less (a,b) = in documentation

fchapoton · fchapoton · commit 7c4a2e23ed63 · 2025-10-09T20:14:22.000+02:00
diff --git a/src/sage/calculus/functional.py b/src/sage/calculus/functional.py
@@ -236,8 +236,8 @@ def integral(f, *args, **kwds):
     `(1,1)`::
 
         sage: t = var('t')
-        sage: (x,y) = (t^4,t)
-        sage: (dx,dy) = (diff(x,t), diff(y,t))
+        sage: x, y = t^4, t
+        sage: dx, dy = diff(x,t), diff(y,t)
         sage: integral(sin(x)*dx, t,-1, 1)
         0
         sage: restore('x,y')   # restore the symbolic variables x and y
diff --git a/src/sage/categories/algebra_functor.py b/src/sage/categories/algebra_functor.py
@@ -32,7 +32,7 @@
 product of the corresponding elements of the group, and the unit of
 the group algebra is indexed by the unit of the group::
 
-    sage: (s, t) = A.algebra_generators()
+    sage: s, t = A.algebra_generators()
     sage: s*t
     (1,2)
     sage: A.one_basis()
diff --git a/src/sage/categories/coalgebras_with_basis.py b/src/sage/categories/coalgebras_with_basis.py
@@ -66,7 +66,7 @@ def coproduct_on_basis(self, i):
                 An example of Hopf algebra with basis:
                  the group algebra of the Dihedral group of order 6
                   as a permutation group over Rational Field
-                sage: (a, b) = A._group.gens()                                          # needs sage.groups sage.modules
+                sage: a, b = A._group.gens()                                          # needs sage.groups sage.modules
                 sage: A.coproduct_on_basis(a)                                           # needs sage.groups sage.modules
                 B[(1,2,3)] # B[(1,2,3)]
             """
@@ -120,7 +120,7 @@ def counit_on_basis(self, i):
                 An example of Hopf algebra with basis:
                  the group algebra of the Dihedral group of order 6
                   as a permutation group over Rational Field
-                sage: (a, b) = A._group.gens()                                          # needs sage.groups sage.modules
+                sage: a, b = A._group.gens()                                          # needs sage.groups sage.modules
                 sage: A.counit_on_basis(a)                                              # needs sage.groups sage.modules
                 1
             """
diff --git a/src/sage/categories/examples/hopf_algebras_with_basis.py b/src/sage/categories/examples/hopf_algebras_with_basis.py
@@ -74,7 +74,7 @@ def product_on_basis(self, g1, g2):
         EXAMPLES::
 
             sage: A = HopfAlgebrasWithBasis(QQ).example()
-            sage: (a, b) = A._group.gens()
+            sage: a, b = A._group.gens()
             sage: a*b
             (1,2)
             sage: A.product_on_basis(a, b)
@@ -107,7 +107,7 @@ def coproduct_on_basis(self, g):
         EXAMPLES::
 
             sage: A = HopfAlgebrasWithBasis(QQ).example()
-            sage: (a, b) = A._group.gens()
+            sage: a, b = A._group.gens()
             sage: A.coproduct_on_basis(a)
             B[(1,2,3)] # B[(1,2,3)]
         """
@@ -123,7 +123,7 @@ def counit_on_basis(self, g):
         EXAMPLES::
 
             sage: A = HopfAlgebrasWithBasis(QQ).example()
-            sage: (a, b) = A._group.gens()
+            sage: a, b = A._group.gens()
             sage: A.counit_on_basis(a)
             1
         """
@@ -138,7 +138,7 @@ def antipode_on_basis(self, g):
         EXAMPLES::
 
             sage: A = HopfAlgebrasWithBasis(QQ).example()
-            sage: (a, b) = A._group.gens()
+            sage: a, b = A._group.gens()
             sage: A.antipode_on_basis(a)
             B[(1,3,2)]
         """
diff --git a/src/sage/categories/filtered_modules_with_basis.py b/src/sage/categories/filtered_modules_with_basis.py
@@ -732,7 +732,7 @@ def is_homogeneous(self):
 
