diff --git a/src/doc/de/tutorial/tour_linalg.rst b/src/doc/de/tutorial/tour_linalg.rst
index 2a5467e8884..1be6540c89e 100644
--- a/src/doc/de/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/en/tutorial/tour_linalg.rst b/src/doc/en/tutorial/tour_linalg.rst
index 054e338cea7..84a45f4931b 100644
--- a/src/doc/en/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/es/tutorial/tour_linalg.rst b/src/doc/es/tutorial/tour_linalg.rst
index eb2caa35440..a9b543cca0e 100644
--- a/src/doc/es/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/fr/tutorial/tour_linalg.rst b/src/doc/fr/tutorial/tour_linalg.rst
index 1343fa126fa..582a915edef 100644
--- a/src/doc/fr/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/ja/tutorial/tour_linalg.rst b/src/doc/ja/tutorial/tour_linalg.rst
index cf24ab37ed1..7af81486a30 100644
--- a/src/doc/ja/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/pt/tutorial/tour_linalg.rst b/src/doc/pt/tutorial/tour_linalg.rst
index 9cdf7671dd7..806a36c6446 100644
--- a/src/doc/pt/tutorial/tour_linalg.rst
+++ b/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
diff --git a/src/doc/ru/tutorial/tour_linalg.rst b/src/doc/ru/tutorial/tour_linalg.rst
index 2e1e6620549..6b4c64764c8 100644
--- a/src/doc/ru/tutorial/tour_linalg.rst
+++ b/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:
 
diff --git a/src/sage/combinat/binary_tree.py b/src/sage/combinat/binary_tree.py
index 8e876ab137a..e150a1fe9cc 100644
--- a/src/sage/combinat/binary_tree.py
+++ b/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"""
diff --git a/src/sage/features/sagemath.py b/src/sage/features/sagemath.py
index ac3922552e4..7404e6d0a8e 100644
--- a/src/sage/features/sagemath.py
+++ b/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]
 
diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
index 86aca6e00d8..a3e98fd2b66 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/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)
@@ -525,7 +532,7 @@ 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
@@ -533,13 +540,13 @@ cdef class Matrix(Matrix1):
         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
diff --git a/src/sage/matrix/matrix_complex_ball_dense.pyx b/src/sage/matrix/matrix_complex_ball_dense.pyx
index 47ca41070fa..3f56772a663 100644
--- a/src/sage/matrix/matrix_complex_ball_dense.pyx
+++ b/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
diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx
index 8c276f2ca29..b093e576f74 100644
--- a/src/sage/matrix/matrix_integer_dense.pyx
+++ b/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".
 
@@ -4162,7 +4162,7 @@ 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
@@ -4170,7 +4170,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
 
         ::
 
-            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
 
diff --git a/src/sage/matrix/matrix_integer_sparse.pyx b/src/sage/matrix/matrix_integer_sparse.pyx
index f6d79abf56a..f4320fcd914 100644
--- a/src/sage/matrix/matrix_integer_sparse.pyx
+++ b/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]
diff --git a/src/sage/matrix/matrix_modn_dense_template.pxi b/src/sage/matrix/matrix_modn_dense_template.pxi
index 69569297923..f00e8bef6ef 100644
--- a/src/sage/matrix/matrix_modn_dense_template.pxi
+++ b/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
 
diff --git a/src/sage/matrix/matrix_modn_sparse.pyx b/src/sage/matrix/matrix_modn_sparse.pyx
index 80a74bf1761..9c12d6b9e1d 100644
--- a/src/sage/matrix/matrix_modn_sparse.pyx
+++ b/src/sage/matrix/matrix_modn_sparse.pyx
@@ -880,7 +880,7 @@ cdef class Matrix_modn_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".
 
