Improve Matrix_mod2_dense solve_right performance

src/sage/libs/m4ri.pxd

@@ -179,6 +179,9 @@ cdef extern from "m4ri/m4ri.h":
     # reduced row echelon form using PLUQ factorization
     cdef mzd_t *mzd_kernel_left_pluq(mzd_t *A, int cutoff)
 
+    # system solving
+    cdef int mzd_solve_left(mzd_t *A, mzd_t *B, int cutoff, int inconsistency_check)
+
     ########################
     # Bit operations
     ########################

src/sage/matrix/matrix_mod2_dense.pyx

@@ -1919,6 +1919,81 @@ cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
         self.cache('rank', r)
         return r
 
+    def _solve_right_general(self, B, check=True):
+        """
+        Solve the matrix equation AX = B for X using the M4RI library.
+
+        INPUT:
+
+        - ``B`` -- a matrix
+        - ``check`` -- boolean (default: ``True``); whether to check if the
+          matrix equation has a solution
+
+        EXAMPLES::
+
+            sage: A = matrix(GF(2), [[1, 0], [0, 1], [1, 1]])
+            sage: A.solve_right(vector([1, 1, 0]))
+            (1, 1)
+            sage: A.solve_right(vector([1, 1, 1]))
+            Traceback (most recent call last):
+            ...
+            ValueError: matrix equation has no solutions
+
+        TESTS::
+
+            sage: n = 128
+            sage: m = 128
+            sage: A = random_matrix(GF(2), n, m)
+            sage: B = A * random_vector(GF(2), m)
+            sage: A * A.solve_right(B) == B
+            True
+            sage: m = 64
+            sage: A = random_matrix(GF(2), n, m)
+            sage: B = A * random_vector(GF(2), m)
+            sage: A * A.solve_right(B) == B
+            True
+            sage: m = 256
+            sage: A = random_matrix(GF(2), n, m)
+            sage: B = A * random_vector(GF(2), m)
+            sage: A * A.solve_right(B) == B
+            True
+        """
+        cdef mzd_t *B_entries = (<Matrix_mod2_dense>B)._entries
+
+        cdef Matrix_mod2_dense X  # the solution
+        X = self.new_matrix(nrows=self._entries.ncols, ncols=B_entries.ncols)
+        if self._entries.ncols == 0 or B_entries.ncols == 0:
+            # special case: empty matrix
+            if B != 0:
+                raise ValueError("matrix equation has no solutions")
+            return X
+        cdef rci_t rows = self._entries.nrows
+        if self._entries.nrows < self._entries.ncols:
+            rows = self._entries.ncols  # mzd_solve_left requires ncols <= nrows
+
+        cdef mzd_t *lhs = mzd_init(rows, self._entries.ncols)
+        mzd_copy(lhs, self._entries)
+        cdef mzd_t *rhs = mzd_init(rows, B_entries.ncols)
+        mzd_copy(rhs, B_entries)
+
+        cdef int ret
+        try:
+            sig_on()
+            # although it is called mzd_solve_left, it does the same thing as solve_right
+            ret = mzd_solve_left(lhs, rhs, 0, check)
+            sig_off()
+
+            if ret == 0:
+                # solution is placed in rhs
+                rhs.nrows = self._entries.ncols
+                mzd_copy(X._entries, rhs)
+                return X
+            else:
+                raise ValueError("matrix equation has no solutions")
+        finally:
+            mzd_free(lhs)
+            mzd_free(rhs)
+
     def _right_kernel_matrix(self, **kwds):
         r"""
         Return a pair that includes a matrix of basis vectors