                 sage: # needs sage.combinat sage.modules
                 sage: S = NonCommutativeSymmetricFunctions(QQ).S()
-                sage: (x, y) = (S[2], S[3])
+                sage: x, y = S[2], S[3]
                 sage: (3*x).is_homogeneous()
                 True
                 sage: (x^3 - y^2).is_homogeneous()
@@ -815,7 +815,7 @@ def homogeneous_degree(self):
 
                 sage: # needs sage.combinat sage.modules
                 sage: S = NonCommutativeSymmetricFunctions(QQ).S()
-                sage: (x, y) = (S[2], S[3])
+                sage: x, y = S[2], S[3]
                 sage: x.homogeneous_degree()
                 2
                 sage: (x^3 + 4*y^2).homogeneous_degree()
@@ -888,7 +888,7 @@ def maximal_degree(self):
 
                 sage: # needs sage.combinat sage.modules
                 sage: S = NonCommutativeSymmetricFunctions(QQ).S()
-                sage: (x, y) = (S[2], S[3])
+                sage: x, y = S[2], S[3]
                 sage: x.maximal_degree()
                 2
                 sage: (x^3 + 4*y^2).maximal_degree()
diff --git a/src/sage/categories/simplicial_sets.py b/src/sage/categories/simplicial_sets.py
@@ -536,7 +536,7 @@ def cover(self, character):
                     sage: S1_.n_cells(1)[0].rename("sigma_1'")
                     sage: W = S1.wedge(S1_)
                     sage: G = CyclicPermutationGroup(3)
-                    sage: (a, b) = W.n_cells(1)
+                    sage: a, b = W.n_cells(1)
                     sage: C = W.cover({a : G.gen(0), b : G.gen(0)^2})
                     sage: C.face_data()
                     {(*, ()): None,
diff --git a/src/sage/combinat/dyck_word.py b/src/sage/combinat/dyck_word.py
@@ -2061,7 +2061,7 @@ def characteristic_symmetric_function(self, q=None,
         EXAMPLES::
 
             sage: R = QQ['q','t'].fraction_field()
-            sage: (q,t) = R.gens()
+            sage: q, t = R.gens()
             sage: f = sum(t**D.area() * D.characteristic_symmetric_function()           # needs sage.modules
             ....:         for D in DyckWords(3)); f
             (q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]
diff --git a/src/sage/combinat/ncsf_qsym/generic_basis_code.py b/src/sage/combinat/ncsf_qsym/generic_basis_code.py
@@ -949,7 +949,7 @@ def degree(self):
             EXAMPLES::
 
                 sage: S = NonCommutativeSymmetricFunctions(QQ).S()
-                sage: (x, y) = (S[2], S[3])
+                sage: x, y = S[2], S[3]
                 sage: x.degree()
                 2
                 sage: (x^3 + 4*y^2).degree()
@@ -960,7 +960,7 @@ def degree(self):
             ::
 
                 sage: F = QuasiSymmetricFunctions(QQ).F()
-                sage: (x, y) = (F[2], F[3])
+                sage: x, y = F[2], F[3]
                 sage: x.degree()
                 2
                 sage: (x^3 + 4*y^2).degree()
diff --git a/src/sage/combinat/parking_functions.py b/src/sage/combinat/parking_functions.py
@@ -1004,7 +1004,7 @@ def characteristic_quasisymmetric_function(self, q=None,
 
             sage: # needs sage.modules
             sage: R = QQ['q','t'].fraction_field()
-            sage: (q,t) = R.gens()
+            sage: q, t = R.gens()
             sage: cqf = sum(t**PF.area() * PF.characteristic_quasisymmetric_function()
             ....:           for PF in ParkingFunctions(3)); cqf
             (q^3+q^2*t+q*t^2+t^3+q*t)*F[1, 1, 1] + (q^2+q*t+t^2+q+t)*F[1, 2]
diff --git a/src/sage/combinat/sf/hall_littlewood.py b/src/sage/combinat/sf/hall_littlewood.py
@@ -233,7 +233,7 @@ def P(self):
         Transitions between bases with the parameter `t` specialized::
 