@@ -914,14 +914,14 @@ cdef class Matrix_modn_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]
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index 6aab58352be..ca77503ba96 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -677,9 +677,9 @@ def __init__(self, base_ring, nrows, ncols, sparse, implementation):
             Vector space of degree 125 and dimension 124 over Rational Field
             Basis matrix:
             124 x 125 dense matrix over Rational Field
-            sage: MatrixSpace(ZZ,20,20)(1) \ MatrixSpace(ZZ,20,1).random_element()
+            sage: MatrixSpace(ZZ,20,20)(1).solve_right(MatrixSpace(ZZ,20,1).random_element())
             20 x 1 dense matrix over Rational Field (use the '.str()' method to see the entries)
-            sage: MatrixSpace(ZZ,200,200)(1) \ MatrixSpace(ZZ,200,1).random_element()
+            sage: MatrixSpace(ZZ,200,200)(1).solve_right(MatrixSpace(ZZ,200,1).random_element())
             200 x 1 dense matrix over Rational Field (use the '.str()' method to see the entries)
             sage: A = MatrixSpace(RDF,1000,1000).random_element()
             sage: B = MatrixSpace(RDF,1000,1000).random_element()
diff --git a/src/sage/matroids/basis_exchange_matroid.pyx b/src/sage/matroids/basis_exchange_matroid.pyx
index 015fa8b8df3..fc902bc19c0 100644
--- a/src/sage/matroids/basis_exchange_matroid.pyx
+++ b/src/sage/matroids/basis_exchange_matroid.pyx
@@ -1134,7 +1134,7 @@ cdef class BasisExchangeMatroid(Matroid):
             sage: M.connectivity(X)
             2
             sage: J = M.groundset()-(S|T|I)
-            sage: N = M/I\J
+            sage: N = (M/I).delete(J)
             sage: N.connectivity(S)
             2
         """
@@ -2132,7 +2132,7 @@ cdef class BasisExchangeMatroid(Matroid):
             sage: N._is_isomorphism(M, {e:e for e in M.groundset()})
             False
 
-            sage: M = matroids.named_matroids.Fano() \ ['g']
+            sage: M = matroids.named_matroids.Fano().delete(['g'])
             sage: N = matroids.Wheel(3)
             sage: morphism = {'a':0, 'b':1, 'c': 2, 'd':4, 'e':5, 'f':3}
             sage: M._is_isomorphism(N, morphism)
diff --git a/src/sage/matroids/catalog.py b/src/sage/matroids/catalog.py
index 4bc93a6b8a0..949f7367b40 100644
--- a/src/sage/matroids/catalog.py
+++ b/src/sage/matroids/catalog.py
@@ -1006,7 +1006,7 @@ def AG(n, q, x=None):
 
     EXAMPLES::
 
-        sage: M = matroids.AG(2, 3) \ 8
+        sage: M = matroids.AG(2, 3).delete(8)
         sage: M.is_isomorphic(matroids.named_matroids.AG23minus())
         True
         sage: matroids.AG(5, 4, 'z').size() == ((4 ^ 6 - 1) / (4 - 1) -                 # needs sage.rings.finite_rings
diff --git a/src/sage/matroids/linear_matroid.pyx b/src/sage/matroids/linear_matroid.pyx
index 36f563aa433..8ba09084c1f 100644
--- a/src/sage/matroids/linear_matroid.pyx
+++ b/src/sage/matroids/linear_matroid.pyx
@@ -819,7 +819,7 @@ cdef class LinearMatroid(BasisExchangeMatroid):
         EXAMPLES::
 
             sage: from sage.matroids.advanced import *
-            sage: M = matroids.named_matroids.Fano() \ ['g']
+            sage: M = matroids.named_matroids.Fano().delete(['g'])
             sage: N = BinaryMatroid(Matrix(matroids.Wheel(3)))
             sage: morphism = {'a':0, 'b':1, 'c': 2, 'd':4, 'e':5, 'f':3}
             sage: M._is_field_isomorphism(N, morphism)
@@ -1004,7 +1004,7 @@ cdef class LinearMatroid(BasisExchangeMatroid):
             False
 
             sage: from sage.matroids.advanced import *
-            sage: M = matroids.named_matroids.Fano() \ ['g']
+            sage: M = matroids.named_matroids.Fano().delete(['g'])
             sage: N = LinearMatroid(reduced_matrix=Matrix(GF(2),
             ....:                       [[-1, 0, 1], [1, -1, 0], [0, 1, -1]]))
             sage: morphism = {'a':0, 'b':1, 'c': 2, 'd':4, 'e':5, 'f':3}
@@ -3413,8 +3413,8 @@ cdef class BinaryMatroid(LinearMatroid):
 
         EXAMPLES::
 
