From 1ed6ea59baf8d9687a7c3aaafd964d3049ebcca1 Mon Sep 17 00:00:00 2001 From: Giorgos Mousa Date: Wed, 5 Jun 2024 14:31:39 +0000 Subject: [PATCH] one-line outputs (2/7) --- src/sage/crypto/block_cipher/sdes.py | 28 +-- src/sage/crypto/stream.py | 8 +- src/sage/data_structures/bitset.pyx | 4 +- src/sage/data_structures/mutable_poset.py | 216 +++++------------- src/sage/databases/cremona.py | 10 +- src/sage/databases/cubic_hecke_db.py | 10 +- src/sage/databases/findstat.py | 64 ++---- src/sage/databases/knotinfo_db.py | 12 +- src/sage/databases/oeis.py | 2 +- src/sage/doctest/control.py | 4 +- src/sage/doctest/forker.py | 2 +- src/sage/doctest/parsing.py | 8 +- .../dynamics/arithmetic_dynamics/affine_ds.py | 6 +- .../arithmetic_dynamics/berkovich_ds.py | 24 +- .../dynamical_semigroup.py | 18 +- .../endPN_automorphism_group.py | 4 +- .../product_projective_ds.py | 6 +- .../arithmetic_dynamics/projective_ds.py | 24 +- .../dynamics/arithmetic_dynamics/wehlerK3.py | 50 ++-- .../dynamics/complex_dynamics/mandel_julia.py | 4 +- .../complex_dynamics/mandel_julia_helper.pyx | 12 +- src/sage/ext/fast_callable.pyx | 2 +- src/sage/features/__init__.py | 4 +- src/sage/features/all.py | 4 +- src/sage/functions/piecewise.py | 20 +- src/sage/functions/spike_function.py | 4 +- src/sage/games/hexad.py | 8 +- src/sage/games/quantumino.py | 16 +- src/sage/games/sudoku.py | 4 +- src/sage/geometry/cone.py | 44 +--- src/sage/geometry/cone_critical_angles.py | 4 +- src/sage/geometry/convex_set.py | 76 ++---- src/sage/geometry/fan.py | 104 +++------ src/sage/geometry/fan_morphism.py | 4 +- .../hyperbolic_space/hyperbolic_isometry.py | 8 +- .../hyperplane_arrangement/affine_subspace.py | 40 +--- .../hyperplane_arrangement/arrangement.py | 116 +++------- .../hyperplane_arrangement/hyperplane.py | 48 +--- .../hyperplane_arrangement/library.py | 8 +- .../ordered_arrangement.py | 16 +- .../geometry/hyperplane_arrangement/plot.py | 8 +- src/sage/geometry/integral_points.pxi | 24 +- src/sage/geometry/lattice_polytope.py | 26 +-- src/sage/geometry/linear_expression.py | 40 +--- src/sage/geometry/newton_polygon.py | 24 +- src/sage/geometry/palp_normal_form.pyx | 4 +- src/sage/geometry/point_collection.pyx | 4 +- src/sage/geometry/polyhedron/backend_field.py | 12 +- .../geometry/polyhedron/backend_normaliz.py | 28 +-- .../geometry/polyhedron/backend_polymake.py | 12 +- src/sage/geometry/polyhedron/base.py | 12 +- src/sage/geometry/polyhedron/base0.py | 48 ++-- src/sage/geometry/polyhedron/base1.py | 36 +-- src/sage/geometry/polyhedron/base3.py | 16 +- src/sage/geometry/polyhedron/base5.py | 30 +-- src/sage/geometry/polyhedron/base6.py | 4 +- src/sage/geometry/polyhedron/base7.py | 22 +- src/sage/geometry/polyhedron/base_QQ.py | 32 +-- src/sage/geometry/polyhedron/base_RDF.py | 12 +- src/sage/geometry/polyhedron/base_ZZ.py | 4 +- .../combinatorial_polyhedron/base.pyx | 4 +- .../combinatorial_polyhedron/conversions.pyx | 2 +- .../face_iterator.pyx | 2 +- .../list_of_faces.pyx | 2 +- src/sage/geometry/polyhedron/constructor.py | 4 +- .../geometry/polyhedron/double_description.py | 36 +-- .../double_description_inhomogeneous.py | 20 +- src/sage/geometry/polyhedron/face.py | 70 ++---- .../polyhedron/generating_function.py | 4 +- src/sage/geometry/polyhedron/library.py | 6 +- src/sage/geometry/polyhedron/misc.py | 8 +- src/sage/geometry/polyhedron/palp_database.py | 32 +-- src/sage/geometry/polyhedron/parent.py | 44 +--- src/sage/geometry/polyhedron/plot.py | 4 +- .../polyhedron/ppl_lattice_polygon.py | 20 +- .../polyhedron/ppl_lattice_polytope.py | 22 +- .../geometry/polyhedron/representation.py | 36 +-- src/sage/geometry/relative_interior.py | 8 +- .../parametrized_surface3d.py | 4 +- src/sage/geometry/toric_lattice.py | 12 +- src/sage/geometry/toric_lattice_element.pyx | 8 +- src/sage/geometry/triangulation/base.pyx | 52 ++--- src/sage/geometry/triangulation/element.py | 16 +- .../triangulation/point_configuration.py | 8 +- src/sage/geometry/voronoi_diagram.py | 8 +- 85 files changed, 510 insertions(+), 1366 deletions(-) diff --git a/src/sage/crypto/block_cipher/sdes.py b/src/sage/crypto/block_cipher/sdes.py index 30b8cf2516c..d1cbe697133 100644 --- a/src/sage/crypto/block_cipher/sdes.py +++ b/src/sage/crypto/block_cipher/sdes.py @@ -654,9 +654,7 @@ def left_shift(self, B, n=1): valid values for ``n`` are 1 and 2, since only up to 2 positions are defined for this circular left shift operation. - OUTPUT: - - The circular left shift of each half of ``B``. + OUTPUT: the circular left shift of each half of ``B`` EXAMPLES: @@ -763,9 +761,7 @@ def list_to_string(self, B): - ``B`` -- a non-empty list of bits - OUTPUT: - - The binary string representation of ``B``. + OUTPUT: the binary string representation of ``B`` EXAMPLES: @@ -823,9 +819,7 @@ def permutation4(self, B): - ``B`` -- a block of 4-bit string - OUTPUT: - - A permutation of ``B``. + OUTPUT: a permutation of ``B`` EXAMPLES: @@ -910,9 +904,7 @@ def permutation8(self, B): - ``B`` -- a block of 10-bit string - OUTPUT: - - Pick out 8 of the 10 bits of ``B`` and permute those 8 bits. + OUTPUT: pick out 8 of the 10 bits of ``B`` and permute those 8 bits EXAMPLES: @@ -1000,9 +992,7 @@ def permutation10(self, B): - ``B`` -- a block of 10-bit string - OUTPUT: - - A permutation of ``B``. + OUTPUT: a permutation of ``B`` EXAMPLES: @@ -1174,9 +1164,7 @@ def permute_substitute(self, B, key): - ``key`` -- an 8-bit subkey - OUTPUT: - - The result of applying the function `\Pi_F` to ``B``. + OUTPUT: the result of applying the function `\Pi_F` to ``B`` EXAMPLES: @@ -1316,9 +1304,7 @@ def string_to_list(self, S): - ``S`` -- a string of bits - OUTPUT: - - A list representation of the string ``S``. + OUTPUT: a list representation of the string ``S`` EXAMPLES: diff --git a/src/sage/crypto/stream.py b/src/sage/crypto/stream.py index 636f588ad97..3bae3f5ae56 100644 --- a/src/sage/crypto/stream.py +++ b/src/sage/crypto/stream.py @@ -35,8 +35,6 @@ def __init__(self, field=None): INPUT: A string monoid over a binary alphabet. - OUTPUT: - EXAMPLES:: sage: E = LFSRCryptosystem(FiniteField(2)) @@ -109,8 +107,6 @@ def __init__(self, field=None): INPUT: A string monoid over a binary alphabet. - OUTPUT: - EXAMPLES:: sage: E = ShrinkingGeneratorCryptosystem() @@ -131,8 +127,8 @@ def __call__(self, key): INPUT: A list or tuple consisting of two LFSR ciphers (e1,e2). - OUTPUT: The shrinking generator cipher with key stream generator e1 - and decimating cipher e2. + OUTPUT: the shrinking generator cipher with key stream generator e1 + and decimating cipher e2 """ if not isinstance(key, (list, tuple)) and len(key) == 2: raise TypeError("Argument key (= %s) must be a list of tuple of length 2" % key) diff --git a/src/sage/data_structures/bitset.pyx b/src/sage/data_structures/bitset.pyx index 9d5e2029407..81300b89e04 100644 --- a/src/sage/data_structures/bitset.pyx +++ b/src/sage/data_structures/bitset.pyx @@ -2353,9 +2353,7 @@ def test_bitset_unpickle(data): - ``data`` -- A tuple of data as would be produced by the internal, Cython-only, method ``bitset_pickle``. - OUTPUT: - - A list form of the bitset corresponding to the pickled data. + OUTPUT: a list form of the bitset corresponding to the pickled data EXAMPLES: diff --git a/src/sage/data_structures/mutable_poset.py b/src/sage/data_structures/mutable_poset.py index 4de44a48e6a..64fdbdcff2e 100644 --- a/src/sage/data_structures/mutable_poset.py +++ b/src/sage/data_structures/mutable_poset.py @@ -163,9 +163,7 @@ class MutablePosetShell(SageObject): - ``element`` -- the element which should be contained/encapsulated in this shell. - OUTPUT: - - A shell for the given element. + OUTPUT: a shell for the given element .. NOTE:: @@ -303,9 +301,7 @@ def predecessors(self, reverse=False): - ``reverse`` -- (default: ``False``) if set, then return successors instead. - OUTPUT: - - A set. + OUTPUT: set .. SEEALSO:: @@ -334,9 +330,7 @@ def successors(self, reverse=False): - ``reverse`` -- (default: ``False``) if set, then return predecessors instead. - OUTPUT: - - A set. + OUTPUT: set .. SEEALSO:: @@ -367,9 +361,7 @@ def is_special(self): Nothing. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. SEEALSO:: @@ -393,9 +385,7 @@ def is_null(self): Return whether this shell contains the null-element, i.e., the element smaller than any possible other element. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. SEEALSO:: @@ -420,9 +410,7 @@ def is_oo(self): Return whether this shell contains the infinity-element, i.e., the element larger than any possible other element. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. SEEALSO:: @@ -450,9 +438,7 @@ def _repr_(self): Nothing. - OUTPUT: - - A string. + OUTPUT: string .. NOTE:: @@ -489,9 +475,7 @@ def __hash__(self): Nothing. - OUTPUT: - - A hash value. + OUTPUT: a hash value This returns the hash value of the key of the element contained in this shell. @@ -517,9 +501,7 @@ def le(self, other, reverse=False): - ``reverse`` -- (default: ``False``) if set, then return whether this shell is greater than or equal to ``other``. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. NOTE:: @@ -611,9 +593,7 @@ def eq(self, other): - ``other`` -- a shell. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. NOTE:: @@ -685,9 +665,7 @@ def _copy_all_linked_(self, memo, poset, mapping): - ``mapping`` -- a function which is applied on each of the elements. - OUTPUT: - - A new shell. + OUTPUT: a new shell .. SEEALSO:: @@ -750,9 +728,7 @@ def lower_covers(self, shell, reverse=False): the upper covers (see also :meth:`upper_covers`) instead of the lower covers. - OUTPUT: - - A set of :class:`shells `. + OUTPUT: a set of :class:`shells ` .. NOTE:: @@ -830,9 +806,7 @@ def upper_covers(self, shell, reverse=False): the lower covers (see also :meth:`lower_covers`) instead of the upper covers. - OUTPUT: - - A set of :class:`shells `. + OUTPUT: a set of :class:`shells ` .. NOTE:: @@ -910,9 +884,7 @@ def _iter_depth_first_visit_(self, marked, always ``True``. Note that the iteration does not go beyond a not included shell. - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -970,9 +942,7 @@ def iter_depth_first(self, reverse=False, key=None, condition=None): always ``True``. Note that the iteration does not go beyond a not included shell. - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -1034,9 +1004,7 @@ def _iter_topological_visit_(self, marked, always ``True``. Note that the iteration does not go beyond a not included shell. - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -1095,9 +1063,7 @@ def iter_topological(self, reverse=False, key=None, condition=None): always ``True``. Note that the iteration does not go beyond a not included shell. - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -1202,9 +1168,7 @@ def merge(self, element, check=True, delete=True): - ``delete`` -- (default: ``True``) if set, then ``element`` is removed from the poset after the merge. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -1345,9 +1309,7 @@ class MutablePoset(SageObject): ``can_merge`` is ``None`` (default) is equivalent to ``can_merge`` returning ``True`` in all cases. - OUTPUT: - - A mutable poset. + OUTPUT: a mutable poset You can find a short introduction and examples :mod:`here `. @@ -1445,9 +1407,7 @@ def clear(self): Nothing. - OUTPUT: - - Nothing. + OUTPUT: nothing .. SEEALSO:: @@ -1485,9 +1445,7 @@ def __len__(self): Nothing. - OUTPUT: - - An integer. + OUTPUT: integer .. NOTE:: @@ -1563,9 +1521,7 @@ def shell(self, key): - ``key`` -- the key of an object. - OUTPUT: - - An instance of :class:`MutablePosetShell`. + OUTPUT: an instance of :class:`MutablePosetShell` .. NOTE:: @@ -1597,9 +1553,7 @@ def element(self, key): - ``key`` -- the key of an object. - OUTPUT: - - An object. + OUTPUT: an object EXAMPLES:: @@ -1662,9 +1616,7 @@ def _copy_shells_(self, other, mapping): - ``mapping`` -- a function that is applied to each element. - OUTPUT: - - Nothing. + OUTPUT: nothing .. SEEALSO:: @@ -1702,9 +1654,7 @@ def copy(self, mapping=None): - ``mapping`` -- a function which is applied on each of the elements. - OUTPUT: - - A poset with the same content as ``self``. + OUTPUT: a poset with the same content as ``self`` .. SEEALSO:: @@ -1743,9 +1693,7 @@ def shells(self, include_special=False): including shells containing a smallest element (`\emptyset`) and a largest element (`\infty`). - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -1796,9 +1744,7 @@ def shells_topological(self, include_special=False, the direct successors of a shell (used in case of a tie). If this is ``None``, no sorting occurs. - OUTPUT: - - An iterator. + OUTPUT: an iterator .. NOTE:: @@ -1845,9 +1791,7 @@ def elements(self, **kwargs): - ``kwargs`` -- arguments are passed to :meth:`shells`. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -1891,9 +1835,7 @@ def elements_topological(self, **kwargs): - ``kwargs`` -- arguments are passed to :meth:`shells_topological`. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -1932,9 +1874,7 @@ def keys(self, **kwargs): - ``kwargs`` -- arguments are passed to :meth:`shells`. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -1978,9 +1918,7 @@ def keys_topological(self, **kwargs): - ``kwargs`` -- arguments are passed to :meth:`shells_topological`. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -2026,9 +1964,7 @@ def repr(self, include_special=False, reverse=False): - ``reverse`` -- (default: ``False``) a boolean. If set, then largest elements are displayed first. - OUTPUT: - - A string. + OUTPUT: string .. SEEALSO:: @@ -2056,9 +1992,7 @@ def repr_full(self, reverse=False): - ``reverse`` -- (default: ``False``) a boolean. If set, then largest elements are displayed first. - OUTPUT: - - A string. + OUTPUT: string .. SEEALSO:: @@ -2104,9 +2038,7 @@ def contains(self, key): - ``key`` -- an object. - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` .. SEEALSO:: @@ -2140,9 +2072,7 @@ def add(self, element): - ``element`` -- an object (hashable and supporting comparison with the operator ``<=``). - OUTPUT: - - Nothing. + OUTPUT: nothing EXAMPLES:: @@ -2308,9 +2238,7 @@ def remove(self, key, raise_key_error=True): - ``raise_key_error`` -- (default: ``True``) switch raising :class:`KeyError` on and off. - OUTPUT: - - Nothing. + OUTPUT: nothing If the element is not a member and ``raise_key_error`` is set (default), raise a :class:`KeyError`. @@ -2488,9 +2416,7 @@ def discard(self, key, raise_key_error=False): - ``raise_key_error`` -- (default: ``False``) switch raising :class:`KeyError` on and off. - OUTPUT: - - Nothing. + OUTPUT: nothing If the element is not a member and ``raise_key_error`` is set (not default), raise a :class:`KeyError`. @@ -2538,9 +2464,7 @@ def pop(self, **kwargs): - ``kwargs`` -- arguments are passed to :meth:`shells_topological`. - OUTPUT: - - An object. + OUTPUT: an object .. NOTE:: @@ -2589,9 +2513,7 @@ def union(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - A poset. + OUTPUT: a poset .. NOTE:: @@ -2647,9 +2569,7 @@ def union_update(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -2716,9 +2636,7 @@ def difference(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - A poset. + OUTPUT: a poset .. NOTE:: @@ -2769,9 +2687,7 @@ def difference_update(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -2818,9 +2734,7 @@ def intersection(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - A poset. + OUTPUT: a poset .. NOTE:: @@ -2867,9 +2781,7 @@ def intersection_update(self, *other): It is possible to specify more than one ``other`` as variadic arguments (arbitrary argument lists). - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -2912,9 +2824,7 @@ def symmetric_difference(self, other): - ``other`` -- a poset. - OUTPUT: - - A poset. + OUTPUT: a poset .. NOTE:: @@ -2954,9 +2864,7 @@ def symmetric_difference_update(self, other): - ``other`` -- a poset. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -3000,9 +2908,7 @@ def is_disjoint(self, other): - ``other`` -- a poset or an iterable. In the latter case the iterated objects are seen as elements of a poset. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -3048,9 +2954,7 @@ def is_subset(self, other): - ``other`` -- a poset or an iterable. In the latter case the iterated objects are seen as elements of a poset. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -3100,9 +3004,7 @@ def is_superset(self, other): - ``other`` -- a poset or an iterable. In the latter case the iterated objects are seen as elements of a poset. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -3163,9 +3065,7 @@ def merge(self, key=None, reverse=False): When ``key=None``, then this also specifies which elements are merged first. - OUTPUT: - - Nothing. + OUTPUT: nothing This method tests all (not necessarily direct) successors and predecessors of the given element whether they can be merged with @@ -3306,9 +3206,7 @@ def maximal_elements(self): Nothing. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -3337,9 +3235,7 @@ def minimal_elements(self): Nothing. - OUTPUT: - - An iterator. + OUTPUT: an iterator EXAMPLES:: @@ -3374,9 +3270,7 @@ def map(self, function, topological=False, reverse=False): - ``reverse`` -- is passed on to topological ordering. - OUTPUT: - - Nothing. + OUTPUT: nothing .. NOTE:: @@ -3438,9 +3332,7 @@ def mapped(self, function): - ``reverse`` -- is passed on to topological ordering. - OUTPUT: - - A :class:`MutablePoset`. + OUTPUT: a :class:`MutablePoset` .. NOTE:: diff --git a/src/sage/databases/cremona.py b/src/sage/databases/cremona.py index c556a64bdff..7d4ae278f16 100644 --- a/src/sage/databases/cremona.py +++ b/src/sage/databases/cremona.py @@ -1034,7 +1034,7 @@ def iter(self, conductors): - ``conductors`` -- list or generator of ints - OUTPUT: generator that iterates over EllipticCurve objects. + OUTPUT: generator that iterates over EllipticCurve objects EXAMPLES:: @@ -1118,9 +1118,7 @@ def iter_optimal(self, conductors): - ``conductors`` -- list or generator of ints - OUTPUT: - - generator that iterates over EllipticCurve objects. + OUTPUT: generator that iterates over EllipticCurve objects EXAMPLES: @@ -1179,9 +1177,7 @@ def list_optimal(self, conductors): - ``conductors`` -- list or generator of ints list of EllipticCurve objects. - OUTPUT: - - list of EllipticCurve objects. + OUTPUT: list of EllipticCurve objects EXAMPLES:: diff --git a/src/sage/databases/cubic_hecke_db.py b/src/sage/databases/cubic_hecke_db.py index 782d3c2f771..bbb58ceb025 100644 --- a/src/sage/databases/cubic_hecke_db.py +++ b/src/sage/databases/cubic_hecke_db.py @@ -239,9 +239,7 @@ def read(self, section, variables=None, nstrands=4): - ``section`` -- instance of enum :class:`CubicHeckeDataSection` to select the data to be read in - OUTPUT: - - A dictionary containing the data corresponding to the section. + OUTPUT: a dictionary containing the data corresponding to the section EXAMPLES:: @@ -310,8 +308,6 @@ def read_matrix_representation(self, representation_type, gen_ind, nstrands, rin :class:`~sage.algebras.hecke_algebras.cubic_hecke_matrix_rep.RepresentationType` specifying the type of the representation - OUTPUT: - EXAMPLES:: sage: from sage.databases.cubic_hecke_db import CubicHeckeDataBase @@ -418,9 +414,7 @@ def braid_tietze(self, strands_embed=None): - ``strands_embed`` -- (optional) the number of strands of the braid if strands should be added - OUTPUT: - - A tuple representing the braid in Tietze form. + OUTPUT: a tuple representing the braid in Tietze form EXAMPLES:: diff --git a/src/sage/databases/findstat.py b/src/sage/databases/findstat.py index cba955c68b3..fb69c30592b 100644 --- a/src/sage/databases/findstat.py +++ b/src/sage/databases/findstat.py @@ -922,9 +922,7 @@ def findstat(query=None, values=None, distribution=None, domain=None, collection, such as ``Permutations(3)``. The keyword arguments ``depth`` and ``max_values`` are passed to the finder. - OUTPUT: - - An instance of a :class:`FindStatStatistic`, represented by + OUTPUT: an instance of a :class:`FindStatStatistic`, represented by - the FindStat identifier together with its name, or @@ -1569,9 +1567,7 @@ def id(self): r""" Return the FindStat identifier of the statistic or map. - OUTPUT: - - The FindStat identifier of the statistic or map, as an integer. + OUTPUT: the FindStat identifier of the statistic or map, as an integer EXAMPLES:: @@ -1584,9 +1580,7 @@ def id_str(self): r""" Return the FindStat identifier of the statistic or map. - OUTPUT: - - The FindStat identifier of the statistic or map, as a string. + OUTPUT: the FindStat identifier of the statistic or map, as a string EXAMPLES:: @@ -1618,9 +1612,7 @@ def description(self): r""" Return the description of the statistic or map. - OUTPUT: - - A string. For statistics, the first line is used as name. + OUTPUT: a string. For statistics, the first line is used as name EXAMPLES:: @@ -1755,9 +1747,7 @@ def sage_code(self): r""" Return the Sage code associated with the statistic or map. - OUTPUT: - - An empty string or a string of the form:: + OUTPUT: an empty string or a string of the form:: def statistic(x): ... @@ -2286,9 +2276,9 @@ def code(self): r""" Return the code associated with the statistic or map. - OUTPUT: + OUTPUT: string - A string. Contributors are encouraged to submit Sage code in the form:: + Contributors are encouraged to submit Sage code in the form:: def statistic(x): ... @@ -3238,9 +3228,7 @@ def codomain(self): r""" Return the FindStat collection which is the codomain of the map. - OUTPUT: - - The codomain of the map as a :class:`FindStatCollection`. + OUTPUT: the codomain of the map as a :class:`FindStatCollection` EXAMPLES:: @@ -3254,9 +3242,7 @@ def properties_raw(self): r""" Return the properties of the map. - OUTPUT: - - The properties as a string. + OUTPUT: the properties as a string EXAMPLES:: @@ -3910,9 +3896,7 @@ def _finite_irreducible_cartan_types_by_rank(n): - n -- an integer. - OUTPUT: - - The list of Cartan types of rank n. + OUTPUT: the list of Cartan types of rank n TESTS:: @@ -3944,9 +3928,7 @@ def _plane_partitions_by_size_aux(n, outer=None): - n -- an integer. - OUTPUT: - - The plane partitions with `n` boxes as lists. + OUTPUT: the plane partitions with `n` boxes as lists TESTS:: @@ -3978,9 +3960,7 @@ def _plane_partitions_by_size(n): - n -- an integer. - OUTPUT: - - The plane partitions with `n` boxes. + OUTPUT: the plane partitions with `n` boxes TESTS:: @@ -4006,9 +3986,7 @@ def _finite_lattices(n): - n -- an integer. - OUTPUT: - - The lattices with `n` elements. + OUTPUT: the lattices with `n` elements TESTS:: @@ -4371,9 +4349,7 @@ def id(self): r""" Return the FindStat identifier of the collection. - OUTPUT: - - The FindStat identifier of the collection as an integer. + OUTPUT: the FindStat identifier of the collection as an integer EXAMPLES:: @@ -4388,9 +4364,7 @@ def id_str(self): r""" Return the FindStat identifier of the collection. - OUTPUT: - - The FindStat identifier of the collection as a string. + OUTPUT: the FindStat identifier of the collection as a string EXAMPLES:: @@ -4465,9 +4439,7 @@ def _repr_(self): r""" Return the representation of the FindStat collection. - OUTPUT: - - The representation, including the identifier and the name. + OUTPUT: the representation, including the identifier and the name EXAMPLES:: @@ -4488,9 +4460,7 @@ def name(self, style="singular"): - a string -- (default:"singular") can be "singular", or "plural". - OUTPUT: - - The name of the FindStat collection, in singular or in plural. + OUTPUT: the name of the FindStat collection, in singular or in plural EXAMPLES:: diff --git a/src/sage/databases/knotinfo_db.py b/src/sage/databases/knotinfo_db.py index dc21575d779..b3a035c4c97 100644 --- a/src/sage/databases/knotinfo_db.py +++ b/src/sage/databases/knotinfo_db.py @@ -660,9 +660,7 @@ def read_column_dict(self): r""" Read the dictionary for the column names from the according sobj-file - OUTPUT: - - A python dictionary containing the column names and types + OUTPUT: a Python dictionary containing the column names and types EXAMPLES:: @@ -737,9 +735,7 @@ def read_num_knots(self): Read the number of knots contained in the database (without proper links) from the according sobj-file. - OUTPUT: - - Integer + OUTPUT: integer EXAMPLES:: @@ -765,9 +761,7 @@ def read(self, column): - ``column`` -- instance of enum :class:`KnotInfoColumns` to select the data to be read in - OUTPUT: - - A python list containing the data corresponding to the column. + OUTPUT: a Python list containing the data corresponding to the column EXAMPLES:: diff --git a/src/sage/databases/oeis.py b/src/sage/databases/oeis.py index 03caa9cc36c..4b17a8fb6e0 100644 --- a/src/sage/databases/oeis.py +++ b/src/sage/databases/oeis.py @@ -1503,7 +1503,7 @@ def links(self, browse=None, format='guess'): - ``format`` -- string (default: 'guess'): how to display the links. - OUTPUT: Tuple of strings (with fancy formatting): + OUTPUT: tuple of strings (with fancy formatting): - if ``format`` is ``url``, returns a tuple of absolute links without description. - if ``format`` is ``html``, returns nothing but prints a tuple of clickable absolute links in their context. diff --git a/src/sage/doctest/control.py b/src/sage/doctest/control.py index cf9c32edd63..edafb400a5c 100644 --- a/src/sage/doctest/control.py +++ b/src/sage/doctest/control.py @@ -1099,9 +1099,7 @@ def source_baseline(self, source): - ``source`` -- a :class:`DocTestSource` instance - OUTPUT: - - A dictionary. + OUTPUT: a dictionary EXAMPLES:: diff --git a/src/sage/doctest/forker.py b/src/sage/doctest/forker.py index 069e03c197d..2c81993b6f2 100644 --- a/src/sage/doctest/forker.py +++ b/src/sage/doctest/forker.py @@ -253,7 +253,7 @@ def showwarning_with_traceback(message, category, filename, lineno, file=None, l INPUT: see :func:`warnings.showwarning`. - OUTPUT: None + OUTPUT: none EXAMPLES:: diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py index 2b682a24d40..9713713aee8 100644 --- a/src/sage/doctest/parsing.py +++ b/src/sage/doctest/parsing.py @@ -338,9 +338,7 @@ def _tag_group(tag): - ``tag`` -- string - OUTPUT: - - a string; one of ``'special'``, ``'optional'``, ``'standard'``, ``'sage'`` + OUTPUT: a string; one of ``'special'``, ``'optional'``, ``'standard'``, ``'sage'`` EXAMPLES:: @@ -1597,9 +1595,7 @@ def do_fixup(self, want, got): - ``want`` -- a string or :class:`MarkedOutput` - ``got`` -- a string - OUTPUT: - - A tuple: + OUTPUT: a tuple: - bool, ``True`` when some fixup were performed and ``False`` otherwise - string, edited wanted string diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py index a1e4bc1700d..bde00df6210 100644 --- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py @@ -819,9 +819,7 @@ def conjugate(self, M): - ``M`` -- a square invertible matrix - OUTPUT: - - An affine dynamical system + OUTPUT: an affine dynamical system EXAMPLES:: @@ -951,7 +949,7 @@ def reduce_base_field(self): the base ring is a number field, ``QQbar``, a finite field, or algebraic closure of a finite field. - OUTPUT: A dynamical system + OUTPUT: a dynamical system EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py index be1ef46b251..e81a9098734 100644 --- a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py @@ -345,7 +345,7 @@ def domain(self): """ Return the domain of this dynamical system. - OUTPUT: A Berkovich space over ``Cp``. + OUTPUT: a Berkovich space over ``Cp`` EXAMPLES:: @@ -361,7 +361,7 @@ def as_scheme_dynamical_system(self): r""" Return this dynamical system as :class:`DynamicalSystem`. - OUTPUT: An affine or projective :class:`DynamicalSystem`. + OUTPUT: an affine or projective :class:`DynamicalSystem` EXAMPLES:: @@ -382,7 +382,7 @@ def __getitem__(self, i): - ``i`` -- an integer. - OUTPUT: An element of polynomial ring or a + OUTPUT: an element of polynomial ring or a fraction field of a polynomial ring EXAMPLES:: @@ -399,7 +399,7 @@ def defining_polynomials(self): """ Return the defining polynomials. - OUTPUT: A tuple of polynomials that defines the + OUTPUT: a tuple of polynomials that defines the dynamical system. EXAMPLES:: @@ -417,7 +417,7 @@ def base_ring(self): """ The base ring of this dynamical system, that is, the field of definition of the coefficients. - OUTPUT: A field. + OUTPUT: a field EXAMPLES:: @@ -442,7 +442,7 @@ def _repr_(self): r""" Return a string representation of this dynamical system. - OUTPUT: a string. + OUTPUT: string EXAMPLES:: @@ -572,7 +572,7 @@ def scale_by(self, t): - ``t`` -- a ring element. - OUTPUT: None. + OUTPUT: none EXAMPLES:: @@ -604,7 +604,7 @@ def normalize_coordinates(self): r""" Normalizes the coordinates of the inducing map. - OUTPUT: None. + OUTPUT: none EXAMPLES:: @@ -657,7 +657,7 @@ def conjugate(self, M, adjugate=False, new_ideal=None): Used to specify an extension in the case where ``M`` is not defined over the same number field as this dynamical system. - OUTPUT: a dynamical system. + OUTPUT: a dynamical system EXAMPLES:: @@ -721,7 +721,7 @@ def resultant(self, normalize=False): - ``normalize`` -- (default: ``False``) boolean. - OUTPUT: an element of the base ring of this map. + OUTPUT: an element of the base ring of this map EXAMPLES:: @@ -754,7 +754,7 @@ def dehomogenize(self, n): - ``n`` -- a tuple of nonnegative integers; if ``n`` is an integer, then the two values of the tuple are assumed to be the same. - OUTPUT: A dynamical system on affine Berkovich space. + OUTPUT: a dynamical system on affine Berkovich space EXAMPLES:: @@ -787,7 +787,7 @@ def __call__(self, x, type_3_pole_check=True): poles of the dynamical system in the disk corresponding to the type III point ``x``. See Examples. - OUTPUT: A point of projective Berkovich space over ``Cp``. + OUTPUT: a point of projective Berkovich space over ``Cp`` EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/dynamical_semigroup.py b/src/sage/dynamics/arithmetic_dynamics/dynamical_semigroup.py index 93c402d4695..2f436ce4b1f 100644 --- a/src/sage/dynamics/arithmetic_dynamics/dynamical_semigroup.py +++ b/src/sage/dynamics/arithmetic_dynamics/dynamical_semigroup.py @@ -388,7 +388,7 @@ def __call__(self, input): - ``input`` -- one value that can be evaluated with the generators of this dynamical semigroup. - OUTPUT: A set of the resulting values after applying all of this dynamical semigroup's generators to ``input``. + OUTPUT: a set of the resulting values after applying all of this dynamical semigroup's generators to ``input`` EXAMPLES:: @@ -423,7 +423,7 @@ def base_ring(self): The base ring of this dynamical semigroup. This is identical to the base ring of all of its defining dynamical system. - OUTPUT: A ring. + OUTPUT: a ring EXAMPLES:: @@ -471,7 +471,7 @@ def domain(self): r""" Return the domain of the generators of this dynamical semigroup. - OUTPUT: A subscheme of a projective space or affine space. + OUTPUT: a subscheme of a projective space or affine space EXAMPLES:: @@ -486,7 +486,7 @@ def codomain(self): r""" Return the codomain of the generators of this dynamical semigroup. - OUTPUT: A subscheme of a projective space or affine space. + OUTPUT: a subscheme of a projective space or affine space EXAMPLES:: @@ -501,7 +501,7 @@ def defining_polynomials(self): r""" Return the set of polynomials that define the generators of this dynamical semigroup. - OUTPUT: A set of polynomials. + OUTPUT: a set of polynomials EXAMPLES:: @@ -519,7 +519,7 @@ def defining_systems(self): r""" Return the generators of this dynamical semigroup. - OUTPUT: A tuple of dynamical systems. + OUTPUT: a tuple of dynamical systems EXAMPLES:: @@ -643,7 +643,7 @@ def orbit(self, p, n): - `n` -- a nonnegative integer or a list or tuple of length 2 describing an interval of the number line containing entirely nonnegative integers - OUTPUT: a tuple of sets of values on the domain of this dynamical semigroup. + OUTPUT: a tuple of sets of values on the domain of this dynamical semigroup EXAMPLES:: @@ -759,7 +759,7 @@ def specialization(self, assignments): - `assignments` -- argument for specialization of the generators of this dynamical semigroup. - OUTPUT: a dynamical semigroup with the specialization of the generators of this dynamical semigroup. + OUTPUT: a dynamical semigroup with the specialization of the generators of this dynamical semigroup EXAMPLES:: @@ -1123,7 +1123,7 @@ def _repr_(self): r""" Return the :class:`String` representation of this dynamical semigroup. - OUTPUT: A :class:`String` displaying information about this dynamical semigroup. + OUTPUT: a :class:`String` displaying information about this dynamical semigroup EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py index d0d662dcc57..df7c2ed1169 100644 --- a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py +++ b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py @@ -2145,7 +2145,7 @@ def conjugating_set_helper(f, g, num_cpus, source, possible_targets): is a list of ``points`` which are possible targets for point(s) in ``source``. ``repeated`` specifies how many points in ``source`` have points in ``points`` as their possible target. - OUTPUT: a list of elements of PGL which conjugate ``f`` to ``g``. + OUTPUT: a list of elements of PGL which conjugate ``f`` to ``g`` EXAMPLES:: @@ -2289,7 +2289,7 @@ def is_conjugate_helper(f, g, num_cpus, source, possible_targets): is a list of ``points`` which are possible targets for point(s) in ``source``. ``repeated`` specifies how many points in ``source`` have points in ``points`` as their possible target. - OUTPUT: ``True`` if ``f`` is