             sage: Sym = SymmetricFunctions(FractionField(QQ['y','z']))
-            sage: (y,z) = Sym.base_ring().gens()
+            sage: y, z = Sym.base_ring().gens()
             sage: HLy = Sym.hall_littlewood(t=y)
             sage: HLz = Sym.hall_littlewood(t=z)
             sage: Qpy = HLy.Qp()
diff --git a/src/sage/combinat/sf/jack.py b/src/sage/combinat/sf/jack.py
@@ -201,7 +201,7 @@ def P(self):
         ::
 
             sage: Sym = SymmetricFunctions(QQ['a','b'].fraction_field())
-            sage: (a,b) = Sym.base_ring().gens()
+            sage: a, b = Sym.base_ring().gens()
             sage: Jacka = Sym.jack(t=a)
             sage: Jackb = Sym.jack(t=b)
             sage: m = Sym.monomial()
diff --git a/src/sage/combinat/sf/llt.py b/src/sage/combinat/sf/llt.py
@@ -73,7 +73,7 @@ class LLT_class(UniqueRepresentation):
     We require that the parameter `t` must be in the base ring::
 
         sage: Symxt = SymmetricFunctions(QQ['x','t'].fraction_field())
-        sage: (x,t) = Symxt.base_ring().gens()
+        sage: x, t = Symxt.base_ring().gens()
         sage: LLT3x = Symxt.llt(3,t=x)
         sage: LLT3 = Symxt.llt(3)
         sage: HS3x = LLT3x.hspin()
diff --git a/src/sage/combinat/sf/macdonald.py b/src/sage/combinat/sf/macdonald.py
@@ -1291,7 +1291,7 @@ def _s_to_self(self, x):
             sage: s = Sym.s()
             sage: H(s[1,1])
             -(1/(q*t-1))*McdH[1, 1] + (t/(q*t-1))*McdH[2]
-            sage: (q,t) = Sym.base_ring().gens()
+            sage: q, t = Sym.base_ring().gens()
             sage: H(q*s[1, 1, 1] + (q*t+1)*s[2, 1] + t*s[3])
             McdH[2, 1]
             sage: H2 = Sym.macdonald(t=0).H()
@@ -1379,7 +1379,7 @@ def _m_to_self( self, f ):
             sage: m = Sym.m()
             sage: H(m[1,1])
             -(1/(q*t-1))*McdH[1, 1] + (t/(q*t-1))*McdH[2]
-            sage: (q,t) = Sym.base_ring().gens()
+            sage: q, t = Sym.base_ring().gens()
             sage: H((2*q*t+q+t+2)*m[1, 1, 1] + (q*t+t+1)*m[2, 1] + t*m[3])
             McdH[2, 1]
 
@@ -1601,7 +1601,7 @@ def _m_to_self( self, f ):
             sage: m = Sym.m()
             sage: Ht(m[1,1])
             (1/(-q+t))*McdHt[1, 1] - (1/(-q+t))*McdHt[2]
-            sage: (q,t) = Sym.base_ring().gens()
+            sage: q, t = Sym.base_ring().gens()
             sage: Ht((q*t+2*q+2*t+1)*m[1, 1, 1] + (q+t+1)*m[2, 1] + m[3])
             McdHt[2, 1]
 
@@ -1834,7 +1834,7 @@ def _creation_by_determinant_helper(self, k, part):
                 sage: a._creation_by_determinant_helper(2,[1])
                 (q^3*t-q^2*t-q+1)*McdS[2, 1] + (q^3-q^2*t-q+t)*McdS[3]
             """
-            (q,t) = QQqt.gens()
+            q, t = QQqt.gens()
             from sage.combinat.sf.sf import SymmetricFunctions
             S = SymmetricFunctions(QQqt).macdonald().S()
 
diff --git a/src/sage/combinat/sf/sf.py b/src/sage/combinat/sf/sf.py
@@ -776,7 +776,7 @@ class function on the symmetric group where the elements
     Here is an example of its use::
 