-            sage: M = matroids.named_matroids.Fano() \ ['a']
-            sage: N = matroids.named_matroids.Fano() \ ['b']
+            sage: M = matroids.named_matroids.Fano().delete(['a'])
+            sage: N = matroids.named_matroids.Fano().delete(['b'])
             sage: morphism = {'b':'a', 'c':'c', 'd':'e', 'e':'d', 'f':'f', 'g':'g'}
             sage: M._is_isomorphism(N, morphism)
             True
@@ -3632,7 +3632,7 @@ cdef class BinaryMatroid(LinearMatroid):
             2
             sage: for i in [-1, 0, 1]:
             ....:     print(sorted(e for e in M.groundset()
-            ....:                    if (M\e).bicycle_dimension() == 2 + i))
+            ....:                    if (M.delete(e)).bicycle_dimension() == 2 + i))
             ['a', 'b', 'c', 'e', 'f', 'g']
             ['d']
             ['h']
@@ -5459,7 +5459,7 @@ cdef class QuaternaryMatroid(LinearMatroid):
         EXAMPLES::
 
             sage: # needs sage.rings.finite_rings
-            sage: M = matroids.named_matroids.Q10()\'a'
+            sage: M = matroids.named_matroids.Q10().delete('a')
             sage: for F in M._principal_tripartition(): print(sorted(F))
             ['b', 'c', 'd', 'e', 'h', 'i']
             ['f', 'g', 'j']
@@ -5468,7 +5468,7 @@ cdef class QuaternaryMatroid(LinearMatroid):
             1
             sage: for i in [-1, 0, 1]:
             ....:     print(sorted(e for e in M.groundset()
-            ....:                  if (M\e).bicycle_dimension() == 1 + i))
+            ....:                  if (M.delete(e)).bicycle_dimension() == 1 + i))
             ['b', 'c', 'd', 'e', 'h', 'i']
             ['f', 'g', 'j']
             []
@@ -5497,8 +5497,8 @@ cdef class QuaternaryMatroid(LinearMatroid):
 
         EXAMPLES::
 
-           sage: M = matroids.named_matroids.Q10()\'a'                                  # needs sage.rings.finite_rings
-           sage: N = matroids.named_matroids.Q10()\'b'                                  # needs sage.rings.finite_rings
+           sage: M = matroids.named_matroids.Q10().delete('a')                          # needs sage.rings.finite_rings
+           sage: N = matroids.named_matroids.Q10().delete('b')                          # needs sage.rings.finite_rings
            sage: M._fast_isom_test(N) is None                                           # needs sage.rings.finite_rings
            True
         """
@@ -6182,8 +6182,8 @@ cdef class RegularMatroid(LinearMatroid):
 
         EXAMPLES::
 
-           sage: M = matroids.named_matroids.R10()\'a'
-           sage: N = matroids.named_matroids.R10()\'b'
+           sage: M = matroids.named_matroids.R10().delete('a')
+           sage: N = matroids.named_matroids.R10().delete('b')
            sage: M._fast_isom_test(N)                                                   # needs sage.graphs
            True
         """
diff --git a/src/sage/matroids/matroid.pyx b/src/sage/matroids/matroid.pyx
index 4d19c589bdf..2fc0129c2d1 100644
--- a/src/sage/matroids/matroid.pyx
+++ b/src/sage/matroids/matroid.pyx
@@ -280,7 +280,7 @@ Minors::
     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]
     sage: N.full_rank()
@@ -337,6 +337,7 @@ from itertools import combinations, product
 from sage.matrix.constructor import matrix
 from sage.misc.lazy_import import LazyImport
 from sage.misc.prandom import shuffle
+from sage.misc.superseded import deprecation
 from sage.rings.integer_ring import ZZ
 from sage.structure.richcmp cimport rich_to_bool, richcmp
 from sage.structure.sage_object cimport SageObject
@@ -2142,7 +2143,7 @@ cdef class Matroid(SageObject):
             sage: M = matroids.named_matroids.Fano().dual()
             sage: M.coloops()
             frozenset()
-            sage: (M \ ['a', 'b']).coloops()
+            sage: (M.delete(['a', 'b'])).coloops()
             frozenset({'f'})
         """
         return self._coclosure(set())
@@ -3475,7 +3476,7 @@ cdef class Matroid(SageObject):
             sage: N.is_isomorphism(M, {e:e for e in M.groundset()})
             False
 
