Deprecate the backslash operator.

src/doc/de/tutorial/tour_linalg.rst

@@ -42,16 +42,6 @@ gelöst werden. Das Auswerten von ``A.solve_right(Y)`` gibt eine Matrix
     sage: A * X   # wir überprüfen unsere Antwort...
     (0, -4, -1)
 
-Anstelle von ``solve_right`` kann auch ein Backslash ``\`` verwendet
-werden. Benutzen Sie ``A \ Y`` anstelle von ``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
 Falls keine Lösung existiert, gibt Sage einen Fehler zurück:
 
 .. skip

src/doc/en/tutorial/tour_linalg.rst

@@ -42,16 +42,6 @@ Evaluating ``A.solve_right(Y)`` returns a matrix (or vector)
     sage: A * X   # checking our answer...
     (0, -4, -1)
 
-A backslash ``\`` can be used in the place of ``solve_right``; use
-``A \ Y`` instead of ``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
 If there is no solution, Sage returns an error:
 
 .. skip

src/doc/es/tutorial/tour_linalg.rst

@@ -49,16 +49,6 @@ Resolver ecuaciones matriciales es sencillo, usando el método
     sage: A * X   # comprobando la solución...
     (0, -4, -1)
 
-Se puede usar una barra invertida ``\``  en lugar de ``solve_right``; 
-usamos ``A \ Y`` en lugar de ``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
 Si no hay solución, Sage lanza un error:
 
 .. skip

src/doc/fr/tutorial/tour_linalg.rst

@@ -42,17 +42,6 @@ une matrice (ou un vecteur)  :math:`X` tel que :math:`AX=Y`:
     sage: A * X   # vérifions la réponse...
     (0, -4, -1)
 
-Un antislash (contre-oblique) ``\`` peut être employé à la place de
-``solve_right`` : il suffit d'écrire ``A \ Y`` au lieu de
-``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
 S'il n'y a aucune solution, Sage renvoie une erreur :
 
 .. skip

src/doc/ja/tutorial/tour_linalg.rst

@@ -45,18 +45,6 @@ Sageでは，行列 :math:`A` の核空間は「左」核空間，すなわち :
     (0, -4, -1)
 
 
-``solve_right`` の代わりにバックスラッシュ ``\`` を使うこともできる．
-つまり ``A.solve_right(Y)``  ではなく ``A \ Y`` と書くわけである．
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
-
-
 解がない場合は，Sageはエラーを返してくる:
 
 .. skip

src/doc/pt/tutorial/tour_linalg.rst

@@ -40,16 +40,6 @@ Calculando ``A.solve_right(Y)`` obtém-se uma matrix (ou vetor)
     sage: A * X   # checking our answer...
     (0, -4, -1)
 
-Uma barra invertida ``\`` pode ser usada no lugar de ``solve_right``;
-use ``A \ Y`` no lugar de ``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
-
 Se não existir solução, o Sage retorna um erro:
 
 .. skip

src/doc/ru/tutorial/tour_linalg.rst

@@ -37,15 +37,6 @@ Sage поддерживает стандартные конструкции из
     sage: A * X   # проверка...
     (0, -4, -1)
 
-``\`` может быть использован вместо ``solve_right``; используйте
-``A \ Y`` вместо ``A.solve_right(Y)``.
-
-.. link
-
-::
-
-    sage: A \ Y
-    (-2, 1, 0)
 
 Если решения не существует, то Sage вернет ошибку:
 

src/sage/combinat/binary_tree.py

@@ -39,6 +39,7 @@
 from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
 from sage.sets.family import Family
 from sage.misc.cachefunc import cached_method
+from sage.misc.superseded import deprecated_function_alias
 
 
 class BinaryTree(AbstractClonableTree, ClonableArray,
@@ -3214,7 +3215,7 @@ def under(self, bt):
 
             sage: b1 = BinaryTree([[],[]])
             sage: b2 = BinaryTree([None,[]])
-            sage: ascii_art((b1, b2, b1 \ b2))
+            sage: ascii_art((b1, b2, b1.under(b2)))
             (   o  , o  ,     _o_   )
             (  / \    \      /   \  )
             ( o   o    o    o     o )
@@ -3276,7 +3277,7 @@ def under(self, bt):
         else:
             return B([self.under(bt[0]), bt[1]])
 
-    _backslash_ = under
+    _backslash_ = deprecated_function_alias(80000, under)
 
     def under_decomposition(self):
         r"""

src/sage/features/sagemath.py

@@ -232,7 +232,7 @@ class sage__graphs(JoinFeature):
         sage: M = Matroid(Matrix(QQ, [[1, 0, 0, 0, 1, 1, 1],
         ....:                         [0, 1, 0, 1, 0, 1, 1],
         ....:                         [0, 0, 1, 1, 1, 0, 1]]))
-        sage: N = M / [2] \ [3, 4]
+        sage: N = (M / [2]).delete([3, 4])
         sage: sorted(N.groundset())
         [0, 1, 5, 6]
 

src/sage/matrix/matrix2.pyx

@@ -106,7 +106,7 @@ from sage.matrix.matrix_misc import permanental_minor_polynomial
 from sage.misc.misc_c import prod
 
 # used to deprecate only adjoint method
-from sage.misc.superseded import deprecated_function_alias
+from sage.misc.superseded import deprecation, deprecated_function_alias
 
 
 # temporary hack to silence the warnings from #34806
@@ -146,21 +146,28 @@ cdef class Matrix(Matrix1):
         Used to compute `A \backslash B`, i.e., the backslash solver
         operator.
 
