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gh-35069: Conform to doc requirements so that the docs look more beautiful These are mostly either of the form of unindenting text that was accidentally put in a code block, or correctly adding `::` or `EXAMPLES::` so that docs render nicely. <!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes #1234" use "Introduce new method to calculate 1+1" --> ### 📚 Description <!-- Describe your changes here in detail --> <!-- Why is this change required? What problem does it solve? --> <!-- If it resolves an open issue, please link to the issue here. For example "Closes #1337" --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> - [ ] I have made sure that the title is self-explanatory and the description concisely explains the PR. - [ ] I have linked an issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open pull requests that this PR logically depends on --> <!-- - #xyz: short description why this is a dependency - #abc: ... --> URL: #35069 Reported by: Alex J Best Reviewer(s): Alex J Best, Frédéric Chapoton, Travis Scrimshaw
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src/sage/algebras/free_algebra_quotient.py

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@@ -295,6 +295,8 @@ def module(self):
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"""
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The free module of the algebra.
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EXAMPLES::
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sage: H = sage.algebras.free_algebra_quotient.hamilton_quatalg(QQ)[0]; H
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Free algebra quotient on 3 generators ('i', 'j', 'k') and dimension 4 over Rational Field
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sage: H.module()

src/sage/algebras/iwahori_hecke_algebra.py

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@@ -2491,6 +2491,8 @@ def __init__(self, IHAlgebra, prefix=None):
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r"""
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Initialize the `A`-basis of the Iwahori-Hecke algebra ``IHAlgebra``.
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EXAMPLES::
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sage: R.<v> = LaurentPolynomialRing(QQ)
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sage: H = IwahoriHeckeAlgebra('A3', v**2)
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sage: A = H.A()

src/sage/algebras/quatalg/quaternion_algebra.py

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@@ -1337,8 +1337,8 @@ def __init__(self, A, basis, check=True):
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sage: type(R)
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<class 'sage.algebras.quatalg.quaternion_algebra.QuaternionOrder_with_category'>
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Over QQ and number fields it is checked whether the given
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basis actually gives an order (as a module over the maximal order):
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Over QQ and number fields it is checked whether the given
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basis actually gives an order (as a module over the maximal order)::
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sage: A.<i,j,k> = QuaternionAlgebra(-1,-1)
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sage: A.quaternion_order([1,i,j,i-j])

src/sage/categories/cartesian_product.py

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sage: _.category()
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Category of Cartesian products of finite enumerated sets
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Check that the empty product is handled correctly:
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Check that the empty product is handled correctly::
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sage: C = cartesian_product([])
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sage: C

src/sage/categories/domains.py

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In rings whose elements can not be represented exactly, there
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may be zero divisors in practice, even though these rings do
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not have them in theory. For such inexact rings, these tests
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are not performed:
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sage: R = ZpFM(5); R
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5-adic Ring of fixed modulus 5^20
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sage: R.is_exact()
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False
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sage: a = R(5^19)
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sage: a.is_zero()
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False
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sage: (a*a).is_zero()
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True
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sage: R._test_zero_divisors()
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are not performed::
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sage: R = ZpFM(5); R
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5-adic Ring of fixed modulus 5^20
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sage: R.is_exact()
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False
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sage: a = R(5^19)
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sage: a.is_zero()
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False
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sage: (a*a).is_zero()
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True
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sage: R._test_zero_divisors()
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EXAMPLES::
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src/sage/categories/examples/sets_cat.py

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datastructure will then be constructed by inheriting from
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:class:`PrimeNumbers_Abstract`.
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This is used by:
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This is used by::
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sage: P = Sets().example("facade")
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sage: P = Sets().example("inherits")

src/sage/categories/magmas.py

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r"""
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Return the unit element of ``self``.
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EXAMPLES::
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sage: from sage.combinat.root_system.extended_affine_weyl_group import ExtendedAffineWeylGroup
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sage: PvW0 = ExtendedAffineWeylGroup(['A',2,1]).PvW0()
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sage: PvW0 in Magmas().Unital().Realizations()

src/sage/coding/abstract_code.py

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....: super().__init__(10)
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We check we get a sensible error message while asking for an
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iterator over the elements of our new class:
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iterator over the elements of our new class::
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sage: C = MyCode()
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sage: list(C)
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....: super().__init__(length)
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We check we get a sensible error message while asking if an element is
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in our new class:
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in our new class::
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sage: C = MyCode(3)
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sage: vector((1, 0, 0, 0, 0, 1, 1)) in C
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....: super().__init__(10)
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We check we get a sensible error message while asking for a string
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representation of an instance of our new class:
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representation of an instance of our new class::
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sage: C = MyCode()
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sage: C #random
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....: super().__init__(10)
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We check we get a sensible error message while asking for a string
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representation of an instance of our new class:
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representation of an instance of our new class::
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sage: C = MyCode()
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sage: latex(C)

src/sage/coding/guruswami_sudan/interpolation.py

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EXAMPLES:
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The following parameters arise from Guruswami-Sudan decoding of an [6,2,5]
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GRS code over F(11) with multiplicity 2 and list size 4.
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GRS code over F(11) with multiplicity 2 and list size 4. ::
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sage: from sage.coding.guruswami_sudan.interpolation import _interpolation_matrix_problem
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sage: F = GF(11)

src/sage/coding/linear_code_no_metric.py

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[1 2 0 1]
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[0 0 1 2]
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Specific systematic positions can also be requested:
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Specific systematic positions can also be requested::
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sage: C.systematic_generator_matrix(systematic_positions=[3,2])
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[1 2 0 1]

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