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sage.{geometry,rings}: More # optional tags in doctests #35136

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merged 9 commits into from
Mar 26, 2023
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sage.{geometry,rings}: More # optional tags in doctests #35136

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7ecdd57
src/sage/geometry/polyhedron: Add # optional - sage.combinat, sage.gr…
mkoeppe Jan 27, 2023
f01367a
sage.geometry.polyhedron: More # optional
mkoeppe Jan 28, 2023
6fd026b
sage.geometry: More # optional
mkoeppe Jan 28, 2023
9400f51
src/sage/rings/integer.pyx: Mark doctests # optional - sage.libs.pari…
mkoeppe Jan 27, 2023
a1d822d
src/sage/geometry/polyhedron/base2.py, src/sage/rings/integer.pyx: Re…
mkoeppe Feb 15, 2023
d6ffafd
src/sage/features/sagemath.py (all_features): Add sage.libs.pari
mkoeppe Feb 15, 2023
f7ec6a1
src/sage/geometry/polyhedral_complex.py: Mark # optional - sage.graphs
mkoeppe Feb 17, 2023
4aa6264
sage.geometry.triangulation: More # optional
mkoeppe Feb 17, 2023
02f15b2
Merge branch 'develop' into sage_geometry_more_optional_tags
mkoeppe Feb 19, 2023
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45 changes: 45 additions & 0 deletions src/sage/features/sagemath.py
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Original file line number Diff line number Diff line change
Expand Up @@ -122,6 +122,28 @@ def __init__(self):
[PythonModule('sage.groups.perm_gps.permgroup')])


class sage__libs__pari(JoinFeature):
r"""
A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.pari`.

EXAMPLES::

sage: from sage.features.sagemath import sage__libs__pari
sage: sage__libs__pari().is_present() # optional - sage.libs.pari
FeatureTestResult('sage.libs.pari', True)
"""
def __init__(self):
r"""
TESTS::

sage: from sage.features.sagemath import sage__libs__pari
sage: isinstance(sage__libs__pari(), sage__libs__pari)
True
"""
JoinFeature.__init__(self, 'sage.libs.pari',
[PythonModule('sage.libs.pari.convert_sage')])


class sage__plot(JoinFeature):
r"""
A :class:`~sage.features.Feature` describing the presence of :mod:`sage.plot`.
Expand Down Expand Up @@ -209,6 +231,27 @@ def __init__(self):
PythonModule.__init__(self, 'sage.rings.real_double')


class sage__rings__real_mpfr(PythonModule):
r"""
A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.real_mpfr`.

EXAMPLES::

sage: from sage.features.sagemath import sage__rings__real_mpfr
sage: sage__rings__real_mpfr().is_present() # optional - sage.rings.real_mpfr
FeatureTestResult('sage.rings.real_mpfr', True)
"""
def __init__(self):
r"""
TESTS::

sage: from sage.features.sagemath import sage__rings__real_mpfr
sage: isinstance(sage__rings__real_mpfr(), sage__rings__real_mpfr)
True
"""
PythonModule.__init__(self, 'sage.rings.real_mpfr')


class sage__symbolic(JoinFeature):
r"""
A :class:`~sage.features.Feature` describing the presence of :mod:`sage.symbolic`.
Expand Down Expand Up @@ -259,8 +302,10 @@ def all_features():
sage__geometry__polyhedron(),
sage__graphs(),
sage__groups(),
sage__libs__pari(),
sage__plot(),
sage__rings__number_field(),
sage__rings__padics(),
sage__rings__real_double(),
sage__rings__real_mpfr(),
sage__symbolic()]
16 changes: 8 additions & 8 deletions src/sage/geometry/cone_catalog.py
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Expand Up @@ -374,8 +374,8 @@ def rearrangement(p, ambient_dim=None, lattice=None):
sage: ambient_dim = ZZ.random_element(2,10).abs()
sage: p = ZZ.random_element(1, ambient_dim)
sage: K = cones.rearrangement(p, ambient_dim)
sage: P = SymmetricGroup(ambient_dim).random_element().matrix()
sage: all( K.contains(P*r) for r in K )
sage: P = SymmetricGroup(ambient_dim).random_element().matrix() # optional - sage.groups
sage: all(K.contains(P*r) for r in K) # optional - sage.groups
True