conjugate to ``g``, ``False`` otherwise. + OUTPUT: ``True`` if ``f`` is conjugate to ``g``, ``False`` otherwise EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py index 706bb28cbef..45b0215301f 100644 --- a/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py @@ -88,7 +88,7 @@ def _call_with_args(self, P, check=True): - ``check`` -- Boolean; whether or not to perform the input checks on the image point (Default: ``True``) - OUTPUT: The image point in the codomain + OUTPUT: the image point in the codomain EXAMPLES:: @@ -129,7 +129,7 @@ def nth_iterate(self, P, n, normalize=False): - ``normalize`` -- (default: ``False``) boolean - OUTPUT: A point in ``self.codomain()`` + OUTPUT: a point in ``self.codomain()`` EXAMPLES:: @@ -257,7 +257,7 @@ def nth_iterate_map(self, n): - ``n`` -- a positive integer - OUTPUT: A dynamical system of products of projective spaces + OUTPUT: a dynamical system of products of projective spaces EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py index 4b3ebd0d89a..c65c7e6230c 100644 --- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py @@ -161,7 +161,7 @@ class DynamicalSystem_projective(SchemeMorphism_polynomial_projective_space, 1-dimensional projective space over the base ring of ``morphism_or_polys`` with coordinate names given by ``names``. - OUTPUT: :class:`DynamicalSystem_projective`. + OUTPUT: :class:`DynamicalSystem_projective` EXAMPLES:: @@ -498,7 +498,7 @@ def _number_field_from_algebraics(self): r""" Return a dynamical system defined over the number field of its coefficients. - OUTPUT: dynamical system. + OUTPUT: dynamical system EXAMPLES:: @@ -3395,7 +3395,7 @@ def affine_preperiodic_model(self, m, n, return_conjugation=False): ``(g, phi)`` where ``g`` is a model with affine (n, m) preperiodic points and ``phi`` is the matrix that moves ``f`` to ``g``. - OUTPUT: a dynamical system conjugate to this one. + OUTPUT: a dynamical system conjugate to this one EXAMPLES:: @@ -6468,7 +6468,7 @@ def postcritical_set(self, check=True): - ``check`` -- (default: ``True``) boolean; whether to check if this dynamical system is postcritically finite or not. - OUTPUT: The set of postcritical points. + OUTPUT: the set of postcritical points EXAMPLES:: @@ -6535,7 +6535,7 @@ def is_chebyshev(self): r""" Check if ``self`` is a Chebyshev polynomial. - OUTPUT: True if ``self`` is Chebyshev, False otherwise. + OUTPUT: true if ``self`` is Chebyshev, False otherwise EXAMPLES:: @@ -7683,9 +7683,7 @@ def connected_rational_component(self, P, n=0): - ``n`` -- (default: 0) integer; maximum distance from ``P`` to branch out; a value of 0 indicates no bound - OUTPUT: - - A list of points connected to ``P`` up to the specified distance. + OUTPUT: a list of points connected to ``P`` up to the specified distance EXAMPLES:: @@ -7805,9 +7803,7 @@ def conjugating_set(self, other, R=None, num_cpus=2): - ``num_cpus`` -- (default: 2) the number of threads to run in parallel. Increasing ``num_cpus`` can potentially greatly speed up this function. - OUTPUT: - - Set of conjugating `n+1` by `n+1` matrices. + OUTPUT: set of conjugating `n+1` by `n+1` matrices AUTHORS: @@ -8583,9 +8579,7 @@ def potential_good_reduction(self, prime, return_conjugation=False): - ``return_conjugation`` -- (default: ``False``) if set to ``True``, the `PGL_2` map used to achieve good reduction will be returned - OUTPUT: - - A tuple: + OUTPUT: a tuple: - The first element is: - ``False`` if this dynamical system does not have potential good reduction. @@ -8773,7 +8767,7 @@ def reduce_base_field(self): the base ring is a number field, QQbar, a finite field, or algebraic closure of a finite field. - OUTPUT: A dynamical system + OUTPUT: a dynamical system EXAMPLES:: diff --git a/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py b/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py index 21d107dee4c..c7b63db6beb 100644 --- a/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py +++ b/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py @@ -434,7 +434,7 @@ def Lxa(self, a): - ``a`` -- Point in `\mathbb{P}^2` - OUTPUT: A polynomial representing the fiber + OUTPUT: a polynomial representing the fiber EXAMPLES:: @@ -472,7 +472,7 @@ def Qxa(self, a): INPUT: ``a`` -- Point in `\mathbb{P}^2` - OUTPUT: A polynomial representing the fiber + OUTPUT: a polynomial representing the fiber EXAMPLES:: @@ -511,7 +511,7 @@ def Sxa(self, a): - ``a`` -- Point in `\mathbb{P}^2` - OUTPUT: A subscheme representing the fiber + OUTPUT: a subscheme representing the fiber EXAMPLES:: @@ -547,7 +547,7 @@ def Lyb(self, b): INPUT: ``b`` -- Point in projective space - OUTPUT: A polynomial representing the fiber + OUTPUT: a polynomial representing the fiber EXAMPLES:: @@ -588,7 +588,7 @@ def Qyb(self, b): - ``b`` -- Point in projective space - OUTPUT: A polynomial representing the fiber + OUTPUT: a polynomial representing the fiber EXAMPLES:: @@ -626,7 +626,7 @@ def Syb(self, b): - ``b`` -- Point in `\mathbb{P}^2` - OUTPUT: A subscheme representing the fiber + OUTPUT: a subscheme representing the fiber EXAMPLES:: @@ -663,7 +663,7 @@ def Ramification_poly(self, i): INPUT: ``i`` -- Integer, either 0 (polynomial in y) or 1 (polynomial in x) - OUTPUT: Polynomial in the coordinate ring of the ambient space + OUTPUT: polynomial in the coordinate ring of the ambient space EXAMPLES:: @@ -776,7 +776,7 @@ def degenerate_fibers(self): This function finds the common solution through elimination via Groebner bases by using the .variety() function on the three affine charts in each component. - OUTPUT: The output is a list of lists where the elements of lists are + OUTPUT: the output is a list of lists where the elements of lists are points in the appropriate projective space. The first list is the points whose pullback by the projection to the first component (projective space) is dimension greater than 0. @@ -905,7 +905,7 @@ def degenerate_primes(self, check=True): is what is checked. The lcm of the coefficients of the monomials `x_i` in a Groebner basis is computed. This may return extra primes. - OUTPUT: List of primes. + OUTPUT: list of primes EXAMPLES:: @@ -1061,7 +1061,7 @@ def sigmaX(self, P, **kwds): - ``normalize`` -- (default: ``True``) boolean normalizes the point - OUTPUT: A point on the K3 surface + OUTPUT: a point on the K3 surface EXAMPLES:: @@ -1308,7 +1308,7 @@ def sigmaY(self,P, **kwds): - ``normalize`` -- (default: ``True``) boolean normalizes the point - OUTPUT: A point on the K3 surface + OUTPUT: a point on the K3 surface EXAMPLES:: @@ -1544,7 +1544,7 @@ def phi(self, a, **kwds): - ``normalize`` -- (default: ``True``) boolean normalizes the point - OUTPUT: A point on this surface + OUTPUT: a point on this surface EXAMPLES:: @@ -1584,7 +1584,7 @@ def psi(self,a, **kwds): - ``normalize`` -- (default: ``True``) boolean normalizes the point - OUTPUT: A point on this surface + OUTPUT: a point on this surface EXAMPLES:: @@ -1628,7 +1628,7 @@ def lambda_plus(self, P, v, N, m, n, prec=100): - ``prec`` -- (default: 100) float point or p-adic precision - OUTPUT: A real number + OUTPUT: a real number EXAMPLES:: @@ -1728,7 +1728,7 @@ def lambda_minus(self, P, v, N, m, n, prec=100): - ``prec`` -- (default: 100) float point or p-adic precision - OUTPUT: A real number + OUTPUT: a real number EXAMPLES:: @@ -1819,7 +1819,7 @@ def canonical_height_plus(self, P, N, badprimes=None, prec=100): - ``prec`` -- (default: 100) float point or p-adic precision - OUTPUT: A real number + OUTPUT: a real number EXAMPLES:: @@ -1883,7 +1883,7 @@ def canonical_height_minus(self, P, N, badprimes=None, prec=100): - ``prec`` -- (default: 100) float point or p-adic precision - OUTPUT: A real number + OUTPUT: a real number EXAMPLES:: @@ -1945,7 +1945,7 @@ def canonical_height(self, P, N, badprimes=None, prec=100): - ``prec`` -- (default: 100) float point or p-adic precision - OUTPUT: A real number + OUTPUT: a real number EXAMPLES:: @@ -1991,7 +1991,7 @@ def fiber(self, p, component): - ``p`` -- a point in `\mathbb{P}^2` - OUTPUT: The corresponding fiber (as a list) + OUTPUT: the corresponding fiber (as a list) EXAMPLES:: @@ -2173,7 +2173,7 @@ def nth_iterate_phi(self, P, n, **kwds): - ``normalize`` -- (default: ``False``) boolean normalizes the point - OUTPUT: The nth iterate of the point given the phi function (if ``n`` is positive), or the + OUTPUT: the nth iterate of the point given the phi function (if ``n`` is positive), or the psi function (if ``n`` is negative) EXAMPLES:: @@ -2238,7 +2238,7 @@ def nth_iterate_psi(self, P, n, **kwds): - ``normalize`` -- (default: ``False``) boolean, normalizes the point - OUTPUT: The nth iterate of the point given the psi function (if ``n`` is positive), + OUTPUT: the nth iterate of the point given the psi function (if ``n`` is positive), or the phi function (if ``n`` is negative) EXAMPLES:: @@ -2295,7 +2295,7 @@ def orbit_phi(self, P, N, **kwds): - ``normalize`` -- (default: ``False``) boolean, normalizes the point - OUTPUT: List of points in the orbit + OUTPUT: list of points in the orbit EXAMPLES:: @@ -2400,7 +2400,7 @@ def is_isomorphic(self, right): - ``right`` -- the K3 surface to compare to the original - OUTPUT: Boolean + OUTPUT: boolean EXAMPLES:: @@ -2439,7 +2439,7 @@ def is_symmetric_orbit(self,orbit): - ``orbit`` -- a periodic cycle of either psi or phi - OUTPUT: Boolean + OUTPUT: boolean EXAMPLES:: @@ -2493,7 +2493,7 @@ def cardinality( self): Enumerate points over `\mathbb{P}^2`, and then count the points on the fiber of each of those points. - OUTPUT: Integer -- total number of points on the surface + OUTPUT: integer -- total number of points on the surface EXAMPLES:: diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia.py b/src/sage/dynamics/complex_dynamics/mandel_julia.py index 00eb7d473eb..d1b7f3c7bac 100644 --- a/src/sage/dynamics/complex_dynamics/mandel_julia.py +++ b/src/sage/dynamics/complex_dynamics/mandel_julia.py @@ -444,9 +444,7 @@ def kneading_sequence(theta): - ``theta`` -- a rational number with odd denominator - OUTPUT: - - a string representing the kneading sequence of theta in RR/ZZ + OUTPUT: a string representing the kneading sequence of theta in RR/ZZ REFERENCES: diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx index 2cb446886e1..93126c6c6d8 100644 --- a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx +++ b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx @@ -208,9 +208,7 @@ cpdef fast_external_ray(double theta, long D=30, long S=10, long R=100, precision used by the Complex Field when using Newton's method to compute points on the external ray. - OUTPUT: - - List of tuples of Real Interval Field Elements. + OUTPUT: list of tuples of Real Interval Field Elements EXAMPLES:: @@ -306,9 +304,7 @@ cpdef convert_to_pixels(point_list, double x_0, double y_0, double width, - ``number_of_pixels`` -- long, width of image in pixels. - OUTPUT: - - List of tuples of integers representing pixels. + OUTPUT: list of tuples of integers representing pixels EXAMPLES:: @@ -349,9 +345,7 @@ cpdef get_line(start, end): - ``end`` -- tuple, ending point of line. - OUTPUT: - - List of tuples of integers approximating the line between two pixels. + OUTPUT: list of tuples of integers approximating the line between two pixels EXAMPLES:: diff --git a/src/sage/ext/fast_callable.pyx b/src/sage/ext/fast_callable.pyx index 9d2db75be3d..503eb7a6ca6 100644 --- a/src/sage/ext/fast_callable.pyx +++ b/src/sage/ext/fast_callable.pyx @@ -506,7 +506,7 @@ def _builder_and_stream(vars, domain): - ``domain`` -- a Sage parent or Python type or ``None``; if non-``None``, all arithmetic is done in that domain - OUTPUT: A :class:`Wrapper`, an class:`InstructionStream` + OUTPUT: a :class:`Wrapper`, an class:`InstructionStream` EXAMPLES:: diff --git a/src/sage/features/__init__.py b/src/sage/features/__init__.py index a5d5ff3c409..f808804247d 100644 --- a/src/sage/features/__init__.py +++ b/src/sage/features/__init__.py @@ -282,9 +282,7 @@ def resolution(self): Return a suggestion on how to make :meth:`is_present` pass if it did not pass. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: diff --git a/src/sage/features/all.py b/src/sage/features/all.py index a53d095c596..14d2480d520 100644 --- a/src/sage/features/all.py +++ b/src/sage/features/all.py @@ -50,7 +50,7 @@ def module_feature(module_name): - ``module_name`` -- string - OUTPUT: a :class:`Feature` or ``None``. + OUTPUT: a :class:`Feature` or ``None`` EXAMPLES:: @@ -93,7 +93,7 @@ def name_feature(name, toplevel=None): - ``toplevel`` -- a module or other namespace - OUTPUT: a :class:`Feature` or ``None``. + OUTPUT: a :class:`Feature` or ``None`` EXAMPLES:: diff --git a/src/sage/functions/piecewise.py b/src/sage/functions/piecewise.py index 677f5a06bd4..6538eb462fd 100644 --- a/src/sage/functions/piecewise.py +++ b/src/sage/functions/piecewise.py @@ -168,9 +168,7 @@ def _print_(self, parameters, variable): """ Return a string representation - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -241,9 +239,7 @@ def in_operands(ex): - ``ex`` -- a symbolic expression. - OUTPUT: - - Boolean + OUTPUT: boolean EXAMPLES:: @@ -416,9 +412,7 @@ def __len__(self, parameters, variable): """ Return the number of "pieces" - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -435,9 +429,7 @@ def expressions(self, parameters, variable): See also :meth:`~domains`. - OUTPUT: - - The collection of expressions of the component functions. + OUTPUT: the collection of expressions of the component functions EXAMPLES:: @@ -530,9 +522,7 @@ def restriction(self, parameters, variable, restricted_domain): :class:`~sage.sets.real_set.RealSet` or something that defines one. - OUTPUT: - - A new piecewise function obtained by restricting the domain. + OUTPUT: a new piecewise function obtained by restricting the domain EXAMPLES:: diff --git a/src/sage/functions/spike_function.py b/src/sage/functions/spike_function.py index c2fb6113e39..7e529f047e6 100644 --- a/src/sage/functions/spike_function.py +++ b/src/sage/functions/spike_function.py @@ -36,9 +36,7 @@ class SpikeFunction: - ``eps`` -- parameter that determines approximation to a true spike - OUTPUT: - - a function with spikes at each point ``x`` in ``v`` with the given height. + OUTPUT: a function with spikes at each point ``x`` in ``v`` with the given height EXAMPLES:: diff --git a/src/sage/games/hexad.py b/src/sage/games/hexad.py index ddc08530b08..20e8226a0e2 100644 --- a/src/sage/games/hexad.py +++ b/src/sage/games/hexad.py @@ -408,9 +408,7 @@ def find_hexad2(self, pts, x0): any "points at infinity" - ``x0`` -- in ``{MINIMOG[0][2], MINIMOG[2][1], MINIMOG[0][0]}`` - OUTPUT: - - hexad containing `S \cup \{x0\}` of type 2 + OUTPUT: hexad containing `S \cup \{x0\}` of type 2 EXAMPLES:: @@ -494,9 +492,7 @@ def find_hexad(self, pts): - ``pts`` -- a list S of 5 elements of MINIMOG - OUTPUT: - - hexad containing `S \cup \{x0\}` of some type + OUTPUT: hexad containing `S \cup \{x0\}` of some type .. NOTE:: diff --git a/src/sage/games/quantumino.py b/src/sage/games/quantumino.py index fa0a013ff6a..bce04348050 100644 --- a/src/sage/games/quantumino.py +++ b/src/sage/games/quantumino.py @@ -215,9 +215,7 @@ def show_pentaminos(box=(5,8,2)): - ``box`` -- tuple of size three (default: ``(5,8,2)``), size of the box - OUTPUT: - - 3D Graphic object + OUTPUT: 3D Graphic object EXAMPLES:: @@ -348,9 +346,7 @@ def show3d(self, size=0.85): r""" Return the solution as a 3D Graphic object. - OUTPUT: - - 3D Graphic Object + OUTPUT: 3D Graphic Object EXAMPLES:: @@ -484,9 +480,7 @@ def solve(self, partial=None): - ``'common'`` -- common part between two consecutive solutions - ``'incremental'`` -- one piece change at a time - OUTPUT: - - iterator of QuantuminoState + OUTPUT: iterator of QuantuminoState EXAMPLES: @@ -574,9 +568,7 @@ def number_of_solutions(self): r""" Return the number of solutions. - OUTPUT: - - integer + OUTPUT: integer EXAMPLES:: diff --git a/src/sage/games/sudoku.py b/src/sage/games/sudoku.py index d8cfb504e14..1442f296727 100644 --- a/src/sage/games/sudoku.py +++ b/src/sage/games/sudoku.py @@ -732,9 +732,7 @@ def dlx(self, count_only=False): simply generate ``None`` for each solution, so the calling routine can count these. - OUTPUT: - - A generator that iterates over all the solutions. + OUTPUT: a generator that iterates over all the solutions This function is intended to be called from the :func:`~sage.games.sudoku.Sudoku.solve` method diff --git a/src/sage/geometry/cone.py b/src/sage/geometry/cone.py index 1b25726832c..fbb01405bb8 100644 --- a/src/sage/geometry/cone.py +++ b/src/sage/geometry/cone.py @@ -507,9 +507,7 @@ def _Cone_from_PPL(cone, lattice, original_rays=None): and ``original_rays`` were given, they will be used as internal rays of the constructed