-            sage: M = matroids.named_matroids.Fano() \ ['g']
+            sage: M = matroids.named_matroids.Fano().delete(['g'])
             sage: N = matroids.Wheel(3)
             sage: morphism = {'a':0, 'b':1, 'c': 2, 'd':4, 'e':5, 'f':3}
             sage: M.is_isomorphism(N, morphism)
@@ -3603,7 +3604,7 @@ cdef class Matroid(SageObject):
             sage: N._is_isomorphism(M, {e:e for e in M.groundset()})
             False
 
-            sage: M = matroids.named_matroids.Fano() \ ['g']
+            sage: M = matroids.named_matroids.Fano().delete(['g'])
             sage: N = matroids.Wheel(3)
             sage: morphism = {'a':0, 'b':1, 'c': 2, 'd':4, 'e':5, 'f':3}
             sage: M._is_isomorphism(N, morphism)
@@ -3907,7 +3908,8 @@ cdef class Matroid(SageObject):
         one. It can be shown that the resulting matroid does not depend on the
         order of the deletions.
 
-        Sage supports the shortcut notation ``M \ X`` for ``M.delete(X)``.
+        DEPRECATED: Sage supports the shortcut notation ``M \ X`` for
+        ``M.delete(X)``.
 
         INPUT:
 
@@ -3932,7 +3934,7 @@ cdef class Matroid(SageObject):
             ['a', 'b', 'c', 'd', 'e', 'f', 'g']
             sage: M.delete(['a', 'c'])
             Binary matroid of rank 3 on 5 elements, type (1, 6)
-            sage: M.delete(['a']) == M \ ['a']
+            sage: M.delete(['a']) == M.delete(['a'])
             True
 
         One can use a single element, rather than a set::
@@ -3940,13 +3942,13 @@ cdef class Matroid(SageObject):
             sage: M = matroids.CompleteGraphic(4)                                       # needs sage.graphs
             sage: M.delete(1) == M.delete([1])                                          # needs sage.graphs
             True
-            sage: M \ 1                                                                 # needs sage.graphs
+            sage: M.delete(1)                                                           # needs sage.graphs
             Graphic matroid of rank 3 on 5 elements
 
         Note that one can iterate over strings::
 
             sage: M = matroids.named_matroids.Fano()
-            sage: M \ 'abc'
+            sage: M.delete('abc')
             Binary matroid of rank 3 on 4 elements, type (0, 5)
 
         The following is therefore ambiguous. Sage will delete the single
@@ -3954,7 +3956,7 @@ cdef class Matroid(SageObject):
 
             sage: M = Matroid(groundset=['a', 'b', 'c', 'abc'],
             ....:             bases=[['a', 'b', 'c'], ['a', 'b', 'abc']])
-            sage: sorted((M \ 'abc').groundset())
+            sage: sorted((M.delete('abc')).groundset())
             ['a', 'b', 'c']
         """
         return self.minor(deletions=X)
@@ -3963,12 +3965,17 @@ cdef class Matroid(SageObject):
         r"""
         Shorthand for ``self.delete(X)``.
 
+        DEPRECATED
+
         EXAMPLES::
 
             sage: M = matroids.CompleteGraphic(4)                                       # needs sage.graphs
             sage: M.delete(1) == M \ 1  # indirect doctest                              # needs sage.graphs
+            doctest:...: DeprecationWarning: the backslash operator has been deprecated; use M.delete(X) instead
+            See https://github.com/sagemath/sage/issues/80000 for details.
             True
         """
+        deprecation(80000, 'the backslash operator has been deprecated; use M.delete(X) instead')
         return self.delete(X)
 
     cpdef dual(self):
@@ -4399,7 +4406,7 @@ cdef class Matroid(SageObject):
         `\{b, f\}`::
 
             sage: M = matroids.named_matroids.S8()
-            sage: N = M \ 'h'
+            sage: N = M.delete('h')
             sage: frozenset('bf') in N.modular_cut(['cg', 'ae'])
             True
 