         sage: QQqt = QQ['q','t'].fraction_field()
-        sage: (q,t) = QQqt.gens()
+        sage: q, t = QQqt.gens()
         sage: st = SFA_st(SymmetricFunctions(QQqt),t)
         sage: st
         Symmetric Functions over Fraction Field of Multivariate Polynomial
@@ -1253,7 +1253,7 @@ def macdonald(self, q='q', t='t'):
             q^2*s[1, 1, 1, 1] + (q^2*t+q*t+q)*s[2, 1, 1] + (q^2*t^2+1)*s[2, 2] + (q*t^2+q*t+t)*s[3, 1] + t^2*s[4]
 
             sage: Sym = SymmetricFunctions(QQ['z','q'].fraction_field())
-            sage: (z,q) = Sym.base_ring().gens()
+            sage: z, q = Sym.base_ring().gens()
             sage: Hzq = Sym.macdonald(q=z,t=q).H()
             sage: H1z = Sym.macdonald(q=1,t=z).H()
             sage: s = Sym.schur()
diff --git a/src/sage/combinat/sf/sfa.py b/src/sage/combinat/sf/sfa.py
@@ -5158,7 +5158,7 @@ def scalar_qt(self, x, q=None, t=None):
             -q^3 + 2*q^2 - 2*q + 1
             sage: a.scalar_qt(a,5,7) # q=5 and t=7
             490/1539
-            sage: (x,y) = var('x,y')                                                    # needs sage.symbolic
+            sage: x, y = var('x,y')                                                    # needs sage.symbolic
             sage: a.scalar_qt(a, q=x, t=y)                                              # needs sage.symbolic
             1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3
             sage: Rn = QQ['q','t','y','z'].fraction_field()
diff --git a/src/sage/graphs/strongly_regular_db.pyx b/src/sage/graphs/strongly_regular_db.pyx
@@ -1425,16 +1425,16 @@ def is_GQqmqp(int v, int k, int l, int mu):
     TESTS::
 
         sage: # needs sage.libs.pari
-        sage: (S,T) = (127,129)
+        sage: S, T = 127, 129
         sage: t = is_GQqmqp((S+1)*(S*T+1), S*(T+1), S-1, T+1); t
         (<function T2starGeneralizedQuadrangleGraph at ...>, 128, False)
-        sage: (S,T) = (129,127)
+        sage: S, T = 129, 127
         sage: t = is_GQqmqp((S+1)*(S*T+1), S*(T+1), S-1, T+1); t
         (<function T2starGeneralizedQuadrangleGraph at ...>, 128, True)
-        sage: (S,T) = (124,126)
+        sage: S, T = 124, 126
         sage: t = is_GQqmqp((S+1)*(S*T+1), S*(T+1), S-1, T+1); t
         (<function AhrensSzekeresGeneralizedQuadrangleGraph at ...>, 125, False)
-        sage: (S,T) = (126,124)
+        sage: S, T = 126, 124
         sage: t = is_GQqmqp((S+1)*(S*T+1), S*(T+1), S-1, T+1); t
         (<function AhrensSzekeresGeneralizedQuadrangleGraph at ...>, 125, True)
         sage: t = is_GQqmqp(5,5,5,5); t
diff --git a/src/sage/libs/mpmath/ext_main.pyx b/src/sage/libs/mpmath/ext_main.pyx
@@ -973,23 +973,24 @@ cdef class Context:
     def _convert_param(ctx, x):
         """
         Internal function for parsing a hypergeometric function parameter.
-        Retrurns (T, x) where T = 'Z', 'Q', 'R', 'C' depending on the
+
+        This returns (T, x) where T = 'Z', 'Q', 'R', 'C' depending on the
         type of the parameter, and with x converted to the canonical
         mpmath type.
 