cone, in the given order. - OUTPUT: - - A :class:`ConvexRationalPolyhedralCone`. + OUTPUT: a :class:`ConvexRationalPolyhedralCone` TESTS:: @@ -837,9 +835,7 @@ def __richcmp__(self, right, op): - ``right`` -- anything. - OUTPUT: - - boolean + OUTPUT: boolean There is equality if ``right`` is of the same type as ``self``, they have the same ambient lattices, and their @@ -1185,9 +1181,7 @@ def codim(self): difference between the dimension of the ambient space and the dimension of the subspace spanned by those rays (of the cone/fan). - OUTPUT: - - A nonnegative integer representing the codimension of ``self``. + OUTPUT: a nonnegative integer representing the codimension of ``self`` .. SEEALSO:: @@ -1280,9 +1274,7 @@ def span(self, base_ring=None): - ``base_ring`` -- (default: from lattice) the base ring to use for the generated module. - OUTPUT: - - A module spanned by the generators of ``self``. + OUTPUT: a module spanned by the generators of ``self`` EXAMPLES: @@ -1552,9 +1544,7 @@ def _PPL_cone(self): r""" Returns the Parma Polyhedra Library (PPL) representation of the cone. - OUTPUT: - - A :class:`~ppl.polyhedron.C_Polyhedron` representing the cone. + OUTPUT: a :class:`~ppl.polyhedron.C_Polyhedron` representing the cone EXAMPLES:: @@ -1944,9 +1934,7 @@ def __richcmp__(self, right, op): - ``right`` -- anything. - OUTPUT: - - boolean + OUTPUT: boolean There is equality if ``self`` and ``right`` are cones of any kind in the same lattice with the same rays listed in the @@ -4660,9 +4648,7 @@ def is_solid(self): An alias is :meth:`is_full_dimensional`. - OUTPUT: - - ``True`` if this cone is solid, and ``False`` otherwise. + OUTPUT: ``True`` if this cone is solid, and ``False`` otherwise .. SEEALSO:: @@ -4709,9 +4695,7 @@ def is_proper(self): convex; therefore it is proper if it is solid and contains no lines. - OUTPUT: - - ``True`` if this cone is proper, and ``False`` otherwise. + OUTPUT: ``True`` if this cone is proper, and ``False`` otherwise .. SEEALSO:: @@ -4865,9 +4849,7 @@ def is_relatively_open(self): r""" Return whether ``self`` is relatively open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -5131,9 +5113,7 @@ def lyapunov_rank(self): the dimension of the Lie algebra of the automorphism group of the cone. - OUTPUT: - - A nonnegative integer representing the Lyapunov rank of this cone. + OUTPUT: a nonnegative integer representing the Lyapunov rank of this cone If the ambient space is trivial, then the Lyapunov rank will be zero. On the other hand, if the dimension of the ambient vector @@ -6473,9 +6453,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None, cone solid. Specify ``True`` for a solid cone, ``False`` for a non-solid cone, or ``None`` if you don't care. - OUTPUT: - - A new, randomly generated cone. + OUTPUT: a new, randomly generated cone A :class:`ValueError` will be thrown under the following conditions: diff --git a/src/sage/geometry/cone_critical_angles.py b/src/sage/geometry/cone_critical_angles.py index 3e39102426a..4dbfc93b08f 100644 --- a/src/sage/geometry/cone_critical_angles.py +++ b/src/sage/geometry/cone_critical_angles.py @@ -626,9 +626,7 @@ def compute_gevp_M(gs, hs): - ``hs`` -- a linearly independent list of unit-norm generators for the cone `Q` - OUTPUT: - - A tuple containing four elements, in order: + OUTPUT: a tuple containing four elements, in order: - The matrix `M` described in Proposition 6 diff --git a/src/sage/geometry/convex_set.py b/src/sage/geometry/convex_set.py index dd7237f0e30..b6d63f12f91 100644 --- a/src/sage/geometry/convex_set.py +++ b/src/sage/geometry/convex_set.py @@ -45,9 +45,7 @@ def is_empty(self): r""" Test whether ``self`` is the empty set. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -62,9 +60,7 @@ def is_finite(self): r""" Test whether ``self`` is a finite set. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -87,9 +83,7 @@ def cardinality(self): """ Return the cardinality of this set. - OUTPUT: - - Either an integer or ``Infinity``. + OUTPUT: either an integer or ``Infinity`` EXAMPLES:: @@ -116,9 +110,7 @@ def is_universe(self): r""" Test whether ``self`` is the whole ambient space. - OUTPUT: - - Boolean. + OUTPUT: boolean TESTS:: @@ -482,9 +474,7 @@ def is_open(self): The default implementation of this method only knows that the empty set and the ambient space are open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -509,9 +499,7 @@ def is_relatively_open(self): sets are also relatively open, and in addition singletons are relatively open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -535,9 +523,7 @@ def is_closed(self): The default implementation of this method only knows that the empty set, a singleton set, and the ambient space are closed. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -560,9 +546,7 @@ def is_compact(self): non-closed set cannot be compact, and that the empty set and a singleton set are compact. - OUTPUT: - - Boolean. + OUTPUT: boolean sage: from sage.geometry.convex_set import ConvexSet_base sage: class ExampleSet(ConvexSet_base): @@ -627,9 +611,7 @@ def representative_point(self): """ Return a "generic" point of ``self``. - OUTPUT: - - A point in the relative interior of ``self`` as a coordinate vector. + OUTPUT: a point in the relative interior of ``self`` as a coordinate vector EXAMPLES:: @@ -790,9 +772,7 @@ def cartesian_product(self, other): - ``other`` -- another convex set - OUTPUT: - - The Cartesian product of ``self`` and ``other``. + OUTPUT: the Cartesian product of ``self`` and ``other`` TESTS:: @@ -908,9 +888,7 @@ def intersection(self, other): - ``other`` -- another convex set - OUTPUT: - - The intersection. + OUTPUT: the intersection TESTS:: @@ -998,9 +976,7 @@ def is_closed(self): r""" Return whether ``self`` is closed. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1014,9 +990,7 @@ def is_open(self): r""" Return whether ``self`` is open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1040,9 +1014,7 @@ def is_universe(self): r""" Return whether ``self`` is the whole ambient space - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1060,9 +1032,7 @@ def is_compact(self): r""" Return whether ``self`` is compact. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1084,9 +1054,7 @@ def is_relatively_open(self): r""" Return whether ``self`` is relatively open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1101,9 +1069,7 @@ def is_open(self): r""" Return whether ``self`` is open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1124,9 +1090,7 @@ def is_open(self): r""" Return whether ``self`` is open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -1141,9 +1105,7 @@ def is_closed(self): r""" Return whether ``self`` is closed. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/fan.py b/src/sage/geometry/fan.py index ccbb9488470..c149a1257f2 100644 --- a/src/sage/geometry/fan.py +++ b/src/sage/geometry/fan.py @@ -271,9 +271,7 @@ def is_Fan(x) -> bool: - ``x`` -- anything. - OUTPUT: - - ``True`` if ``x`` is a fan and ``False`` otherwise + OUTPUT: ``True`` if ``x`` is a fan and ``False`` otherwise EXAMPLES:: @@ -376,9 +374,7 @@ def Fan(cones, rays=None, lattice=None, check=True, normalize=True, union of the cones in the polyhedral fan equals to the union of the given cones, and each given cone is the union of some cones in the polyhedral fan. - OUTPUT: - - a :class:`fan ` + OUTPUT: a :class:`fan ` .. SEEALSO:: @@ -694,9 +690,7 @@ def FaceFan(polytope, lattice=None): other object that behaves like these. If not specified, an attempt will be made to determine an appropriate toric lattice automatically. - OUTPUT: - - :class:`rational polyhedral fan ` + OUTPUT: :class:`rational polyhedral fan ` See also :func:`NormalFan`. @@ -802,9 +796,7 @@ def NormalFan(polytope, lattice=None): other object that behaves like these. If not specified, an attempt will be made to determine an appropriate toric lattice automatically. - OUTPUT: - - :class:`rational polyhedral fan ` + OUTPUT: :class:`rational polyhedral fan ` See also :func:`FaceFan`. @@ -1026,9 +1018,7 @@ class Cone_of_fan(ConvexRationalPolyhedralCone): - ``ambient_ray_indices`` -- increasing list or tuple of integers, indices of rays of ``ambient`` generating this cone. - OUTPUT: - - cone of ``ambient`` + OUTPUT: cone of ``ambient`` EXAMPLES: @@ -1067,9 +1057,7 @@ def _repr_(self) -> str: r""" Return a string representation of ``self``. - OUTPUT: - - string + OUTPUT: string TESTS:: @@ -1089,9 +1077,7 @@ def star_generator_indices(self): Return indices of generating cones of the "ambient fan" containing ``self``. - OUTPUT: - - increasing :class:`tuple` of integers + OUTPUT: increasing :class:`tuple` of integers EXAMPLES:: @@ -1141,9 +1127,7 @@ def star_generators(self): Return indices of generating cones of the "ambient fan" containing ``self``. - OUTPUT: - - increasing :class:`tuple` of integers + OUTPUT: increasing :class:`tuple` of integers EXAMPLES:: @@ -1309,9 +1293,7 @@ def __richcmp__(self, right, op): - ``right`` -- anything. - OUTPUT: - - boolean + OUTPUT: boolean There is equality if ``right`` is also a fan, their rays are the same and stored in the same order, and their generating @@ -1372,9 +1354,7 @@ def __iter__(self): r""" Return an iterator over generating cones of ``self``. - OUTPUT: - - iterator + OUTPUT: iterator TESTS:: @@ -1735,9 +1715,7 @@ def common_refinement(self, other): - ``other`` -- a :class:`fan ` in the same :meth:`lattice` and with the same support as this fan - OUTPUT: - - a :class:`fan ` + OUTPUT: a :class:`fan ` EXAMPLES: @@ -1791,9 +1769,7 @@ def _latex_(self) -> str: r""" Return a LaTeX representation of ``self``. - OUTPUT: - - string + OUTPUT: string TESTS:: @@ -1848,9 +1824,7 @@ def _repr_(self) -> str: r""" Return a string representation of ``self``. - OUTPUT: - - string + OUTPUT: string TESTS:: @@ -1884,9 +1858,7 @@ def _subdivide_stellar(self, new_rays, verbose): - ``verbose`` -- if ``True``, some timing information will be printed. - OUTPUT: - - rational polyhedral fan + OUTPUT: rational polyhedral fan TESTS:: @@ -2180,9 +2152,7 @@ def __getstate__(self): r""" Return the dictionary that should be pickled. - OUTPUT: - - :class:`dict` + OUTPUT: :class:`dict` TESTS:: @@ -2456,9 +2426,7 @@ def Gale_transform(self): r""" Return the Gale transform of ``self``. - OUTPUT: - - A matrix over `ZZ` + OUTPUT: a matrix over `ZZ` EXAMPLES:: @@ -2481,9 +2449,7 @@ def generating_cone(self, n): - ``n`` -- integer, the index of a generating cone. - OUTPUT: - - :class:`cone of fan` + OUTPUT: :class:`cone of fan` EXAMPLES:: @@ -2497,9 +2463,7 @@ def generating_cones(self): r""" Return generating cones of ``self``. - OUTPUT: - - :class:`tuple` of :class:`cones of fan` + OUTPUT: :class:`tuple` of :class:`cones of fan` EXAMPLES:: @@ -2572,9 +2536,7 @@ def is_complete(self) -> bool: A rational polyhedral fan is *complete* if its cones fill the whole space. - OUTPUT: - - ``True`` if ``self`` is complete and ``False`` otherwise + OUTPUT: ``True`` if ``self`` is complete and ``False`` otherwise EXAMPLES:: @@ -2755,9 +2717,7 @@ def _2d_echelon_forms(self): """ Return all echelon forms of the cyclically ordered rays of a 2-d fan. - OUTPUT: - - A set of integer matrices + OUTPUT: a set of integer matrices EXAMPLES:: @@ -2777,9 +2737,7 @@ def _2d_echelon_form(self): """ Return the echelon form of one particular cyclic order of rays of a 2-d fan. - OUTPUT: - - An integer matrix whose columns are the rays in the echelon form + OUTPUT: an integer matrix whose columns are the rays in the echelon form EXAMPLES:: @@ -2843,9 +2801,7 @@ def is_simplicial(self) -> bool: i.e. primitive vectors along generating rays of every cone form a part of a *rational* basis of the ambient space. - OUTPUT: - - ``True`` if ``self`` is simplicial and ``False`` otherwise + OUTPUT: ``True`` if ``self`` is simplicial and ``False`` otherwise EXAMPLES:: @@ -2962,9 +2918,7 @@ def ngenerating_cones(self): r""" Return the number of generating cones of ``self``. - OUTPUT: - - integer + OUTPUT: integer EXAMPLES:: @@ -2988,9 +2942,7 @@ def plot(self, **options): - any options for toric plots (see :func:`toric_plotter.options `), none are mandatory. - OUTPUT: - - a plot + OUTPUT: a plot EXAMPLES:: @@ -3435,9 +3387,7 @@ def toric_variety(self, *args, **kwds): same arguments as :func:`~sage.schemes.toric.variety.ToricVariety` - OUTPUT: - - a toric variety + OUTPUT: a toric variety This is equivalent to the command ``ToricVariety(self)`` and is provided only as a convenient alternative method to go from the @@ -3653,9 +3603,7 @@ def _refine_arrangement_to_fan(cones): - ``cones`` -- a list of rational cones that are possibly overlapping. - OUTPUT: - - a list of refined cones + OUTPUT: a list of refined cones EXAMPLES:: diff --git a/src/sage/geometry/fan_morphism.py b/src/sage/geometry/fan_morphism.py index 7ef46b80d17..4804c683bfd 100644 --- a/src/sage/geometry/fan_morphism.py +++ b/src/sage/geometry/fan_morphism.py @@ -1484,9 +1484,7 @@ def is_dominant(self): of toric varieties is dominant in the algebraic-geometric sense (that is, surjective onto a dense subset). - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py b/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py index 89e73b83a07..49867d73b09 100644 --- a/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py +++ b/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py @@ -539,9 +539,7 @@ def fixed_point_set(self): Return a list containing the fixed point set of orientation-preserving isometries. - OUTPUT: - - list of hyperbolic points or a hyperbolic geodesic + OUTPUT: list of hyperbolic points or a hyperbolic geodesic EXAMPLES:: @@ -761,9 +759,7 @@ def fixed_point_set(self): # UHP Return a list or geodesic containing the fixed point set of orientation-preserving isometries. - OUTPUT: - - list of hyperbolic points or a hyperbolic geodesic + OUTPUT: list of hyperbolic points or a hyperbolic geodesic EXAMPLES:: diff --git a/src/sage/geometry/hyperplane_arrangement/affine_subspace.py b/src/sage/geometry/hyperplane_arrangement/affine_subspace.py index 7c1065553c4..94d004f987f 100644 --- a/src/sage/geometry/hyperplane_arrangement/affine_subspace.py +++ b/src/sage/geometry/hyperplane_arrangement/affine_subspace.py @@ -82,9 +82,7 @@ class AffineSubspace(SageObject): - ``V`` -- vector subspace - OUTPUT: - - Affine subspace parallel to ``V`` and passing through ``p``. + OUTPUT: affine subspace parallel to ``V`` and passing through ``p`` EXAMPLES:: @@ -136,9 +134,7 @@ def _repr_(self): r""" String representation for an :class:`AffineSubspace`. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -159,9 +155,7 @@ def __eq__(self, other): - ``other`` -- an :class:`AffineSubspace` - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -186,9 +180,7 @@ def __ne__(self, other): - ``other`` -- an :class:`AffineSubspace` - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -212,9 +204,7 @@ def __le__(self, other): - ``other`` -- an :class:`AffineSubspace` - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -243,9 +233,7 @@ def __lt__(self, other): - ``other`` -- an :class:`AffineSubspace` - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -274,9 +262,7 @@ def __contains__(self, q): - ``q`` -- point as a list/tuple/iterable - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -294,9 +280,7 @@ def linear_part(self): r""" Return the linear part of the affine space. - OUTPUT: - - A vector subspace of the ambient space. + OUTPUT: a vector subspace of the ambient space EXAMPLES:: @@ -316,9 +300,7 @@ def point(self): r""" Return a point ``p`` in the affine space. - OUTPUT: - - A point of the affine space as a vector in the ambient space. + OUTPUT: a point of the affine space as a vector in the ambient space EXAMPLES:: @@ -333,9 +315,7 @@ def dimension(self): r""" Return the dimension of the affine space. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: diff --git a/src/sage/geometry/hyperplane_arrangement/arrangement.py b/src/sage/geometry/hyperplane_arrangement/arrangement.py index fa526356278..6aa47557297 100644 --- a/src/sage/geometry/hyperplane_arrangement/arrangement.py +++ b/src/sage/geometry/hyperplane_arrangement/arrangement.py @@ -423,9 +423,7 @@ def _first_ngens(self, n): """ Workaround to support the construction with names. - INPUT/OUTPUT: - - See :meth:`HyperplaneArrangements._first_ngens`. + INPUT/OUTPUT: see :meth:`HyperplaneArrangements._first_ngens` EXAMPLES:: @@ -474,9 +472,7 @@ def n_hyperplanes(self): r""" Return the number of hyperplanes in the arrangement. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -495,9 +491,7 @@ def hyperplanes(self): r""" Return the hyperplanes in the arrangement as a tuple. - OUTPUT: - - A tuple + OUTPUT: a tuple EXAMPLES:: @@ -517,9 +511,7 @@ def _repr_(self): r""" String representation for a hyperplane arrangement. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -543,9 +535,7 @@ def dimension(self): """ Return the ambient space dimension of the arrangement. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -599,9 +589,7 @@ def backend(self): """ Return the backend used for polyhedral objects - OUTPUT: - - A string giving the backend or ``None`` if none is specified. + OUTPUT: a string giving the backend or ``None`` if none is specified EXAMPLES: @@ -648,9 +636,7 @@ def union(self, other): - ``other`` -- a hyperplane arrangement or something that can be converted into a hyperplane arrangement - OUTPUT: - - A new hyperplane arrangement. + OUTPUT: a new hyperplane arrangement EXAMPLES:: @@ -689,9 +675,7 @@ def plot(self, **kwds): """ Plot the hyperplane arrangement. - OUTPUT: - - A graphics object. + OUTPUT: a graphics object EXAMPLES:: @@ -930,9 +914,7 @@ def characteristic_polynomial(self): r""" Return the characteristic polynomial of the hyperplane arrangement. - OUTPUT: - - The characteristic polynomial in `\QQ[x]`. + OUTPUT: the characteristic polynomial in `\QQ[x]` EXAMPLES:: @@ -970,9 +952,7 @@ def poincare_polynomial(self): r""" Return the Poincaré polynomial of the hyperplane arrangement. - OUTPUT: - - The Poincaré polynomial in `\QQ[x]`. + OUTPUT: the Poincaré polynomial in `\QQ[x]` EXAMPLES:: @@ -1002,9 +982,7 @@ def cocharacteristic_polynomial(self): element of `L` (here, the `0` dimensional subspace), and `\mu` is the Möbius function of `L`. - OUTPUT: - - The cocharacteristic polynomial in `\ZZ[z]`. + OUTPUT: the cocharacteristic polynomial in `\ZZ[z]` EXAMPLES:: @@ -1052,9 +1030,7 @@ def primitive_eulerian_polynomial(self): element of `L` (here, the `0` dimensional subspace), and `\mu` is the Möbius function of `L`. - OUTPUT: - - The primitive Eulerian polynomial in `\ZZ[z]`. + OUTPUT: the primitive Eulerian polynomial in `\ZZ[z]` EXAMPLES:: @@ -1357,9 +1333,7 @@ def n_regions(self): r""" The number of regions of the hyperplane arrangement. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -1448,9 +1422,7 @@ def has_good_reduction(self, p): - ``p`` -- prime number - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -1480,9 +1452,7 @@ def is_linear(self): r""" Test whether all hyperplanes pass through the origin. - OUTPUT: - - A boolean. Whether all the hyperplanes pass through the origin. + OUTPUT: a boolean. Whether all the hyperplanes pass through the origin EXAMPLES:: @@ -1513,9 +1483,7 @@ def is_essential(self): :meth:`essentialization` - OUTPUT: - - A boolean indicating whether the hyperplane arrangement is essential. + OUTPUT: a boolean indicating whether the hyperplane arrangement is essential EXAMPLES:: @@ -1541,9 +1509,7 @@ def is_central(self, certificate=False): to return the center as a polyhedron (possibly empty) as part of the output - OUTPUT: - - If ``certificate`` is ``True``, returns a tuple containing: + OUTPUT: if ``certificate`` is ``True``, returns a tuple containing: 1. A boolean 2. The polyhedron defined to be the intersection of all the hyperplanes @@ -1612,9 +1578,7 @@ def center(self): ambient space of the arrangement that lie on all of the hyperplanes. - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES: @@ -1650,9 +1614,7 @@ def is_simplicial(self): are linearly independent. A hyperplane arrangement is said to be simplicial if every region is simplicial. - OUTPUT: - - A boolean whether the hyperplane arrangement is simplicial. + OUTPUT: a boolean whether the hyperplane arrangement is simplicial EXAMPLES:: @@ -1820,9 +1782,7 @@ def face_vector(self): r""" Return the face vector. - OUTPUT: - - A vector of integers. + OUTPUT: a vector of integers The `d`-th entry is the number of faces of dimension `d`. A *face* is the intersection of a region with a hyperplane of @@ -2008,9 +1968,7 @@ def regions(self): The base field must have characteristic zero. - OUTPUT: - - A tuple containing the regions as polyhedra. + OUTPUT: a tuple containing the regions as polyhedra The regions are the connected components of the complement of the union of the hyperplanes as a subset of `\RR^n`. @@ -2189,9 +2147,7 @@ def poset_of_regions(self, B=None, numbered_labels=True): then the elements of the poset are numbered. Else they are labelled with the regions themselves. - OUTPUT: - - A Poset object containing the poset of regions. + OUTPUT: a Poset object containing the poset of regions EXAMPLES:: @@ -3111,9 +3067,7 @@ def distance_between_regions(self, region1, region2): - ``region1``, ``region2`` -- regions of the arrangement or representative points of regions - OUTPUT: - - An integer. The number of hyperplanes separating the two regions. + OUTPUT: an integer. The number of hyperplanes separating the two regions EXAMPLES:: @@ -3174,9 +3128,7 @@ def varchenko_matrix(self, names='h'): - ``names`` -- string or list/tuple/iterable of strings. The variable names for the polynomial ring `S`. - OUTPUT: - - The Varchenko matrix. + OUTPUT: the Varchenko matrix EXAMPLES:: @@ -3683,9 +3635,7 @@ def base_ring(self): """ Return the base ring. - OUTPUT: - - The base ring of the hyperplane arrangement. + OUTPUT: the base ring of the hyperplane arrangement EXAMPLES:: @@ -3746,9 +3696,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -3864,9 +3812,7 @@ def ngens(self): """ Return the number of linear variables. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -3883,9 +3829,7 @@ def gens(self) -> tuple: """ Return the coordinate hyperplanes. - OUTPUT: - - A tuple of linear expressions, one for each linear variable. + OUTPUT: a tuple of linear expressions, one for each linear variable EXAMPLES:: @@ -3905,9 +3849,7 @@ def gen(self, i): - ``i`` -- integer - OUTPUT: - - A linear expression. + OUTPUT: a linear expression EXAMPLES:: diff --git a/src/sage/geometry/hyperplane_arrangement/hyperplane.py b/src/sage/geometry/hyperplane_arrangement/hyperplane.py index b7f493d9acb..70d82b1b640 100644 --- a/src/sage/geometry/hyperplane_arrangement/hyperplane.py +++ b/src/sage/geometry/hyperplane_arrangement/hyperplane.py @@ -166,9 +166,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -182,9 +180,7 @@ def _latex_(self): r""" Return a LaTeX representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -208,9 +204,7 @@ def normal(self): """ Return the normal vector. - OUTPUT: - - A vector over the base ring. + OUTPUT: a vector over the base ring EXAMPLES:: @@ -228,9 +222,7 @@ def _normal_pivot(self): """ Return the index of the largest entry of the normal vector. - OUTPUT: - - An integer. The index of the largest entry. + OUTPUT: an integer. The index of the largest entry EXAMPLES:: @@ -265,9 +257,7 @@ def __contains__(self, q): - ``q`` -- point (as a vector, list, or tuple) - OUTPUT: - - A boolean. + OUTPUT: boolean EXAMPLES:: @@ -287,9 +277,7 @@ def polyhedron(self, **kwds): """ Return the hyperplane as a polyhedron. - OUTPUT: - - A :func:`~sage.geometry.polyhedron.constructor.Polyhedron` instance. + OUTPUT: a :func:`~sage.geometry.polyhedron.constructor.Polyhedron` instance EXAMPLES:: @@ -426,9 +414,7 @@ def dimension(self): r""" The dimension of the hyperplane. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -448,9 +434,7 @@ def intersection(self, other): - ``other`` -- a hyperplane, a polyhedron, or something that defines a polyhedron - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES:: @@ -634,9 +618,7 @@ def plot(self, **kwds): """ Plot the hyperplane. - OUTPUT: - - A graphics object. + OUTPUT: a graphics object EXAMPLES:: @@ -716,9 +698,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -736,9 +716,7 @@ def dimension(self): """ Return the ambient space dimension. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -760,9 +738,7 @@ def change_ring(self, base_ring): - ``base_ring`` -- a ring; the new base ring - OUTPUT: - - A new :class:`AmbientVectorSpace`. + OUTPUT: a new :class:`AmbientVectorSpace` EXAMPLES:: diff --git a/src/sage/geometry/hyperplane_arrangement/library.py b/src/sage/geometry/hyperplane_arrangement/library.py index 085cdd32e21..8aa58d192cc 100644 --- a/src/sage/geometry/hyperplane_arrangement/library.py +++ b/src/sage/geometry/hyperplane_arrangement/library.py @@ -367,9 +367,7 @@ def G_Shi(self, G, K=QQ, names=None): - ``names`` -- tuple of strings or ``None`` (default); the variable names for the ambient space - OUTPUT: - - The Shi hyperplane arrangement of the given graph ``G``. + OUTPUT: the Shi hyperplane arrangement of the given graph ``G`` EXAMPLES:: @@ -519,9 +517,7 @@ def IshB(self, n, K=QQ, names=None): - ``names`` -- tuple of strings or ``None`` (default); the variable names for the ambient space - OUTPUT: - - The type `B` Ish arrangement, which is the set of `2n^2` hyperplanes + OUTPUT: the type `B` Ish arrangement, which is the set of `2n^2` hyperplanes .. MATH:: diff --git a/src/sage/geometry/hyperplane_arrangement/ordered_arrangement.py b/src/sage/geometry/hyperplane_arrangement/ordered_arrangement.py index bb16768e13b..eaf5e4fe381 100644 --- a/src/sage/geometry/hyperplane_arrangement/ordered_arrangement.py +++ b/src/sage/geometry/hyperplane_arrangement/ordered_arrangement.py @@ -250,9 +250,7 @@ def affine_fundamental_group(self): hyperplane arrangement in `\CC^n` whose equations have coefficients in a subfield of `\QQbar`. - OUTPUT: - - A finitely presented fundamental group. + OUTPUT: a finitely presented fundamental group .. NOTE:: @@ -340,9 +338,7 @@ def affine_meridians(self): r""" Return the meridians of each hyperplane (including the one at infinity). - OUTPUT: - - A dictionary + OUTPUT: a dictionary .. NOTE:: @@ -479,9 +475,7 @@ def projective_meridians(self): r""" Return the meridian of each hyperplane. - OUTPUT: - - A dictionary + OUTPUT: a dictionary .. NOTE:: @@ -637,9 +631,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: diff --git a/src/sage/geometry/hyperplane_arrangement/plot.py b/src/sage/geometry/hyperplane_arrangement/plot.py index c7b413114e6..2e407aeb639 100644 --- a/src/sage/geometry/hyperplane_arrangement/plot.py +++ b/src/sage/geometry/hyperplane_arrangement/plot.py @@ -138,9 +138,7 @@ def plot(hyperplane_arrangement, **kwds): - ``**kwds`` -- plot options: see :mod:`sage.geometry.hyperplane_arrangement.plot`. - OUTPUT: - - A graphics object of the plot. + OUTPUT: a graphics object of the plot EXAMPLES:: @@ -292,9 +290,7 @@ def plot_hyperplane(hyperplane, **kwds): - ``**kwds`` -- plot options: see below - OUTPUT: - - A graphics object of the plot. + OUTPUT: a graphics object of the plot .. RUBRIC:: Plot Options diff --git a/src/sage/geometry/integral_points.pxi b/src/sage/geometry/integral_points.pxi index 649eb281a1c..18c010eea5f 100644 --- a/src/sage/geometry/integral_points.pxi +++ b/src/sage/geometry/integral_points.pxi @@ -153,9 +153,7 @@ cpdef tuple ray_matrix_normal_form(R): - ``R`` -- `\ZZ`-matrix whose columns are the rays spanning the parallelotope. - OUTPUT: - - A tuple containing ``e``, ``d``, and ``VDinv``. + OUTPUT: a tuple containing ``e``, ``d``, and ``VDinv`` EXAMPLES:: @@ -729,9 +727,7 @@ cdef class Inequality_generic: - ``b`` -- element - OUTPUT: - - Inequality `A x + b \geq 0`. + OUTPUT: inequality `A x + b \geq 0` EXAMPLES:: @@ -771,9 +767,7 @@ cdef class Inequality_generic: """ Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -937,9 +931,7 @@ cdef class Inequality_int: """ Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -1031,9 +1023,7 @@ cdef class InequalityCollection: r""" Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -1343,9 +1333,7 @@ cdef class InequalityCollection: - ``inner_loop_variable`` -- Integer. the 0-th coordinate of the lattice point. - OUTPUT: - - Boolean. Whether the lattice point is in the polyhedron. + OUTPUT: boolean. Whether the lattice point is in the polyhedron EXAMPLES:: diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py index 0f83da4c96b..542e882cb8f 100644 --- a/src/sage/geometry/lattice_polytope.py +++ b/src/sage/geometry/lattice_polytope.py @@ -2710,9 +2710,7 @@ def linearly_independent_vertices(self): r""" Return a maximal set of linearly independent vertices. - OUTPUT: - - A tuple of vertex indices. + OUTPUT: a tuple of vertex indices EXAMPLES:: @@ -2893,7 +2891,7 @@ def nef_x(self, keys): key "-f" is added automatically. - OUTPUT: the output of nef.x as a string. + OUTPUT: the output of nef.x as a string EXAMPLES: This call is used internally for computing nef-partitions:: @@ -3234,9 +3232,7 @@ def _palp_modified_normal_form(self, permutation=False): - ``permutation`` -- boolean (default: ``False``); whether to return the permutation of the order of the vertices that was applied to obtain this matrix. - OUTPUT: - - A matrix or a tuple of a matrix and a permutation. + OUTPUT: a matrix or a tuple of a matrix and a permutation EXAMPLES:: @@ -3286,9 +3282,7 @@ def _palp_native_normal_form(self, permutation=False): of the order of the vertices that was applied to obtain this matrix. - OUTPUT: - - A matrix or a tuple of a matrix and a permutation. + OUTPUT: a matrix or a tuple of a matrix and a permutation EXAMPLES:: @@ -3906,7 +3900,7 @@ def poly_x(self, keys, reduce_dimension=False): polytope is not full-dimensional, poly.x will be called for the vertices of this polytope in some basis of the spanned affine space. - OUTPUT: the output of poly.x as a string. + OUTPUT: the output of poly.x as a string EXAMPLES: This call is used for determining if a polytope is reflexive or not:: @@ -5221,9 +5215,7 @@ def _palp_convert_permutation(permutation): - ``permutation`` -- A string specifying a PALP style permutation. - OUTPUT: - - A :class:`permutation group element `. + OUTPUT: a :class:`permutation group element ` EXAMPLES:: @@ -5631,7 +5623,7 @@ def minkowski_sum(points1, points2): converted into vectors of the same dimension, treated as vertices of two polytopes. - OUTPUT: list of vertices of the Minkowski sum, given as vectors. + OUTPUT: list of vertices of the Minkowski sum, given as vectors EXAMPLES: Let's compute the Minkowski sum of two line segments:: @@ -5808,9 +5800,7 @@ def read_palp_matrix(data, permutation=False): the permutation output by PALP. This parameter makes sense only when PALP computed the normal form of a lattice polytope. - OUTPUT: - - A matrix or a tuple of a matrix and a permutation. + OUTPUT: a matrix or a tuple of a matrix and a permutation EXAMPLES:: diff --git a/src/sage/geometry/linear_expression.py b/src/sage/geometry/linear_expression.py index 8cee8aa7c12..5224d3a4cdb 100644 --- a/src/sage/geometry/linear_expression.py +++ b/src/sage/geometry/linear_expression.py @@ -103,9 +103,7 @@ def A(self): """ Return the coefficient vector. - OUTPUT: - - The coefficient vector of the linear expression. + OUTPUT: the coefficient vector of the linear expression EXAMPLES:: @@ -124,9 +122,7 @@ def b(self): """ Return the constant term. - OUTPUT: - - The constant term of the linear expression. + OUTPUT: the constant term of the linear expression EXAMPLES:: @@ -228,9 +224,7 @@ def _repr_linear(self, include_zero=True, include_constant=True, multiplication= - ``multiplication`` -- string (default: ``*``); the multiplication symbol to use - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -359,9 +353,7 @@ def change_ring(self, base_ring): - ``base_ring`` -- a ring; the new base ring - OUTPUT: - - A new linear expression over the new base ring. + OUTPUT: a new linear expression over the new base ring EXAMPLES:: @@ -427,9 +419,7 @@ def evaluate(self, point): - ``point`` -- list/tuple/iterable of coordinates; the coordinates of a point - OUTPUT: - - The linear expression `Ax + b` evaluated at the point `x`. + OUTPUT: the linear expression `Ax + b` evaluated at the point `x` EXAMPLES:: @@ -520,9 +510,7 @@ def ngens(self): """ Return the number of linear variables. - OUTPUT: - - An integer. + OUTPUT: integer EXAMPLES:: @@ -538,9 +526,7 @@ def gens(self) -> tuple: """ Return the generators of ``self``. - OUTPUT: - - A tuple of linear expressions, one for each linear variable. + OUTPUT: a tuple of linear expressions, one for each linear variable EXAMPLES:: @@ -561,9 +547,7 @@ def gen(self, i): - ``i`` -- integer - OUTPUT: - - A linear expression. + OUTPUT: a linear expression EXAMPLES:: @@ -752,9 +736,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -773,9 +755,7 @@ def change_ring(self, base_ring): - ``base_ring`` -- a ring; the new base ring - OUTPUT: - - A new linear expression over the new base ring. + OUTPUT: a new linear expression over the new base ring EXAMPLES:: diff --git a/src/sage/geometry/newton_polygon.py b/src/sage/geometry/newton_polygon.py index c8e185d01e6..ef984e95082 100644 --- a/src/sage/geometry/newton_polygon.py +++ b/src/sage/geometry/newton_polygon.py @@ -202,9 +202,7 @@ def _add_(self, other): - ``other`` -- a Newton polygon - OUTPUT: - - The Newton polygon, which is the convex hull of this Newton polygon and ``other`` + OUTPUT: the Newton polygon, which is the convex hull of this Newton polygon and ``other`` EXAMPLES:: @@ -228,9 +226,7 @@ def _mul_(self, other): - ``other`` -- a Newton polygon - OUTPUT: - - The Newton polygon, which is the Minkowski sum of this Newton polygon and ``other``. + OUTPUT: the Newton polygon, which is the Minkowski sum of this Newton polygon and ``other`` .. NOTE:: @@ -269,9 +265,7 @@ def __pow__(self, exp, ignored=None): - ``exp`` -- a positive integer - OUTPUT: - - This Newton polygon scaled by a factor ``exp``. + OUTPUT: this Newton polygon scaled by a factor ``exp`` .. NOTE:: @@ -346,9 +340,7 @@ def __call__(self, x): - ``x`` -- a real number - OUTPUT: - - The value of this Newton polygon at abscissa `x` + OUTPUT: the value of this Newton polygon at abscissa `x` EXAMPLES:: @@ -539,9 +531,7 @@ class ParentNewtonPolygon(Parent, UniqueRepresentation): - ``last_slope`` -- rational or infinity (default: ``Infinity``). The last slope of the Newton polygon - OUTPUT: - - The corresponding Newton polygon. + OUTPUT: the corresponding Newton polygon .. note:: @@ -703,9 +693,7 @@ def _element_constructor_(self, arg, sort_slopes=True, last_slope=Infinity): - a list/tuple/iterable of slopes - OUTPUT: - - The corresponding Newton polygon. + OUTPUT: the corresponding Newton polygon For more informations, see :class:`ParentNewtonPolygon`. diff --git a/src/sage/geometry/palp_normal_form.pyx b/src/sage/geometry/palp_normal_form.pyx index fa756fe65b0..8dad123a7cb 100644 --- a/src/sage/geometry/palp_normal_form.pyx +++ b/src/sage/geometry/palp_normal_form.pyx @@ -356,9 +356,7 @@ def _palp_canonical_order(vertices, PM_max, permutations): - ``permutation`` -- the permutations of the vertices yielding ``PM_max``. - OUTPUT: - - The PALP normal form as an iterable of integer vectors. + OUTPUT: the PALP normal form as an iterable of integer vectors TESTS:: diff --git a/src/sage/geometry/point_collection.pyx b/src/sage/geometry/point_collection.pyx index ae4c92ffd75..e530ad2f365 100644 --- a/src/sage/geometry/point_collection.pyx +++ b/src/sage/geometry/point_collection.pyx @@ -279,9 +279,7 @@ cdef class PointCollection(SageObject): - ``right`` -- another PointCollection - OUTPUT: - - boolean + OUTPUT: boolean First compare according to the underlying :meth:`module` and then according to the list of points. diff --git a/src/sage/geometry/polyhedron/backend_field.py b/src/sage/geometry/polyhedron/backend_field.py index 7026cca98b8..a180ef9fbd6 100644 --- a/src/sage/geometry/polyhedron/backend_field.py +++ b/src/sage/geometry/polyhedron/backend_field.py @@ -81,9 +81,7 @@ def _is_zero(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -103,9 +101,7 @@ def _is_nonneg(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -125,9 +121,7 @@ def _is_positive(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/backend_normaliz.py b/src/sage/geometry/polyhedron/backend_normaliz.py index 29b914531c4..6f803a4fc37 100644 --- a/src/sage/geometry/polyhedron/backend_normaliz.py +++ b/src/sage/geometry/polyhedron/backend_normaliz.py @@ -428,9 +428,7 @@ def _is_zero(self, x) -> bool: - ``x`` -- a number in the base ring - OUTPUT: - - Boolean + OUTPUT: boolean EXAMPLES:: @@ -450,9 +448,7 @@ def _is_nonneg(self, x) -> bool: - ``x`` -- a number in the base ring - OUTPUT: - - Boolean + OUTPUT: boolean EXAMPLES:: @@ -472,9 +468,7 @@ def _is_positive(self, x) -> bool: - ``x`` -- a number in the base ring - OUTPUT: - - Boolean + OUTPUT: boolean EXAMPLES:: @@ -1647,9 +1641,7 @@ def ehrhart_series(self, variable='t'): - ``variable`` -- string (default: ``'t'``) - OUTPUT: - - A rational function. + OUTPUT: a rational function EXAMPLES:: @@ -1737,9 +1729,7 @@ def _ehrhart_quasipolynomial_normaliz(self, variable='t'): - ``variable`` -- string (default: ``'t'``) - OUTPUT: - - A polynomial or tuple of polynomials. + OUTPUT: a polynomial or tuple of polynomials EXAMPLES:: @@ -1810,9 +1800,7 @@ def hilbert_series(self, grading, variable='t'): - ``variable`` -- string (default: ``'t'``) - OUTPUT: - - A rational function. + OUTPUT: a rational function EXAMPLES:: @@ -2453,9 +2441,7 @@ class functions of the acting group. A character `\rho` is effective if a linear combination of irreducible representations with coefficients in the field of rational functions in `t`. - OUTPUT: - - Boolean. Whether the ``Hstar`` series is effective. + OUTPUT: boolean. Whether the ``Hstar`` series is effective EXAMPLES: diff --git a/src/sage/geometry/polyhedron/backend_polymake.py b/src/sage/geometry/polyhedron/backend_polymake.py index 0c19d8b5c91..5f2a37bf044 100644 --- a/src/sage/geometry/polyhedron/backend_polymake.py +++ b/src/sage/geometry/polyhedron/backend_polymake.py @@ -144,9 +144,7 @@ def _is_zero(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -166,9 +164,7 @@ def _is_nonneg(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -188,9 +184,7 @@ def _is_positive(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py index 67ac7d9ec9e..c734d310362 100644 --- a/src/sage/geometry/polyhedron/base.py +++ b/src/sage/geometry/polyhedron/base.py @@ -66,9 +66,7 @@ def is_Polyhedron(X): - ``X`` -- anything. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -462,9 +460,7 @@ def is_inscribed(self, certificate=False): - ``certificate`` -- (default: ``False``) boolean; specifies whether to return the circumcenter, if found. - OUTPUT: - - If ``certificate`` is true, returns a tuple containing: + OUTPUT: if ``certificate`` is true, returns a tuple containing: 1. Boolean. 2. The circumcenter of the polytope or None. @@ -849,9 +845,7 @@ def barycentric_subdivision(self, subdivision_frac=None): the value should be smaller than `\frac{1}{2}`. The subdivision is computed on the polar polyhedron. - OUTPUT: - - A Polyhedron object, subdivided as described above. + OUTPUT: a Polyhedron object, subdivided as described above EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base0.py b/src/sage/geometry/polyhedron/base0.py index b2e2ece5467..43ea046f035 100644 --- a/src/sage/geometry/polyhedron/base0.py +++ b/src/sage/geometry/polyhedron/base0.py @@ -344,9 +344,7 @@ def base_extend(self, base_ring, backend=None): Otherwise, use the same defaulting behavior as described there. - OUTPUT: - - The same polyhedron, but over a larger base ring and possibly with a changed backend. + OUTPUT: the same polyhedron, but over a larger base ring and possibly with a changed backend EXAMPLES:: @@ -643,9 +641,7 @@ def Hrepresentation_str(self, separator='\n', latex=False, style='>=', align=Non - ``indices`` -- a tuple or other iterable - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -761,9 +757,7 @@ def n_Hrepresentation(self): Return the number of objects that make up the H-representation of the polyhedron. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -814,9 +808,7 @@ def n_Vrepresentation(self): Return the number of objects that make up the V-representation of the polyhedron. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -849,9 +841,7 @@ def inequality_generator(self): Return a generator for the defining inequalities of the polyhedron. - OUTPUT: - - A generator of the inequality Hrepresentation objects. + OUTPUT: a generator of the inequality Hrepresentation objects EXAMPLES:: @@ -876,9 +866,7 @@ def inequalities(self): """ Return all inequalities. - OUTPUT: - - A tuple of inequalities. + OUTPUT: a tuple of inequalities EXAMPLES:: @@ -947,9 +935,7 @@ def equations(self): """ Return all linear constraints of the polyhedron. - OUTPUT: - - A tuple of equations. + OUTPUT: a tuple of equations EXAMPLES:: @@ -1065,9 +1051,7 @@ def vertices(self): """ Return all vertices of the polyhedron. - OUTPUT: - - A tuple of vertices. + OUTPUT: a tuple of vertices .. WARNING:: @@ -1178,9 +1162,7 @@ def rays(self): """ Return a list of rays of the polyhedron. - OUTPUT: - - A tuple of rays. + OUTPUT: a tuple of rays EXAMPLES:: @@ -1202,9 +1184,7 @@ def rays_list(self): :meth:`ray_generator` instead to iterate over the list of :class:`~sage.geometry.polyhedron.representation.Ray` objects. - OUTPUT: - - A list of rays as lists of coordinates. + OUTPUT: a list of rays as lists of coordinates EXAMPLES:: @@ -1235,9 +1215,7 @@ def lines(self): """ Return all lines of the polyhedron. - OUTPUT: - - A tuple of lines. + OUTPUT: a tuple of lines EXAMPLES:: @@ -1336,7 +1314,7 @@ def cdd_Hrepresentation(self): :meth:`write_cdd_Hrepresentation` -- export the polyhedron as a H-representation to a file. - OUTPUT: a string + OUTPUT: string EXAMPLES:: @@ -1408,7 +1386,7 @@ def cdd_Vrepresentation(self): :meth:`write_cdd_Vrepresentation` -- export the polyhedron as a V-representation to a file. - OUTPUT: a string + OUTPUT: string EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base1.py b/src/sage/geometry/polyhedron/base1.py index 507316f26a3..e84723c8d95 100644 --- a/src/sage/geometry/polyhedron/base1.py +++ b/src/sage/geometry/polyhedron/base1.py @@ -243,9 +243,7 @@ def _is_subpolyhedron(self, other): - ``other`` -- a :class:`Polyhedron` - OUTPUT: - - Boolean + OUTPUT: boolean EXAMPLES:: @@ -264,9 +262,7 @@ def is_empty(self): """ Test whether the polyhedron is the empty polyhedron - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -291,9 +287,7 @@ def is_universe(self): """ Test whether the polyhedron is the whole ambient space - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -351,9 +345,7 @@ def Vrepresentation_space(self): r""" Return the ambient free module. - OUTPUT: - - A free module over the base ring of dimension :meth:`ambient_dim`. + OUTPUT: a free module over the base ring of dimension :meth:`ambient_dim` EXAMPLES:: @@ -369,9 +361,7 @@ def Hrepresentation_space(self): r""" Return the linear space containing the H-representation vectors. - OUTPUT: - - A free module over the base ring of dimension :meth:`ambient_dim` + 1. + OUTPUT: a free module over the base ring of dimension :meth:`ambient_dim` + 1 EXAMPLES:: @@ -599,9 +589,7 @@ def contains(self, point): - ``point`` -- coordinates of a point (an iterable) - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -731,9 +719,7 @@ def interior_contains(self, point): - ``point`` -- coordinates of a point - OUTPUT: - - ``True`` or ``False``. + OUTPUT: ``True`` or ``False`` EXAMPLES:: @@ -783,9 +769,7 @@ def is_relatively_open(self): r""" Return whether ``self`` is relatively open. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -857,9 +841,7 @@ def relative_interior_contains(self, point): - ``point`` -- coordinates of a point - OUTPUT: - - ``True`` or ``False`` + OUTPUT: ``True`` or ``False`` EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base3.py b/src/sage/geometry/polyhedron/base3.py index 3b57c4f2055..de394b3d76a 100644 --- a/src/sage/geometry/polyhedron/base3.py +++ b/src/sage/geometry/polyhedron/base3.py @@ -838,9 +838,7 @@ def bounded_edges(self): """ Return the bounded edges (excluding rays and lines). - OUTPUT: - - A generator for pairs of vertices, one pair per edge. + OUTPUT: a generator for pairs of vertices, one pair per edge EXAMPLES:: @@ -1253,9 +1251,7 @@ def is_pyramid(self, certificate=False): to return a vertex of the polytope which is the apex of a pyramid, if found - OUTPUT: - - If ``certificate`` is ``True``, returns a tuple containing: + OUTPUT: if ``certificate`` is ``True``, returns a tuple containing: 1. Boolean. 2. The apex of the pyramid or ``None``. @@ -1303,9 +1299,7 @@ def is_bipyramid(self, certificate=False): to return two vertices of the polytope which are the apices of a bipyramid, if found - OUTPUT: - - If ``certificate`` is ``True``, returns a tuple containing: + OUTPUT: if ``certificate`` is ``True``, returns a tuple containing: 1. Boolean. 2. ``None`` or a tuple containing: @@ -1360,9 +1354,7 @@ def is_prism(self, certificate=False): to return two facets of the polytope which are the bases of a prism, if found - OUTPUT: - - If ``certificate`` is ``True``, returns a tuple containing: + OUTPUT: if ``certificate`` is ``True``, returns a tuple containing: 1. Boolean. 2. ``None`` or a tuple containing: diff --git a/src/sage/geometry/polyhedron/base5.py b/src/sage/geometry/polyhedron/base5.py index 2ac8b75cdd8..b8cf6e69868 100644 --- a/src/sage/geometry/polyhedron/base5.py +++ b/src/sage/geometry/polyhedron/base5.py @@ -582,9 +582,7 @@ def truncation(self, cut_frac=None): - ``cut_frac`` -- integer, how deeply to cut into the edge. Default is `\frac{1}{3}`. - OUTPUT: - - A Polyhedron object, truncated as described above. + OUTPUT: a Polyhedron object, truncated as described above EXAMPLES:: @@ -684,9 +682,7 @@ def minkowski_sum(self, other): - ``other`` -- a :class:`~sage.geometry.polyhedron.base.Polyhedron_base` - OUTPUT: - - The Minkowski sum of ``self`` and ``other`` + OUTPUT: the Minkowski sum of ``self`` and ``other`` EXAMPLES:: @@ -1292,9 +1288,7 @@ def convex_hull(self, other): - ``other`` -- a :class:`Polyhedron` - OUTPUT: - - The convex hull. + OUTPUT: the convex hull EXAMPLES:: @@ -1320,9 +1314,7 @@ def intersection(self, other): - ``other`` -- a :class:`Polyhedron` - OUTPUT: - - The intersection. + OUTPUT: the intersection Note that the intersection of two `\ZZ`-polyhedra might not be a `\ZZ`-polyhedron. In this case, a `\QQ`-polyhedron is @@ -1460,9 +1452,7 @@ def translation(self, displacement): - ``displacement`` -- a displacement vector or a list/tuple of coordinates that determines a displacement vector - OUTPUT: - - The translated polyhedron. + OUTPUT: the translated polyhedron EXAMPLES:: @@ -1503,7 +1493,7 @@ def _translation_double_description(self, displacement): - ``displacement`` -- a displacement vector or a list/tuple of coordinates that determines a displacement vector - OUTPUT: Tuple of consisting of new Vrepresentation, Hrepresentation and parent. + OUTPUT: tuple of consisting of new Vrepresentation, Hrepresentation and parent .. SEEALSO:: @@ -1933,9 +1923,7 @@ def face_truncation(self, face, linear_coefficients=None, cut_frac=None): vertex (according to the normal vector of the cutting hyperplane). Default is `\frac{1}{3}`. - OUTPUT: - - A Polyhedron object, truncated as described above. + OUTPUT: a Polyhedron object, truncated as described above EXAMPLES:: @@ -2089,9 +2077,7 @@ def stack(self, face, position=None): new vertex close to the face and a large value further away. Default is `1`. If the given value is too large, an error is returned. - OUTPUT: - - A Polyhedron object + OUTPUT: a Polyhedron object EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base6.py b/src/sage/geometry/polyhedron/base6.py index cb1577c10b1..f441d396113 100644 --- a/src/sage/geometry/polyhedron/base6.py +++ b/src/sage/geometry/polyhedron/base6.py @@ -843,9 +843,7 @@ def schlegel_projection(self, facet=None, position=None): projection point close to the facet and a large value further away. Default is `1`. If the given value is too large, an error is returned. - OUTPUT: - - A :class:`~sage.geometry.polyhedron.plot.Projection` object. + OUTPUT: a :class:`~sage.geometry.polyhedron.plot.Projection` object EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base7.py b/src/sage/geometry/polyhedron/base7.py index aca38a58404..1239d76568f 100644 --- a/src/sage/geometry/polyhedron/base7.py +++ b/src/sage/geometry/polyhedron/base7.py @@ -78,7 +78,7 @@ def centroid(self, engine='auto', **kwds): - ``**kwds`` -- keyword arguments that are passed to the triangulation engine (see :meth:`triangulate`). - OUTPUT: The centroid as vector. + OUTPUT: the centroid as vector ALGORITHM: @@ -314,9 +314,7 @@ def _volume_lrs(self, verbose=False): """ Computes the volume of a polytope using lrs. - OUTPUT: - - The exact volume as a rational number. + OUTPUT: the exact volume as a rational number EXAMPLES:: @@ -380,9 +378,7 @@ def _volume_latte(self, verbose=False, algorithm='triangulate', **kwargs): - For all other options, consult the LattE manual. - OUTPUT: - - A rational value, or a string if ``raw_output`` if set to ``True``. + OUTPUT: a rational value, or a string if ``raw_output`` if set to ``True`` .. NOTE:: @@ -492,9 +488,7 @@ def volume(self, measure='ambient', engine='auto', **kwds): - ``**kwds`` -- keyword arguments that are passed to the triangulation engine - OUTPUT: - - The volume of the polytope + OUTPUT: the volume of the polytope EXAMPLES:: @@ -788,9 +782,7 @@ def integrate(self, function, measure='ambient', **kwds): - ``**kwds`` -- additional keyword arguments that are passed to the engine - OUTPUT: - - The integral of the polynomial over the polytope + OUTPUT: the integral of the polynomial over the polytope .. NOTE:: @@ -961,9 +953,7 @@ def _integrate_latte_(self, polynomial, **kwds): - ``**kwds`` -- additional keyword arguments that are passed to the engine - OUTPUT: - - The integral of the polynomial over the polytope. + OUTPUT: the integral of the polynomial over the polytope .. NOTE:: diff --git a/src/sage/geometry/polyhedron/base_QQ.py b/src/sage/geometry/polyhedron/base_QQ.py index a6d1aa719f3..b2aec040e05 100644 --- a/src/sage/geometry/polyhedron/base_QQ.py +++ b/src/sage/geometry/polyhedron/base_QQ.py @@ -26,9 +26,7 @@ def _is_zero(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -48,9 +46,7 @@ def _is_nonneg(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -70,9 +66,7 @@ def _is_positive(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -274,9 +268,7 @@ def ehrhart_polynomial(self, engine=None, variable='t', verbose=False, * ``triangulation_max_height`` -- integer; use a uniform distribution of height from 1 to this number - OUTPUT: - - A univariate polynomial in ``variable`` over a rational field. + OUTPUT: a univariate polynomial in ``variable`` over a rational field .. SEEALSO:: @@ -693,9 +685,7 @@ def _ehrhart_polynomial_latte(self, verbose=False, dual=None, Any additional argument is forwarded to LattE's executable ``count``. All occurrences of '_' will be replaced with a '-'. - OUTPUT: - - A univariate polynomial over a rational field. + OUTPUT: a univariate polynomial over a rational field ALGORITHM: @@ -816,9 +806,7 @@ def fixed_subpolytope(self, vertex_permutation): - ``vertex_permutation`` -- permutation; a permutation of the vertices of ``self``. - OUTPUT: - - A subpolytope of ``self``. + OUTPUT: a subpolytope of ``self`` .. NOTE:: @@ -1167,9 +1155,7 @@ class functions of the acting group. A character `\rho` is effective if a linear combination of irreducible representations with coefficients in the field of rational functions in `t`. - OUTPUT: - - Boolean. Whether the ``Hstar`` series is effective. + OUTPUT: boolean. Whether the ``Hstar`` series is effective .. SEEALSO:: @@ -1244,9 +1230,7 @@ class functions of the acting group. A character `\rho` is effective if a linear combination of irreducible representations with coefficients in the field of rational functions in `t`. - OUTPUT: - - Boolean. Whether the ``Hstar`` series is effective. + OUTPUT: boolean. Whether the ``Hstar`` series is effective TESTS:: diff --git a/src/sage/geometry/polyhedron/base_RDF.py b/src/sage/geometry/polyhedron/base_RDF.py index 93914ded471..82f269e52d1 100644 --- a/src/sage/geometry/polyhedron/base_RDF.py +++ b/src/sage/geometry/polyhedron/base_RDF.py @@ -27,9 +27,7 @@ def _is_zero(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -54,9 +52,7 @@ def _is_nonneg(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -81,9 +77,7 @@ def _is_positive(self, x): - ``x`` -- a number in the base ring. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/base_ZZ.py b/src/sage/geometry/polyhedron/base_ZZ.py index dd3d32d9e51..6648aae0e3c 100644 --- a/src/sage/geometry/polyhedron/base_ZZ.py +++ b/src/sage/geometry/polyhedron/base_ZZ.py @@ -269,9 +269,7 @@ def _ehrhart_polynomial_normaliz(self, variable='t'): - ``variable`` -- (string, default='t'); the variable in which the Ehrhart polynomial is expressed. - OUTPUT: - - A univariate polynomial over a rational field. + OUTPUT: a univariate polynomial over a rational field EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx index d21b824da0c..17cc24665e8 100644 --- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx +++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx @@ -3594,9 +3594,7 @@ cdef class CombinatorialPolyhedron(SageObject): * ``'edges'`` * ``'ridges'`` - OUTPUT: - - Either ``'primal'`` or ``'dual'``. + OUTPUT: either ``'primal'`` or ``'dual'`` EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/conversions.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/conversions.pyx index 951dd9e5420..7dd7a34b586 100644 --- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/conversions.pyx +++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/conversions.pyx @@ -425,7 +425,7 @@ def _bit_rep_to_Vrep_list_wrapper(ListOfFaces faces, index=0): - ``faces`` -- a :class:`~sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces.ListOfFaces` - ``index`` -- (default: ``0``); the face to obtain - OUTPUT: The face as tuple of integers. + OUTPUT: the face as tuple of integers EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/face_iterator.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/face_iterator.pyx index 99cfef13db2..d1daed6ad8b 100644 --- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/face_iterator.pyx +++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/face_iterator.pyx @@ -2140,7 +2140,7 @@ cdef inline int prepare_face_iterator_for_partial_job( The first digit determines which facet to visit. The next digit determines which facet of the facet should be visited. - OUTPUT: ``1`` if the job exists and ``0`` otherwise. + OUTPUT: ``1`` if the job exists and ``0`` otherwise In addition, the first job treating a face will "visit" this face and increase the corresponding entry of the f-vector. diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/list_of_faces.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/list_of_faces.pyx index 468347f5256..8589e33045b 100644 --- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/list_of_faces.pyx +++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/list_of_faces.pyx @@ -529,7 +529,7 @@ cdef tuple face_as_combinatorial_polyhedron(ListOfFaces facets, ListOfFaces Vrep - ``face`` -- face in Vrepresentation or ``NULL`` - ``dual`` -- boolean - OUTPUT: A tuple of new facets and new Vrepresentation as :class:`ListOfFaces`. + OUTPUT: a tuple of new facets and new Vrepresentation as :class:`ListOfFaces`. """ cdef ListOfFaces new_facets, new_Vrep cdef bint* delete diff --git a/src/sage/geometry/polyhedron/constructor.py b/src/sage/geometry/polyhedron/constructor.py index 5a5db0b43ae..93f466d7c34 100644 --- a/src/sage/geometry/polyhedron/constructor.py +++ b/src/sage/geometry/polyhedron/constructor.py @@ -385,9 +385,7 @@ def Polyhedron(vertices=None, rays=None, lines=None, - ``mutable`` -- boolean (default: ``False``); whether the polyhedron is mutable - OUTPUT: - - The polyhedron defined by the input data. + OUTPUT: the polyhedron defined by the input data EXAMPLES: diff --git a/src/sage/geometry/polyhedron/double_description.py b/src/sage/geometry/polyhedron/double_description.py index 089580e3146..e236af000cb 100644 --- a/src/sage/geometry/polyhedron/double_description.py +++ b/src/sage/geometry/polyhedron/double_description.py @@ -89,9 +89,7 @@ def random_inequalities(d, n): - ``n`` -- integer. The number of random inequalities to generate. - OUTPUT: - - A random set of inequalities as a :class:`StandardAlgorithm` instance. + OUTPUT: a random set of inequalities as a :class:`StandardAlgorithm` instance EXAMPLES:: @@ -192,9 +190,7 @@ def __repr__(self): r""" Return string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -354,9 +350,7 @@ def zero_set(self, ray): - ``ray`` -- a ray vector. - OUTPUT: - - A set containing the inequality vectors that are zero on ``ray``. + OUTPUT: a set containing the inequality vectors that are zero on ``ray`` EXAMPLES:: @@ -429,9 +423,7 @@ def are_adjacent(self, r1, r2): - ``r1``, ``r2`` -- two rays. - OUTPUT: - - Boolean. Whether the two rays are adjacent. + OUTPUT: boolean; whether the two rays are adjacent EXAMPLES:: @@ -554,9 +546,7 @@ def A(self): """ Return the rows of the defining matrix `A`. - OUTPUT: - - The matrix `A` whose rows are the inequalities. + OUTPUT: the matrix `A` whose rows are the inequalities EXAMPLES:: @@ -574,9 +564,7 @@ def A_matrix(self): """ Return the defining matrix `A`. - OUTPUT: - - Matrix whose rows are the inequalities. + OUTPUT: matrix whose rows are the inequalities EXAMPLES:: @@ -592,9 +580,7 @@ def base_ring(self): """ Return the base field. - OUTPUT: - - A field. + OUTPUT: a field EXAMPLES:: @@ -610,9 +596,7 @@ def dim(self): """ Return the ambient space dimension. - OUTPUT: - - Integer. The ambient space dimension of the cone. + OUTPUT: integer; the ambient space dimension of the cone EXAMPLES:: @@ -627,9 +611,7 @@ def __repr__(self): r""" Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/double_description_inhomogeneous.py b/src/sage/geometry/polyhedron/double_description_inhomogeneous.py index 9b7882a5bcd..ac6c44968d7 100644 --- a/src/sage/geometry/polyhedron/double_description_inhomogeneous.py +++ b/src/sage/geometry/polyhedron/double_description_inhomogeneous.py @@ -100,9 +100,7 @@ def _pivot_inequalities(self, A): - ``A`` -- matrix. The inequalities. - OUTPUT: - - The matrix of pivot columns. + OUTPUT: the matrix of pivot columns EXAMPLES:: @@ -127,9 +125,7 @@ def _unpivot_ray(self, ray): - ``ray`` -- ray in the pivoted coordinates. - OUTPUT: - - Ray in the original coordinates. + OUTPUT: ray in the original coordinates EXAMPLES:: @@ -219,9 +215,7 @@ def _init_Vrep(self, inequalities, equations): - ``inequalities``, ``equations`` -- see :class:`Vrep2Hrep`. - OUTPUT: - - The pivoted inequalities. + OUTPUT: the pivoted inequalities TESTS:: @@ -467,9 +461,7 @@ def _init_Vrep(self, vertices, rays, lines): - ``vertices``, ``rays``, ``lines`` -- see :class:`Vrep2Hrep`. - OUTPUT: - - Matrix of pivoted inequalities for the dual homogenized cone. + OUTPUT: matrix of pivoted inequalities for the dual homogenized cone TESTS:: @@ -520,9 +512,7 @@ def _repr_(self): r""" Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/face.py b/src/sage/geometry/polyhedron/face.py index 97319ed1740..0a28f8b8699 100644 --- a/src/sage/geometry/polyhedron/face.py +++ b/src/sage/geometry/polyhedron/face.py @@ -96,9 +96,7 @@ class PolyhedronFace(ConvexSet_closed): manually create :class:`PolyhedronFace` objects unless you know what you are doing. - OUTPUT: - - A :class:`PolyhedronFace`. + OUTPUT: a :class:`PolyhedronFace` EXAMPLES:: @@ -200,9 +198,7 @@ def vertices(self): """ Return all vertices of the face. - OUTPUT: - - A tuple of vertices. + OUTPUT: a tuple of vertices EXAMPLES:: @@ -222,9 +218,7 @@ def n_vertices(self): """ Return the number of vertices of the face. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -263,9 +257,7 @@ def rays(self): """ Return the rays of the face. - OUTPUT: - - A tuple of rays. + OUTPUT: a tuple of rays EXAMPLES:: @@ -281,9 +273,7 @@ def n_rays(self): """ Return the number of rays of the face. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -318,9 +308,7 @@ def lines(self): """ Return all lines of the face. - OUTPUT: - - A tuple of lines. + OUTPUT: a tuple of lines EXAMPLES:: @@ -335,9 +323,7 @@ def n_lines(self): """ Return the number of lines of the face. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -471,9 +457,7 @@ def n_ambient_Hrepresentation(self): See also :meth:`ambient_Hrepresentation`. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -497,9 +481,7 @@ def n_ambient_Vrepresentation(self): See also :meth:`ambient_Vrepresentation`. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -520,9 +502,7 @@ def ambient_H_indices(self): See also :meth:`ambient_Hrepresentation`. - OUTPUT: - - Tuple of indices + OUTPUT: tuple of indices EXAMPLES:: @@ -551,9 +531,7 @@ def ambient_V_indices(self): See also :meth:`ambient_Vrepresentation`. - OUTPUT: - - Tuple of indices + OUTPUT: tuple of indices EXAMPLES:: @@ -587,9 +565,7 @@ def dim(self): """ Return the dimension of the face. - OUTPUT: - - Integer. + OUTPUT: integer EXAMPLES:: @@ -714,7 +690,7 @@ def is_relatively_open(self): r""" Return whether ``self`` is relatively open. - OUTPUT: Boolean. + OUTPUT: boolean EXAMPLES:: @@ -731,7 +707,7 @@ def is_compact(self): r""" Return whether ``self`` is compact. - OUTPUT: Boolean. + OUTPUT: boolean EXAMPLES:: @@ -750,9 +726,7 @@ def as_polyhedron(self, **kwds): """ Return the face as an independent polyhedron. - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES:: @@ -855,9 +829,7 @@ def normal_cone(self, direction='outer'): which to consider the normals. The other allowed option is ``'inner'``. - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES:: @@ -933,9 +905,7 @@ def affine_tangent_cone(self): It is equal to the sum of ``self`` and the cone of feasible directions at any point of the relative interior of ``self``. - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES:: @@ -983,9 +953,7 @@ def stacking_locus(self): Return the polyhedron containing the points that sees every facet containing ``self``. - OUTPUT: - - A polyhedron. + OUTPUT: a polyhedron EXAMPLES:: @@ -1036,7 +1004,7 @@ def combinatorial_face_to_polyhedral_face(polyhedron, combinatorial_face): - ``polyhedron`` -- a polyhedron containing ``combinatorial_face`` - ``combinatorial_face`` -- a :class:`CombinatorialFace` - OUTPUT: a :class:`PolyhedronFace`. + OUTPUT: a :class:`PolyhedronFace` EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/generating_function.py b/src/sage/geometry/polyhedron/generating_function.py index 89d86058c2d..34c2594a144 100644 --- a/src/sage/geometry/polyhedron/generating_function.py +++ b/src/sage/geometry/polyhedron/generating_function.py @@ -707,9 +707,7 @@ def _generating_function_via_Omega_(inequalities, B, skip_indices=()): The variables corresponding to ``skip_indices`` are not handled (e.g. because they are determined by an equation). - OUTPUT: - - A pair of + OUTPUT: a pair of - a Laurent polynomial specifying the numerator and diff --git a/src/sage/geometry/polyhedron/library.py b/src/sage/geometry/polyhedron/library.py index 6ea6e5c32be..202298b0cfe 100644 --- a/src/sage/geometry/polyhedron/library.py +++ b/src/sage/geometry/polyhedron/library.py @@ -341,7 +341,7 @@ def gale_transform_to_primal(vectors, base_ring=None, backend=None): used internally in case the center is not the origin, see :func:`~sage.geometry.polyhedron.constructor.Polyhedron` - OUTPUT: An ordered point configuration as list of vectors. + OUTPUT: an ordered point configuration as list of vectors .. NOTE:: @@ -3363,9 +3363,7 @@ def cube(self, intervals=None, backend=None): - ``backend`` -- the backend to use to create the polytope. - OUTPUT: - - A cube as a polyhedron object. + OUTPUT: a cube as a polyhedron object EXAMPLES: diff --git a/src/sage/geometry/polyhedron/misc.py b/src/sage/geometry/polyhedron/misc.py index b47e51f79b8..dbf07d7d334 100644 --- a/src/sage/geometry/polyhedron/misc.py +++ b/src/sage/geometry/polyhedron/misc.py @@ -21,9 +21,7 @@ def _to_space_separated_string(l, base_ring=None): - ``base_ring`` -- ring (default: ``None``); convert this ring, if given - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -68,9 +66,7 @@ def _make_listlist(x): - ``x`` -- ``None`` or an iterable of iterables. - OUTPUT: - - A list of lists. + OUTPUT: a list of lists EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/palp_database.py b/src/sage/geometry/polyhedron/palp_database.py index 60846d8df23..c4c97d3b8e6 100644 --- a/src/sage/geometry/polyhedron/palp_database.py +++ b/src/sage/geometry/polyhedron/palp_database.py @@ -125,9 +125,7 @@ def _palp_Popen(self): """ Open PALP. - OUTPUT: - - A PALP subprocess. + OUTPUT: a PALP subprocess EXAMPLES:: @@ -144,9 +142,7 @@ def _read_vertices(self, stdout, rows, cols): r""" Read vertex data from the PALP output pipe. - OUTPUT: - - A list of lists. + OUTPUT: a list of lists EXAMPLES:: @@ -168,9 +164,7 @@ def _read_vertices_transposed(self, stdout, rows, cols): r""" Read vertex data from the PALP output pipe. - OUTPUT: - - A list of lists. + OUTPUT: a list of lists EXAMPLES:: @@ -196,9 +190,7 @@ def _iterate_list(self, start, stop, step): - ``start``, ``stop``, ``step`` -- integers specifying the range to iterate over. - OUTPUT: - - A generator for vertex data as a list of lists. + OUTPUT: a generator for vertex data as a list of lists EXAMPLES:: @@ -248,9 +240,7 @@ def _iterate_Polyhedron(self, start, stop, step): - ``start``, ``stop``, ``step`` -- integers specifying the range to iterate over. - OUTPUT: - - A generator for lattice polyhedra. + OUTPUT: a generator for lattice polyhedra EXAMPLES:: @@ -328,9 +318,7 @@ def _iterate(self, output=None): - ``output`` -- as in the :class:`PALPreader` constructor. - OUTPUT: - - A function generating lattice polytopes in the specified output format. + OUTPUT: a function generating lattice polytopes in the specified output format EXAMPLES:: @@ -360,9 +348,7 @@ def __iter__(self): """ Iterate over all polytopes. - OUTPUT: - - An iterator for all polytopes. + OUTPUT: an iterator for all polytopes TESTS:: @@ -449,9 +435,7 @@ def _palp_Popen(self): """ Open PALP. - OUTPUT: - - A PALP subprocess. + OUTPUT: a PALP subprocess EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/parent.py b/src/sage/geometry/polyhedron/parent.py index 79a77e51556..29d706d645b 100644 --- a/src/sage/geometry/polyhedron/parent.py +++ b/src/sage/geometry/polyhedron/parent.py @@ -465,9 +465,7 @@ def Vrepresentation_space(self): This is the vector space or module containing the Vrepresentation vectors. - OUTPUT: - - A free module over the base ring of dimension :meth:`ambient_dim`. + OUTPUT: a free module over the base ring of dimension :meth:`ambient_dim` EXAMPLES:: @@ -490,9 +488,7 @@ def Hrepresentation_space(self): r""" Return the linear space containing the H-representation vectors. - OUTPUT: - - A free module over the base ring of dimension :meth:`ambient_dim` + 1. + OUTPUT: a free module over the base ring of dimension :meth:`ambient_dim` + 1 EXAMPLES:: @@ -540,9 +536,7 @@ def _repr_ambient_module(self) -> str: Return an abbreviated string representation of the ambient space. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -562,9 +556,7 @@ def _repr_(self): """ Return a string representation. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -920,9 +912,7 @@ def _coerce_map_from_(self, X): - ``X`` -- anything. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -956,9 +946,7 @@ def _get_action_(self, other, op, self_is_left): - ``self_is_left`` -- boolean. Whether ``self`` is on the left of the operator. - OUTPUT: - - An action that is used by the coercion model. + OUTPUT: an action that is used by the coercion model EXAMPLES:: @@ -1050,9 +1038,7 @@ def _make_Inequality(self, polyhedron, data): - ``data`` -- the H-representation data. - OUTPUT: - - A new :class:`~sage.geometry.polyhedron.representation.Inequality` object. + OUTPUT: a new :class:`~sage.geometry.polyhedron.representation.Inequality` object EXAMPLES:: @@ -1077,9 +1063,7 @@ def _make_Equation(self, polyhedron, data): - ``data`` -- the H-representation data. - OUTPUT: - - A new :class:`~sage.geometry.polyhedron.representation.Equation` object. + OUTPUT: a new :class:`~sage.geometry.polyhedron.representation.Equation` object EXAMPLES:: @@ -1104,9 +1088,7 @@ def _make_Vertex(self, polyhedron, data): - ``data`` -- the V-representation data. - OUTPUT: - - A new :class:`~sage.geometry.polyhedron.representation.Vertex` object. + OUTPUT: a new :class:`~sage.geometry.polyhedron.representation.Vertex` object EXAMPLES:: @@ -1131,9 +1113,7 @@ def _make_Ray(self, polyhedron, data): - ``data`` -- the V-representation data. - OUTPUT: - - A new :class:`~sage.geometry.polyhedron.representation.Ray` object. + OUTPUT: a new :class:`~sage.geometry.polyhedron.representation.Ray` object EXAMPLES:: @@ -1158,9 +1138,7 @@ def _make_Line(self, polyhedron, data): - ``data`` -- the V-representation data. - OUTPUT: - - A new :class:`~sage.geometry.polyhedron.representation.Line` object. + OUTPUT: a new :class:`~sage.geometry.polyhedron.representation.Line` object EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py index 9c8a93624ec..0bc940fd46a 100644 --- a/src/sage/geometry/polyhedron/plot.py +++ b/src/sage/geometry/polyhedron/plot.py @@ -1270,9 +1270,7 @@ def tikz(self, view=[0, 0, 1], angle=0, scale=1, :class:`str`) or a :class:`TikzPicture` object from module :mod:`sage.misc.latex_standalone` - OUTPUT: - - :class:`LatexExpr` object or :class:`TikzPicture` object + OUTPUT: :class:`LatexExpr` object or :class:`TikzPicture` object .. NOTE:: diff --git a/src/sage/geometry/polyhedron/ppl_lattice_polygon.py b/src/sage/geometry/polyhedron/ppl_lattice_polygon.py index a3ddeda66a2..6063f3f9c38 100644 --- a/src/sage/geometry/polyhedron/ppl_lattice_polygon.py +++ b/src/sage/geometry/polyhedron/ppl_lattice_polygon.py @@ -339,9 +339,7 @@ def is_isomorphic(self, polytope): - ``polytope`` -- a lattice polytope. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -399,9 +397,7 @@ def plot(self): """ Plot the lattice polygon. - OUTPUT: - - A graphics object. + OUTPUT: a graphics object EXAMPLES:: @@ -487,9 +483,7 @@ def subpolygons_of_polar_P2(): """ The lattice sub-polygons of the polar `P^2` polytope - OUTPUT: - - A tuple of lattice polytopes. + OUTPUT: a tuple of lattice polytopes EXAMPLES:: @@ -505,9 +499,7 @@ def subpolygons_of_polar_P2_112(): """ The lattice sub-polygons of the polar `P^2[1,1,2]` polytope - OUTPUT: - - A tuple of lattice polytopes. + OUTPUT: a tuple of lattice polytopes EXAMPLES:: @@ -523,9 +515,7 @@ def subpolygons_of_polar_P1xP1(): r""" The lattice sub-polygons of the polar `P^1 \times P^1` polytope - OUTPUT: - - A tuple of lattice polytopes. + OUTPUT: a tuple of lattice polytopes EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py index 3cde1c6af81..6e027a5c70b 100644 --- a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py +++ b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py @@ -89,9 +89,7 @@ def _class_for_LatticePolytope(dim): - ``dim`` -- integer. The ambient space dimension. - OUTPUT: - - The appropriate class for the lattice polytope. + OUTPUT: the appropriate class for the lattice polytope EXAMPLES:: @@ -197,9 +195,7 @@ def __repr__(self): """ Return the string representation - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -233,9 +229,7 @@ def is_bounded(self): """ Return whether the lattice polytope is compact. - OUTPUT: - - Always ``True``, since polytopes are by definition compact. + OUTPUT: always ``True``, since polytopes are by definition compact EXAMPLES:: @@ -250,9 +244,7 @@ def n_vertices(self): """ Return the number of vertices. - OUTPUT: - - An integer, the number of vertices. + OUTPUT: an integer, the number of vertices EXAMPLES:: @@ -716,7 +708,7 @@ def contains(self, point_coordinates): - ``point_coordinates`` -- a list/tuple/iterable of rational numbers. The coordinates of the point. - OUTPUT: Boolean. + OUTPUT: boolean EXAMPLES:: @@ -739,7 +731,7 @@ def contains_origin(self): """ Test whether the polytope contains the origin - OUTPUT: Boolean. + OUTPUT: boolean EXAMPLES:: @@ -922,7 +914,7 @@ def has_IP_property(self): That is, the polytope is full-dimensional and the origin is a interior point not on the boundary. - OUTPUT: Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/polyhedron/representation.py b/src/sage/geometry/polyhedron/representation.py index 49993d6ada1..634813ff072 100644 --- a/src/sage/geometry/polyhedron/representation.py +++ b/src/sage/geometry/polyhedron/representation.py @@ -124,9 +124,7 @@ def __richcmp__(self, other, op): - ``other`` -- anything. - OUTPUT: - - boolean + OUTPUT: boolean EXAMPLES:: @@ -323,9 +321,7 @@ def __add__(self, coordinate_list): - ``coordinate_list`` -- a list. - OUTPUT: - - The coordinates of ``self`` concatenated with ``coordinate_list``. + OUTPUT: the coordinates of ``self`` concatenated with ``coordinate_list`` EXAMPLES:: @@ -347,9 +343,7 @@ def __radd__(self, coordinate_list): - ``coordinate_list`` -- a list. - OUTPUT: - - ``coordinate_list`` concatenated with the coordinates of ``self``. + OUTPUT: ``coordinate_list`` concatenated with the coordinates of ``self`` EXAMPLES:: @@ -371,9 +365,7 @@ def count(self, i): - ``i`` -- Anything. - OUTPUT: - - Integer. The number of occurrences of ``i`` in the coordinates. + OUTPUT: integer; the number of occurrences of ``i`` in the coordinates EXAMPLES:: @@ -688,9 +680,7 @@ def repr_pretty(self, **kwds): - ``latex`` -- a boolean - OUTPUT: - - A string + OUTPUT: string EXAMPLES:: @@ -708,9 +698,7 @@ def _latex_(self): r""" Return a LaTeX-representation of this equality/inequality. - OUTPUT: - - A string. + OUTPUT: string EXAMPLES:: @@ -988,9 +976,7 @@ def outer_normal(self): r""" Return the outer normal vector of ``self``. - OUTPUT: - - The normal vector directed away from the interior of the polyhedron. + OUTPUT: the normal vector directed away from the interior of the polyhedron EXAMPLES:: @@ -1392,9 +1378,7 @@ def _repr_(self): """ Return a string representation of the vertex. - OUTPUT: - - String. + OUTPUT: string TESTS:: @@ -1449,9 +1433,7 @@ def is_integral(self): r""" Return whether the coordinates of the vertex are all integral. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/relative_interior.py b/src/sage/geometry/relative_interior.py index e62a9182211..4ebd390d606 100644 --- a/src/sage/geometry/relative_interior.py +++ b/src/sage/geometry/relative_interior.py @@ -218,9 +218,7 @@ def is_universe(self): r""" Return whether ``self`` is the whole ambient space - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: @@ -240,9 +238,7 @@ def is_closed(self): r""" Return whether ``self`` is closed. - OUTPUT: - - Boolean. + OUTPUT: boolean EXAMPLES:: diff --git a/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py b/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py index 43fecdc0609..b3d3966b6fa 100644 --- a/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py +++ b/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py @@ -1227,9 +1227,7 @@ def second_fundamental_form_coefficients(self): When only one component is needed, consider instead the function :meth:`second_fundamental_form_coefficient`. - OUTPUT: - - Dictionary of second fundamental form coefficients. + OUTPUT: dictionary of second fundamental form coefficients EXAMPLES:: diff --git a/src/sage/geometry/toric_lattice.py b/src/sage/geometry/toric_lattice.py index 8c2d0418595..d0bde4e6d1d 100644 --- a/src/sage/geometry/toric_lattice.py +++ b/src/sage/geometry/toric_lattice.py @@ -945,9 +945,7 @@ def __richcmp__(self, right, op): - ``right`` -- anything. - OUTPUT: - - boolean + OUTPUT: boolean There is equality if ``right`` is a toric lattice of the same dimension as ``self`` and their associated names are the @@ -1760,9 +1758,7 @@ def rank(self): r""" Return the rank of ``self``. - OUTPUT: - - Integer. The dimension of the free part of the quotient. + OUTPUT: integer; the dimension of the free part of the quotient EXAMPLES:: @@ -1796,9 +1792,7 @@ def coordinate_vector(self, x, reduce=False): - ``reduce`` -- (default: ``False``); if ``True``, reduce coefficients modulo invariants - OUTPUT: - - The coordinates as a vector. + OUTPUT: the coordinates as a vector EXAMPLES:: diff --git a/src/sage/geometry/toric_lattice_element.pyx b/src/sage/geometry/toric_lattice_element.pyx index 5fb647a60ba..cb539ab9798 100644 --- a/src/sage/geometry/toric_lattice_element.pyx +++ b/src/sage/geometry/toric_lattice_element.pyx @@ -176,9 +176,7 @@ cdef class ToricLatticeElement(Vector_integer_dense): - ``right`` -- another ToricLatticeElement - OUTPUT: - - boolean + OUTPUT: boolean First compare the ambient toric lattice, then compare the vectors. @@ -424,9 +422,7 @@ def unpickle_v1(parent, entries, degree, is_mutable): - ``is_mutable`` -- boolean. Whether the lattice element is mutable. - OUTPUT: - - The :class:`ToricLatticeElement` determined by the input data. + OUTPUT: the :class:`ToricLatticeElement` determined by the input data EXAMPLES:: diff --git a/src/sage/geometry/triangulation/base.pyx b/src/sage/geometry/triangulation/base.pyx index cb9cb948256..92b9d5ba537 100644 --- a/src/sage/geometry/triangulation/base.pyx +++ b/src/sage/geometry/triangulation/base.pyx @@ -113,9 +113,7 @@ cdef class Point(SageObject): r""" Return the point configuration to which the point belongs. - OUTPUT: - - A :class:`~sage.geometry.triangulation.point_configuration.PointConfiguration`. + OUTPUT: a :class:`~sage.geometry.triangulation.point_configuration.PointConfiguration` EXAMPLES:: @@ -176,9 +174,7 @@ cdef class Point(SageObject): r""" Return the projective coordinates of the point in the ambient space. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -202,9 +198,7 @@ cdef class Point(SageObject): r""" Return the affine coordinates of the point in the ambient space. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -229,9 +223,7 @@ cdef class Point(SageObject): Return the affine coordinates of the point on the hyperplane spanned by the point configuration. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -256,9 +248,7 @@ cdef class Point(SageObject): Return the projective coordinates of the point on the hyperplane spanned by the point configuration. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -283,9 +273,7 @@ cdef class Point(SageObject): Return the affine coordinates of the point on the hyperplane spanned by the point configuration. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -310,9 +298,7 @@ cdef class Point(SageObject): Return the affine coordinates of the point on the hyperplane spanned by the point configuration. - OUTPUT: - - A tuple containing the coordinates. + OUTPUT: a tuple containing the coordinates EXAMPLES:: @@ -338,9 +324,7 @@ cdef class Point(SageObject): """ Return a string representation of the point. - OUTPUT: - - String. + OUTPUT: string EXAMPLES:: @@ -470,9 +454,7 @@ cdef class PointConfiguration_base(Parent): """ Return the vector space that contains the affine points. - OUTPUT: - - A vector space over the fraction field of :meth:`base_ring`. + OUTPUT: a vector space over the fraction field of :meth:`base_ring` EXAMPLES:: @@ -491,9 +473,7 @@ cdef class PointConfiguration_base(Parent): Return the vector space that is spanned by the homogeneous coordinates. - OUTPUT: - - A vector space over the fraction field of :meth:`base_ring`. + OUTPUT: a vector space over the fraction field of :meth:`base_ring` EXAMPLES:: @@ -545,9 +525,7 @@ cdef class PointConfiguration_base(Parent): Return the base ring, that is, the ring containing the coordinates of the points. - OUTPUT: - - A ring. + OUTPUT: a ring EXAMPLES:: @@ -688,9 +666,7 @@ cdef class PointConfiguration_base(Parent): - ``i`` -- integer. - OUTPUT: - - A point of the point configuration. + OUTPUT: a point of the point configuration EXAMPLES:: @@ -744,9 +720,7 @@ cdef class PointConfiguration_base(Parent): - ``simplex`` -- iterable, for example a list. The elements are the vertex indices of the simplex. - OUTPUT: - - An integer that uniquely specifies the simplex. + OUTPUT: an integer that uniquely specifies the simplex EXAMPLES:: diff --git a/src/sage/geometry/triangulation/element.py b/src/sage/geometry/triangulation/element.py index 3e6e0ed152d..5c623361d2a 100644 --- a/src/sage/geometry/triangulation/element.py +++ b/src/sage/geometry/triangulation/element.py @@ -433,9 +433,7 @@ def gkz_phi(self): that is, the total volume of all simplices containing `p_i`. See also [GKZ1994]_ page 220 equation 1.4. - OUTPUT: - - The phi vector of self. + OUTPUT: the phi vector of self EXAMPLES:: @@ -456,9 +454,7 @@ def enumerate_simplices(self): r""" Return the enumerated simplices. - OUTPUT: - - A tuple of integers that uniquely specifies the triangulation. + OUTPUT: a tuple of integers that uniquely specifies the triangulation EXAMPLES:: @@ -558,9 +554,7 @@ def simplicial_complex(self): r""" Return ``self`` as an (abstract) simplicial complex. - OUTPUT: - - A :class:`~sage.topology.simplicial_complex.SimplicialComplex`. + OUTPUT: a :class:`~sage.topology.simplicial_complex.SimplicialComplex` EXAMPLES:: @@ -660,9 +654,7 @@ def boundary_simplicial_complex(self): r""" Return the boundary of ``self`` as an (abstract) simplicial complex. - OUTPUT: - - A :class:`~sage.topology.simplicial_complex.SimplicialComplex`. + OUTPUT: a :class:`~sage.topology.simplicial_complex.SimplicialComplex` EXAMPLES:: diff --git a/src/sage/geometry/triangulation/point_configuration.py b/src/sage/geometry/triangulation/point_configuration.py index b71ae4cb348..500e5b56083 100644 --- a/src/sage/geometry/triangulation/point_configuration.py +++ b/src/sage/geometry/triangulation/point_configuration.py @@ -1911,9 +1911,7 @@ def placing_triangulation(self, point_order=None): will be placed in some arbitrary order that attempts to produce a small number of simplices. - OUTPUT: - - A :class:`~sage.geometry.triangulation.triangulation.Triangulation`. + OUTPUT: a :class:`~sage.geometry.triangulation.triangulation.Triangulation` EXAMPLES:: @@ -2053,9 +2051,7 @@ def Gale_transform(self, points=None): (default). A subset of points for which to compute the Gale transform. By default, all points are used. - OUTPUT: - - A matrix over :meth:`base_ring`. + OUTPUT: a matrix over :meth:`base_ring` EXAMPLES:: diff --git a/src/sage/geometry/voronoi_diagram.py b/src/sage/geometry/voronoi_diagram.py index a4c110ff647..5002f343efc 100644 --- a/src/sage/geometry/voronoi_diagram.py +++ b/src/sage/geometry/voronoi_diagram.py @@ -32,9 +32,7 @@ class VoronoiDiagram(SageObject): - ``points`` -- a list of points. Any valid input for the :class:`PointConfiguration` will do. - OUTPUT: - - An instance of the VoronoiDiagram class. + OUTPUT: an instance of the VoronoiDiagram class EXAMPLES: @@ -253,9 +251,7 @@ def plot(self, cell_colors=None, **kwds): - ``**kwds`` -- optional keyword parameters, passed on as arguments for plot(). - OUTPUT: - - A graphics object. + OUTPUT: a graphics object EXAMPLES::