@@ -4768,7 +4775,7 @@ cdef class Matroid(SageObject):
             sage: M = matroids.named_matroids.Fano().dual()
             sage: M.is_cosimple()
             True
-            sage: N = M \ 'a'
+            sage: N = M.delete('a')
             sage: N.is_cosimple()
             False
         """
@@ -4977,7 +4984,7 @@ cdef class Matroid(SageObject):
             sage: M.connectivity(X)
             2
             sage: J = M.groundset()-(S|T|I)
-            sage: N = M/I\J
+            sage: N = (M/I).delete(J)
             sage: N.connectivity(S)
             2
         """
@@ -5026,7 +5033,7 @@ cdef class Matroid(SageObject):
             sage: M.connectivity(X)
             2
             sage: J = M.groundset()-(S|T|I)
-            sage: N = M/I\J
+            sage: N = (M/I).delete(J)
             sage: N.connectivity(S)
             2
         """
diff --git a/src/sage/matroids/minor_matroid.py b/src/sage/matroids/minor_matroid.py
index 98856348ac1..ff27affc665 100644
--- a/src/sage/matroids/minor_matroid.py
+++ b/src/sage/matroids/minor_matroid.py
@@ -14,11 +14,11 @@
 EXAMPLES::
 
     sage: M = matroids.named_matroids.Fano()
-    sage: M \ ['a', 'c' ] == M.delete(['a', 'c'])
+    sage: M.delete(['a', 'c' ]) == M.delete(['a', 'c'])
     True
     sage: M / 'a' == M.contract('a')
     True
-    sage: M / 'c' \ 'ab' == M.minor(contractions='c', deletions='ab')
+    sage: (M / 'c').delete('ab') == M.minor(contractions='c', deletions='ab')
     True
 
 If a contraction set is not independent (or a deletion set not coindependent),
@@ -27,9 +27,9 @@
     sage: M = matroids.named_matroids.Fano()
     sage: M.rank('abf')
     2
-    sage: M / 'abf' == M / 'ab' \ 'f'
+    sage: M / 'abf' == (M / 'ab').delete('f')
     True
-    sage: M / 'abf' == M / 'af' \ 'b'
+    sage: M / 'abf' == (M / 'af').delete('b')
     True
 
 .. SEEALSO::
diff --git a/src/sage/misc/misc.py b/src/sage/misc/misc.py
index a4f8ebb826e..ba75dd92506 100644
--- a/src/sage/misc/misc.py
+++ b/src/sage/misc/misc.py
@@ -560,12 +560,20 @@ def __rmul__(self, left):
             ....:     A = random_matrix(ZZ, 4)
             sage: B = random_matrix(ZZ, 4)
             sage: temp = A * BackslashOperator()
+            doctest:...:
+            DeprecationWarning: the backslash operator has been deprecated
+            See https://github.com/sagemath/sage/issues/80000 for details.
             sage: temp.left is A
             True
             sage: X = temp * 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.
             sage: A * X == B
             True
         """
+        from sage.misc.superseded import deprecation
+        deprecation(80000, 'the backslash operator has been deprecated')
         self.left = left
         return self
 
@@ -577,15 +585,26 @@ def __mul__(self, right):
             sage: A = matrix(RDF, 5, 5, 2)
             sage: b = vector(RDF, 5, range(5))
             sage: v = 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.
             sage: v.zero_at(1e-19)  # On at least one platform, we get a "negative zero"
             (0.0, 0.5, 1.0, 1.5, 2.0)
             sage: v = A._backslash_(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.
             sage: v.zero_at(1e-19)
             (0.0, 0.5, 1.0, 1.5, 2.0)
             sage: v = A * BackslashOperator() * 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.
             sage: v.zero_at(1e-19)
             (0.0, 0.5, 1.0, 1.5, 2.0)
         """
+        from sage.misc.superseded import deprecation
+        deprecation(80000, 'the backslash operator has been deprecated')
         return self.left._backslash_(right)
 
 
diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py
index 5b99bdfa6ac..c2d51fb2f87 100644
--- a/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py
+++ b/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py
@@ -288,6 +288,8 @@
 Sage example in ./linalg.tex, line 1855::
 
   sage: A.solve_right(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 example in ./linalg.tex, line 1910::
diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py
index 7932167b41d..7c5b83423ea 100644
--- a/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py
+++ b/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py
@@ -49,7 +49,7 @@
 
   sage: A = matrix(RDF, [[-1,2],[3,4]])
   sage: b = vector(RDF, [2,3])
-  sage: x = A\b; x
+  sage: x = A.solve_right(b); x
   (-0.20000000000000018, 0.9000000000000001)
 
 Sage example in ./linsolve.tex, line 666::