+        DEPRECATED
+
         EXAMPLES::
 
             sage: A = matrix(QQ, 3, [1,2,4,2,3,1,0,1,2])
             sage: B = matrix(QQ, 3, 2, [1,7,5, 2,1,3])
             sage: C = A._backslash_(B); C
+            doctest:...: DeprecationWarning: the backslash operator has been deprecated; use A.solve_right(B) instead
+            See https://github.com/sagemath/sage/issues/80000 for details.
             [  -1    1]
             [13/5 -3/5]
             [-4/5  9/5]
             sage: A*C == B
             True
             sage: A._backslash_(B) == A \ B
+            doctest:...: DeprecationWarning: the backslash operator has been deprecated; use A.solve_right(B) instead
+            See https://github.com/sagemath/sage/issues/80000 for details.
             True
             sage: A._backslash_(B) == A.solve_right(B)
             True
         """
+        deprecation(80000, 'the backslash operator has been deprecated; use A.solve_right(B) instead')
         return self.solve_right(B)
 
     def subs(self, *args, **kwds):
@@ -462,7 +469,7 @@ cdef class Matrix(Matrix1):
 
         .. NOTE::
 
-            In Sage one can also write ``A \ B`` for
+            DEPRECATED. In Sage one can also write ``A \ B`` for
             ``A.solve_right(B)``, that is, Sage implements "the
             MATLAB/Octave backslash operator".
 
@@ -506,7 +513,7 @@ cdef class Matrix(Matrix1):
 
             sage: A = matrix(QQ, 3, [1,2,3,-1,2,5,2,3,1])
             sage: b = vector(QQ,[1,2,3])
-            sage: x = A \ b; x
+            sage: x = A.solve_right(b); x
             (-13/12, 23/12, -7/12)
             sage: A * x
             (1, 2, 3)
@@ -525,21 +532,21 @@ cdef class Matrix(Matrix1):
         Another nonsingular example::
 
             sage: A = matrix(QQ,2,3, [1,2,3,2,4,6]); v = vector([-1/2,-1])
-            sage: x = A \ v; x
+            sage: x = A.solve_right(v); x
             (-1/2, 0, 0)
             sage: A*x == v
             True
 
         Same example but over `\ZZ`::
 
             sage: A = matrix(ZZ,2,3, [1,2,3,2,4,6]); v = vector([-1,-2])
-            sage: A \ v
+            sage: A.solve_right(v)
             (-1, 0, 0)
 
         An example in which there is no solution::
 
             sage: A = matrix(QQ,2,3, [1,2,3,2,4,6]); v = vector([1,1])
-            sage: A \ v
+            sage: A.solve_right(v)
             Traceback (most recent call last):
             ...
             ValueError: matrix equation has no solutions
@@ -564,24 +571,24 @@ cdef class Matrix(Matrix1):
             sage: A*X == B
             True
 
-        We illustrate left associativity, etc., of the backslash operator.
+        We illustrate left associativity, etc., of the ``solve_right`` operator.
 
         ::
 
             sage: A = matrix(QQ, 2, [1,2,3,4])
-            sage: A \ A
+            sage: A.solve_right(A)
             [1 0]
             [0 1]
-            sage: A \ A \ A
+            sage: (A.solve_right(A)).solve_right(A)
             [1 2]
             [3 4]
-            sage: A.parent()(1) \ A
+            sage: A.parent()(1).solve_right(A)
             [1 2]
             [3 4]
-            sage: A \ (A \ A)
+            sage: A.solve_right(A.solve_right(A))
             [  -2    1]
             [ 3/2 -1/2]
-            sage: X = A \ (A - 2); X
+            sage: X = A.solve_right(A - 2); X
             [ 5 -2]
             [-3  2]
             sage: A * X
@@ -593,7 +600,7 @@ cdef class Matrix(Matrix1):
             sage: x = polygen(QQ, 'x')
             sage: A = matrix(2, [x,2*x,-5*x^2+1,3])
             sage: v = vector([3,4*x - 2])
-            sage: X = A \ v
+            sage: X = A.solve_right(v)
             sage: X
             ((-4/5*x^2 + 2/5*x + 9/10)/(x^3 + 1/10*x), (19/10*x^2 - 1/5*x - 3/10)/(x^3 + 1/10*x))
             sage: A * X == v
@@ -635,7 +642,7 @@ cdef class Matrix(Matrix1):
             [    2 + O(5^4)     5 + O(5^5)     4 + O(5^4)]
             [    1 + O(5^4)     1 + O(5^4)     2 + O(5^4)]
             sage: v = vector(k, 3, [1,2,3])
-            sage: x = a \ v; x
+            sage: x = a.solve_right(v); x
             (4 + 5 + 5^2 + 3*5^3 + O(5^4), 2 + 5 + 3*5^2 + 5^3 + O(5^4), 1 + 5 + O(5^4))
             sage: a * x == v
             True

src/sage/matrix/matrix_complex_ball_dense.pyx

@@ -569,14 +569,14 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
         r"""
         TESTS::
 
