first_mat`` and ``second_mat``, with ``first_col_index1``
+        and ``first_col_index2`` being the indices of the column vectors of the matrix, which are identical except for one row
+        having a 0 in one column and the other a non-zero entry in that row. The method assumes the nonzero entry is one. The same goes
+        are made for ``second_mat``, ``second_col_index1``, and  ``second_col_index2``.
+
+        The operation performed is effectively as in Schrijver:=
+        [first_submat  first_subcol  first_subcol]  ___|___   [second_submat  second_subcol  second_suncol]
+        [ first_row         0             1      ]     |   3  [ second_row          0              1      ]
+        -----  [         first_submat       first_subcol x second_row]
+        -----  [second_subcol x first_row          second_subcol     ]
+
+        INPUT:
+
+        - ``first_mat`` -- integer matrix having two collumns which are identical in every entry except for one row in 
+        which one is 0 and the other is 1
+        - ``second_mat`` -- integer matrix having two collumns which are identical in every entry except for one row in 
+        which one is 0 and the other is 1
+        - ``first_col_index1`` -- index of a column in ``first_mat`` identical to some other column in every entry except for one row in 
+        which one is 0 and the other is 1
+        - ``first_col_index2`` -- index of the other column which is identical to first_mat[first_col_index1] in every entry except for one 
+        row in which one is 0 and the other is 1
+        - ``second_col_index1`` -- index of a column in ``second_mat`` identical to some other column in every entry except for one row in 
+        which one is 0 and the other is 1
+        - ``first_col_index2`` -- index of the other column which is identical to second_mat[second_col_index1] in every entry except for one 
+        row in which one is 0 and the other is 1
 
         EXAMPLES::
 

src/sage/matrix/seymour_decomposition.pyx

@@ -440,7 +440,31 @@ cdef class PlanarNode(BaseGraphicNode):
 
 cdef class SeriesParallelReductionNode(DecompositionNode):
 
-    pass
+    def core(self):
+        r"""
+        EXAMPLES::
+
+            sage: from sage.matrix.matrix_cmr_sparse import Matrix_cmr_chr_sparse
+            sage: M = Matrix_cmr_chr_sparse(MatrixSpace(ZZ, 5, 6, sparse=True),
+            ....:                                   [[1, 1, 1, 1, 1, 0], [1, 1, 1, 0,0, 0],
+            ....:                                 [1, 0, 1, 1, 0, 1] ,[1, 0,0, 1, 1, 0], 
+            ....:                                   [1, 1, 0, 0, 1, 0]]); M
+            [1 1 1 1 1 0]
+            [1 1 1 0 0 0]
+            [1 0 1 1 0 1]
+            [1 0 0 1 1 0]
+            [1 1 0 0 1 0]
+            sage: result, certificate = M.is_totally_unimodular(certificate = True); result
+            ....: , certificate
+            (True, SeriesParallelReductionNode (5×6))
+            sage: certificate.core()
+            [1 1 1 1 1]
+            [1 1 1 0 0]
+            [1 0 1 1 0]
+            [1 0 0 1 1]
+            [1 1 0 0 1]
+        """
+        return self._children()[0].matrix()
 
 
 cdef class SpecialLeafNode(DecompositionNode):
@@ -475,8 +499,17 @@ cdef class SpecialLeafNode(DecompositionNode):
         assert False, 'special leaf node with unknown type'
 
     def _repr_(self):
-        return f'Minor isomorphic to {self._matroid()}'
+        return f'Isomorphic to a minor of {self._matroid()}'
+
+    def rep_matrix(self):
+        r"""
+        WIP
+        """
+        assert NotImplementedError
 
+        cdef int representation_matrix
+        cdef CMR_DEC_TYPE typ = CMRdecIsSpecialLeaf(self._dec, &representation_matrix)
+        return Matrix_cmr_chr_sparse._from_data(representation_matrix, immutable=False)
 
 cdef _class(CMR_DEC *dec):
     k = CMRdecIsSum(dec, NULL, NULL)