         TESTS::
 
             sage: from mpmath import mp
-            sage: (x, T) = mp._convert_param(3)
+            sage: x, T = mp._convert_param(3)
             sage: (x, type(x).__name__, T)
             (3, 'int', 'Z')
-            sage: (x, T) = mp._convert_param(2.5)
+            sage: x, T = mp._convert_param(2.5)
             sage: (x, type(x).__name__, T)
             (mpq(5,2), 'mpq', 'Q')
-            sage: (x, T) = mp._convert_param(2.3)
+            sage: x, T = mp._convert_param(2.3)
             sage: (str(x), type(x).__name__, T)
             ('2.3', 'mpf', 'R')
-            sage: (x, T) = mp._convert_param(2+3j)
+            sage: x, T = mp._convert_param(2+3j)
             sage: (x, type(x).__name__, T)
             (mpc(real='2.0', imag='3.0'), 'mpc', 'C')
             sage: mp.pretty = False
diff --git a/src/sage/manifolds/continuous_map.py b/src/sage/manifolds/continuous_map.py
@@ -2077,7 +2077,7 @@ def __invert__(self):
         Checking that applying successively the homeomorphism and its
         inverse results in the identity::
 
-            sage: (a, b) = var('a b')
+            sage: a, b = var('a b')
             sage: p = M.point((a,b)) # a generic point on M
             sage: q = rot(p)
             sage: p1 = rot.inverse()(q)
diff --git a/src/sage/manifolds/manifold.py b/src/sage/manifolds/manifold.py
@@ -1556,7 +1556,7 @@ def chart(
 
         They can be recovered by the operator ``[:]`` applied to the chart::
 
-            sage: (x, y) = X[:]
+            sage: x, y = X[:]
             sage: y
             y
             sage: type(y)
diff --git a/src/sage/manifolds/point.py b/src/sage/manifolds/point.py
@@ -122,7 +122,7 @@ class ManifoldPoint(Element):
 
         sage: M = Manifold(2, 'M', structure='topological')
         sage: c_xy.<x,y> = M.chart()
-        sage: (a, b) = var('a b') # generic coordinates for the point
+        sage: a, b = var('a b')  # generic coordinates for the point
         sage: p = M.point((a, b), name='P'); p
         Point P on the 2-dimensional topological manifold M
         sage: p.coordinates()  # coordinates of P in the subset's default chart
@@ -329,7 +329,7 @@ def coordinates(self, chart=None, old_chart=None):
 
             sage: M = Manifold(2, 'M', structure='topological')
             sage: c_xy.<x,y> = M.chart()
-            sage: (a, b) = var('a b') # generic coordinates for the point
+            sage: a, b = var('a b')  # generic coordinates for the point
             sage: P = M.point((a, b), name='P')
 
         Coordinates of ``P`` in the manifold's default chart::
diff --git a/src/sage/matrix/matrix_polynomial_dense.pyx b/src/sage/matrix/matrix_polynomial_dense.pyx
@@ -3306,7 +3306,7 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense):
             sage: A = matrix(pR, 2, 2,
             ....:     [[5*x^3 + 2*x^2 + 4*x + 1,           x^3 + 4*x + 4],
             ....:      [2*x^3 + 5*x^2 + 2*x + 4,         2*x^3 + 3*x + 2]])
-            sage: (Q,R) = A.reduce(B,row_wise=False, return_quotient=True); R
+            sage: Q, R = A.reduce(B, row_wise=False, return_quotient=True); R
             [0 3]
             [0 0]
             sage: A == B*Q + R
diff --git a/src/sage/modular/modform_hecketriangle/hecke_triangle_groups.py b/src/sage/modular/modform_hecketriangle/hecke_triangle_groups.py
@@ -610,7 +610,7 @@ def get_FD(self, z):
             sage: from sage.modular.modform_hecketriangle.hecke_triangle_groups import HeckeTriangleGroup
             sage: G = HeckeTriangleGroup(8)
             sage: z = AlgebraicField()(1+i/2)
-            sage: (A, w) = G.get_FD(z)
+            sage: A, w = G.get_FD(z)
             sage: A
             [-lam    1]
             [  -1    0]
@@ -619,7 +619,7 @@ def get_FD(self, z):
 
             sage: from sage.modular.modform_hecketriangle.space import ModularForms
             sage: z = (134.12 + 0.22*i).n()
-            sage: (A, w) = G.get_FD(z)
+            sage: A, w = G.get_FD(z)
             sage: A
             [-73*lam^3 + 74*lam       73*lam^2 - 1]
             [        -lam^2 + 1                lam]
diff --git a/src/sage/modular/modform_hecketriangle/readme.py b/src/sage/modular/modform_hecketriangle/readme.py
@@ -176,7 +176,7 @@
       sage: z = AlgebraicField()(4 + 1/7*i)
       sage: G.in_FD(z)
       False
-      sage: (A, w) = G.get_FD(z)
+      sage: A, w = G.get_FD(z)
       sage: A
       T^2*S*T^(-1)*S
       sage: w
diff --git a/src/sage/modular/modsym/p1list.pyx b/src/sage/modular/modsym/p1list.pyx
@@ -1120,7 +1120,7 @@ cdef class P1List():
         EXAMPLES::
 