The smallest ``p`` components of every element of the rearrangement
Expand Down Expand Up @@ -529,11 +529,11 @@ def schur(ambient_dim=None, lattice=None):

sage: P = cones.schur(5)
sage: Q = cones.nonnegative_orthant(5)
sage: G = ( g.change_ring(QQbar).normalized() for g in P )
sage: H = ( h.change_ring(QQbar).normalized() for h in Q )
sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H)
sage: expected = 3*pi/4
sage: abs(actual - expected).n() < 1e-12
sage: G = ( g.change_ring(QQbar).normalized() for g in P ) # optional - sage.rings.number_fields
sage: H = ( h.change_ring(QQbar).normalized() for h in Q ) # optional - sage.rings.number_fields
sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H) # optional - sage.rings.number_fields
sage: expected = 3*pi/4 # optional - sage.rings.number_fields
sage: abs(actual - expected).n() < 1e-12 # optional - sage.rings.number_fields
True

The dual of the Schur cone is the "downward monotonic cone"
Expand Down Expand Up @@ -566,7 +566,7 @@ def schur(ambient_dim=None, lattice=None):
True
sage: x = V.random_element()
sage: y = V.random_element()
sage: majorized_by(x,y) == ( (y-x) in S )
sage: majorized_by(x,y) == ( (y-x) in S ) # optional - sage.rings.number_fields
True

If a ``lattice`` was given, it is actually used::
Expand Down
10 changes: 5 additions & 5 deletions src/sage/geometry/hyperplane_arrangement/affine_subspace.py
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Expand Up @@ -33,8 +33,8 @@
True
sage: c < b
False
sage: A = AffineSubspace([8,38,21,250], VectorSpace(GF(19),4))
sage: A
sage: A = AffineSubspace([8,38,21,250], VectorSpace(GF(19),4)) # optional - sage.libs.pari
sage: A # optional - sage.libs.pari
Affine space p + W where:
p = (8, 0, 2, 3)
W = Vector space of dimension 4 over Finite Field of size 19
Expand Down Expand Up @@ -384,9 +384,9 @@ def intersection(self, other):
[]
sage: A.intersection(C).intersection(B)

sage: D = AffineSubspace([1,2,3], VectorSpace(GF(5),3))
sage: E = AffineSubspace([3,4,5], VectorSpace(GF(5),3))
sage: D.intersection(E)
sage: D = AffineSubspace([1,2,3], VectorSpace(GF(5),3)) # optional - sage.libs.pari
sage: E = AffineSubspace([3,4,5], VectorSpace(GF(5),3)) # optional - sage.libs.pari
sage: D.intersection(E) # optional - sage.libs.pari
Affine space p + W where:
p = (3, 4, 0)
W = Vector space of dimension 3 over Finite Field of size 5
Expand Down
90 changes: 48 additions & 42 deletions src/sage/geometry/hyperplane_arrangement/arrangement.py
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Expand Up @@ -60,30 +60,30 @@
The default base field is `\QQ`, the rational numbers. Finite fields are also
supported::

sage: H.<x,y,z> = HyperplaneArrangements(GF(5))
sage: a = H([(1,2,3), 4], [(5,6,7), 8]); a
sage: H.<x,y,z> = HyperplaneArrangements(GF(5)) # optional - sage.libs.pari
sage: a = H([(1,2,3), 4], [(5,6,7), 8]); a # optional - sage.libs.pari
Arrangement <y + 2*z + 3 | x + 2*y + 3*z + 4>

Number fields are also possible::

sage: x = var('x')
sage: NF.<a> = NumberField(x**4 - 5*x**2 + 5,embedding=1.90)
sage: H.<y,z> = HyperplaneArrangements(NF)
sage: A = H([[(-a**3 + 3*a, -a**2 + 4), 1], [(a**3 - 4*a, -1), 1],
sage: NF.<a> = NumberField(x**4 - 5*x**2 + 5, embedding=1.90) # optional - sage.rings.number_field
sage: H.<y,z> = HyperplaneArrangements(NF) # optional - sage.rings.number_field
sage: A = H([[(-a**3 + 3*a, -a**2 + 4), 1], [(a**3 - 4*a, -1), 1], # optional - sage.rings.number_field
....: [(0, 2*a**2 - 6), 1], [(-a**3 + 4*a, -1), 1],
....: [(a**3 - 3*a, -a**2 + 4), 1]])
sage: A
sage: A # optional - sage.rings.number_field
Arrangement of 5 hyperplanes of dimension 2 and rank 2
sage: A.base_ring()
sage: A.base_ring() # optional - sage.rings.number_field
Number Field in a with defining polynomial x^4 - 5*x^2 + 5 with a = 1.902113032590308?