-            sage: matrix(CBF, [[1/2, 1/3], [1, 1]]) \ vector([-1, 1])
+            sage: matrix(CBF, [[1/2, 1/3], [1, 1]]).solve_right(vector([-1, 1]))
             ([-8.00000000000000 +/- ...], [9.00000000000000 +/- ...])
-            sage: matrix(CBF, 2, 2, 0) \ vector([-1, 1])
+            sage: matrix(CBF, 2, 2, 0).solve_right(vector([-1, 1]))
             Traceback (most recent call last):
             ...
             ValueError: unable to invert this matrix
             sage: b = CBF(0, RBF(0, rad=.1r))
-            sage: matrix(CBF, [[1, 1], [0, b]]) \ vector([-1, 1])
+            sage: matrix(CBF, [[1, 1], [0, b]]).solve_right(vector([-1, 1]))
             Traceback (most recent call last):
             ...
             ValueError: unable to invert this matrix

src/sage/matrix/matrix_integer_dense.pyx

@@ -4138,7 +4138,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
 
         .. NOTE::
 
-           In Sage one can also write ``A \ B`` for
+           DEPRECATED. In Sage one can also write ``A \ B`` for
            ``A.solve_right(B)``, i.e., Sage implements the "the
            MATLAB/Octave backslash operator".
 
@@ -4162,15 +4162,15 @@ cdef class Matrix_integer_dense(Matrix_dense):
 
             sage: a = matrix(ZZ, 2, [0, -1, 1, 0])
             sage: v = vector(ZZ, [2, 3])
-            sage: a \ v
+            sage: a.solve_right(v)
             (3, -2)
 
         Note that the output vector or matrix is always over
         `\QQ`.
 
         ::
 
-            sage: parent(a\v)
+            sage: parent(a.solve_right(v))
             Vector space of dimension 2 over Rational Field
 
         We solve a bigger system where the answer is over the rationals.
@@ -4179,7 +4179,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
 
             sage: a = matrix(ZZ, 3, 3, [1,2,3,4, 5, 6, 8, -2, 3])
             sage: v = vector(ZZ, [1,2,3])
-            sage: w = a \ v; w
+            sage: w = a.solve_right(v); w
             (2/15, -4/15, 7/15)
             sage: parent(w)
             Vector space of dimension 3 over Rational Field
@@ -4193,7 +4193,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
 
             sage: a = matrix(ZZ, 3, 3, [1,2,3,4, 5, 6, 8, -2, 3])
             sage: b = matrix(ZZ, 3, 2, [1,5, 2, -3, 3, 0])
-            sage: w = a \ b; w
+            sage: w = a.solve_right(b); w
             [ 2/15 -19/5]
             [-4/15 -27/5]
             [ 7/15 98/15]
@@ -4214,7 +4214,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
             sage: n = 100
             sage: a = random_matrix(ZZ,n)
             sage: v = vector(ZZ,n,range(n))
-            sage: x = a \ v
+            sage: x = a.solve_right(v)
             sage: a * x == v
             True
 

src/sage/matrix/matrix_integer_sparse.pyx

@@ -985,7 +985,7 @@ cdef class Matrix_integer_sparse(Matrix_sparse):
 
         .. NOTE::
 
-           In Sage one can also write ``A \ B`` for
+           DEPRECATED. In Sage one can also write ``A \ B`` for
            ``A.solve_right(B)``, i.e., Sage implements the "the
            MATLAB/Octave backslash operator".
 
@@ -1019,14 +1019,14 @@ cdef class Matrix_integer_sparse(Matrix_sparse):
 
             sage: A = matrix(ZZ, 3, [1,2,3,-1,2,5,2,3,1], sparse=True)
             sage: b = vector(ZZ, [1,2,3])
-            sage: x = A \ b
+            sage: x = A.solve_right(b)
             sage: x
             (-13/12, 23/12, -7/12)
             sage: A * x
             (1, 2, 3)
 
             sage: u = matrix(ZZ, 3, 2, [0,1,1,1,0,2])
-            sage: x = A \ u
+            sage: x = A.solve_right(u)
             sage: x
             [-7/12  -1/6]
             [ 5/12   5/6]

src/sage/matrix/matrix_modn_dense_template.pxi

@@ -23,7 +23,7 @@ EXAMPLES::
     sage: A.rank()
     4
     sage: v = vector(GF(127), 4, (100, 93, 47, 110))
-    sage: x = A\v
+    sage: x = A.solve_right(v)
     sage: A*x == v
     True