             sage: L = P1List(120)
-            sage: (u,v) = (555555555,7777)
+            sage: u, v = 555555555, 7777
             sage: uu,vv = L.normalize(555555555,7777)
             sage: (uu,vv)
             (15, 13)
@@ -1149,11 +1149,11 @@ cdef class P1List():
         EXAMPLES::
 
             sage: L = P1List(120)
-            sage: (u,v) = (555555555,7777)
+            sage: u, v = 555555555, 7777
             sage: uu,vv,ss = L.normalize_with_scalar(555555555,7777)
-            sage: (uu,vv)
+            sage: uu, vv
             (15, 13)
-            sage: ((ss*uu-u)%L.N(), (ss*vv-v)%L.N())
+            sage: (ss*uu-u)%L.N(), (ss*vv-v)%L.N()
             (0, 0)
             sage: (uu*v-vv*u) % L.N() == 0
             True
diff --git a/src/sage/monoids/string_monoid_element.py b/src/sage/monoids/string_monoid_element.py
diff --git a/src/sage/plot/matrix_plot.py b/src/sage/plot/matrix_plot.py
diff --git a/src/sage/rings/asymptotic/asymptotic_ring.py b/src/sage/rings/asymptotic/asymptotic_ring.py
diff --git a/src/sage/rings/multi_power_series_ring.py b/src/sage/rings/multi_power_series_ring.py
diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py
diff --git a/src/sage/rings/number_field/number_field_ideal_rel.py b/src/sage/rings/number_field/number_field_ideal_rel.py
diff --git a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
diff --git a/src/sage/schemes/plane_conics/con_field.py b/src/sage/schemes/plane_conics/con_field.py
diff --git a/src/sage/schemes/plane_conics/con_rational_field.py b/src/sage/schemes/plane_conics/con_rational_field.py
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/mpoly_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/mpoly_doctest.py

Original file line number	Diff line number	Diff line change
`@@ -236,8 +236,8 @@ def integral(f, args, *kwds):`
`236`	`236`	`(1,1)`::
`237`	`237`
`238`	`238`	`sage: t = var('t')`
`239`		`- sage: (x,y) = (t^4,t)`
`240`		`- sage: (dx,dy) = (diff(x,t), diff(y,t))`
	`239`	`+ sage: x, y = t^4, t`
	`240`	`+ sage: dx, dy = diff(x,t), diff(y,t)`
`241`	`241`	`sage: integral(sin(x)*dx, t,-1, 1)`
`242`	`242`	`0`
`243`	`243`	`sage: restore('x,y') # restore the symbolic variables x and y`
Original file line number	Diff line number	Diff line change
`@@ -949,7 +949,7 @@ def degree(self):`
`949`	`949`	`EXAMPLES::`
`950`	`950`
`951`	`951`	`sage: S = NonCommutativeSymmetricFunctions(QQ).S()`
`952`		`- sage: (x, y) = (S[2], S[3])`
	`952`	`+ sage: x, y = S[2], S[3]`
`953`	`953`	`sage: x.degree()`
`954`	`954`	`2`
`955`	`955`	`sage: (x^3 + 4*y^2).degree()`
`@@ -960,7 +960,7 @@ def degree(self):`
`960`	`960`	`::`
`961`	`961`
`962`	`962`	`sage: F = QuasiSymmetricFunctions(QQ).F()`
`963`		`- sage: (x, y) = (F[2], F[3])`
	`963`	`+ sage: x, y = F[2], F[3]`
`964`	`964`	`sage: x.degree()`
`965`	`965`	`2`
`966`	`966`	`sage: (x^3 + 4*y^2).degree()`