Notation (iii): a list or tuple of hyperplanes::

sage: H.<x,y,z> = HyperplaneArrangements(GF(5))
sage: k = [x+i for i in range(4)]; k
sage: H.<x,y,z> = HyperplaneArrangements(GF(5)) # optional - sage.libs.pari
sage: k = [x+i for i in range(4)]; k # optional - sage.libs.pari
[Hyperplane x + 0*y + 0*z + 0, Hyperplane x + 0*y + 0*z + 1,
Hyperplane x + 0*y + 0*z + 2, Hyperplane x + 0*y + 0*z + 3]
sage: H(k)
sage: H(k) # optional - sage.libs.pari
Arrangement <x | x + 1 | x + 2 | x + 3>

Notation (iv): using the library of arrangements::
Expand Down Expand Up @@ -264,10 +264,10 @@
sage: a = hyperplane_arrangements.semiorder(3)
sage: a.has_good_reduction(5)
True
sage: b = a.change_ring(GF(5))
sage: b = a.change_ring(GF(5)) # optional - sage.libs.pari
sage: pa = a.intersection_poset()
sage: pb = b.intersection_poset()
sage: pa.is_isomorphic(pb)
sage: pb = b.intersection_poset() # optional - sage.libs.pari
sage: pa.is_isomorphic(pb) # optional - sage.libs.pari
True
sage: a.face_vector()
(0, 12, 30, 19)
Expand Down Expand Up @@ -356,7 +356,6 @@
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

from sage.geometry.hyperplane_arrangement.hyperplane import AmbientVectorSpace, Hyperplane
from sage.combinat.posets.posets import Poset


class HyperplaneArrangementElement(Element):
Expand Down Expand Up @@ -1129,7 +1128,7 @@ def change_ring(self, base_ring):

sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: A = H([(1,1), 0], [(2,3), -1])
sage: A.change_ring(FiniteField(2))
sage: A.change_ring(FiniteField(2)) # optional - sage.libs.pari
Arrangement <y + 1 | x + y>

TESTS:
Expand Down Expand Up @@ -1165,25 +1164,30 @@ def n_regions(self):

sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: A = H([(1,1), 0], [(2,3), -1], [(4,5), 3])
sage: B = A.change_ring(FiniteField(7))
sage: B.n_regions()
sage: B = A.change_ring(FiniteField(7)) # optional - sage.libs.pari
sage: B.n_regions() # optional - sage.libs.pari
Traceback (most recent call last):
...
TypeError: base field must have characteristic zero

Check that :trac:`30749` is fixed::

sage: R.<y> = QQ[]
sage: v1 = AA.polynomial_root(AA.common_polynomial(y^2 - 3), RIF(RR(1.7320508075688772), RR(1.7320508075688774)))
sage: v2 = QQbar.polynomial_root(AA.common_polynomial(y^4 - y^2 + 1), CIF(RIF(RR(0.8660254037844386), RR(0.86602540378443871)), RIF(-RR(0.50000000000000011), -RR(0.49999999999999994))))
sage: my_vectors = (vector(AA, [-v1, -1, 1]), vector(AA, [0, 2, 1]), vector(AA,[v1, -1, 1]), vector(AA, [1, 0, 0]), vector(AA, [1/2, AA(-1/2*v2^3 + v2),0]), vector(AA, [-1/2, AA(-1/2*v2^3 + v2), 0]))
sage: H = HyperplaneArrangements(AA, names='xyz')
sage: x,y,z = H.gens()
sage: A = H(backend="normaliz") # optional - pynormaliz
sage: for v in my_vectors: # optional - pynormaliz
sage: v1 = AA.polynomial_root(AA.common_polynomial(y^2 - 3), # optional - sage.rings.number_field
....: RIF(RR(1.7320508075688772), RR(1.7320508075688774)))
sage: v2 = QQbar.polynomial_root(AA.common_polynomial(y^4 - y^2 + 1), # optional - sage.rings.number_field
....: CIF(RIF(RR(0.8660254037844386), RR(0.86602540378443871)),
....: RIF(-RR(0.50000000000000011), -RR(0.49999999999999994))))
sage: my_vectors = (vector(AA, [-v1, -1, 1]), vector(AA, [0, 2, 1]), vector(AA, [v1, -1, 1]), # optional - sage.rings.number_field
....: vector(AA, [1, 0, 0]), vector(AA, [1/2, AA(-1/2*v2^3 + v2),0]),
....: vector(AA, [-1/2, AA(-1/2*v2^3 + v2), 0]))
sage: H = HyperplaneArrangements(AA, names='xyz') # optional - sage.rings.number_field
sage: x,y,z = H.gens() # optional - sage.rings.number_field
sage: A = H(backend="normaliz") # optional - pynormaliz # optional - sage.rings.number_field
sage: for v in my_vectors: # optional - pynormaliz # optional - sage.rings.number_field
....: a, b, c = v
....: A = A.add_hyperplane(a*x + b*y + c*z)
sage: A.n_regions() # optional - pynormaliz
sage: A.n_regions() # optional - pynormaliz # optional - sage.rings.number_field
24
"""
if self.base_ring().characteristic() != 0:
Expand Down Expand Up @@ -1211,8 +1215,8 @@ def n_bounded_regions(self):

sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: A = H([(1,1),0], [(2,3),-1], [(4,5),3])
sage: B = A.change_ring(FiniteField(7))
sage: B.n_bounded_regions()
sage: B = A.change_ring(FiniteField(7)) # optional - sage.libs.pari
sage: B.n_bounded_regions() # optional - sage.libs.pari
Traceback (most recent call last):
...
TypeError: base field must have characteristic zero
Expand Down Expand Up @@ -1243,14 +1247,14 @@ def has_good_reduction(self, p):
EXAMPLES::

sage: a = hyperplane_arrangements.semiorder(3)
sage: a.has_good_reduction(5)
sage: a.has_good_reduction(5) # optional - sage.libs.pari
True
sage: a.has_good_reduction(3)
sage: a.has_good_reduction(3) # optional - sage.libs.pari
False
sage: b = a.change_ring(GF(3))
sage: b = a.change_ring(GF(3)) # optional - sage.libs.pari
sage: a.characteristic_polynomial()
x^3 - 6*x^2 + 12*x
sage: b.characteristic_polynomial() # not equal to that for a
sage: b.characteristic_polynomial() # not equal to that for a # optional - sage.libs.pari
x^3 - 6*x^2 + 10*x
"""
if self.base_ring() != QQ:
Expand Down Expand Up @@ -1495,9 +1499,9 @@ def essentialization(self):
Hyperplane arrangements in 1-dimensional linear space over
Rational Field with coordinate x

sage: H.<x,y> = HyperplaneArrangements(GF(2))
sage: C = H([(1,1),1], [(1,1),0])
sage: C.essentialization()
sage: H.<x,y> = HyperplaneArrangements(GF(2)) # optional - sage.libs.pari
sage: C = H([(1,1),1], [(1,1),0]) # optional - sage.libs.pari
sage: C.essentialization() # optional - sage.libs.pari
Arrangement <y | y + 1>

sage: h = hyperplane_arrangements.semiorder(4)
Expand Down Expand Up @@ -1587,9 +1591,9 @@ def sign_vector(self, p):

TESTS::

sage: H.<x,y> = HyperplaneArrangements(GF(3))
sage: A = H(x, y)
sage: A.sign_vector([1, 2])
sage: H.<x,y> = HyperplaneArrangements(GF(3)) # optional - sage.libs.pari
sage: A = H(x, y) # optional - sage.libs.pari
sage: A.sign_vector([1, 2]) # optional - sage.libs.pari
Traceback (most recent call last):
...
ValueError: characteristic must be zero
Expand Down Expand Up @@ -1992,6 +1996,8 @@ def poset_of_regions(self, B=None, numbered_labels=True):
sage: A.poset_of_regions(B=base_region)
Finite poset containing 14 elements
"""
from sage.combinat.posets.posets import Poset

# We use RX to keep track of indexes and R to keep track of which regions
# we've already hit. This poset is graded, so we can go one set at a time
RX = self.regions()
Expand Down Expand Up @@ -2480,7 +2486,7 @@ def face_semigroup_algebra(self, field=None, names='e'):
sage: (e3 + 2*e4) * (e1 - e7)
e4 - e6

sage: U3 = a.face_semigroup_algebra(field=GF(3)); U3
sage: U3 = a.face_semigroup_algebra(field=GF(3)); U3 # optional - sage.libs.pari
Finite-dimensional algebra of degree 13 over Finite Field of size 3

TESTS:
Expand Down Expand Up @@ -2550,8 +2556,8 @@ def region_containing_point(self, p):
TESTS::

sage: A = H([(1,1),0], [(2,3),-1], [(4,5),3])
sage: B = A.change_ring(FiniteField(7))
sage: B.region_containing_point((1,2))
sage: B = A.change_ring(FiniteField(7)) # optional - sage.libs.pari
sage: B.region_containing_point((1,2)) # optional - sage.libs.pari
Traceback (most recent call last):
...
ValueError: base field must have characteristic zero
Expand Down Expand Up @@ -2991,8 +2997,8 @@ def matroid(self):
intersection lattice::

sage: f = sum([list(M.flats(i)) for i in range(M.rank()+1)], [])
sage: PF = Poset([f, lambda x,y: x < y])
sage: PF.is_isomorphic(A.intersection_poset())
sage: PF = Poset([f, lambda x, y: x < y]) # optional - sage.combinat
sage: PF.is_isomorphic(A.intersection_poset()) # optional - sage.combinat
True
"""
if not self.is_central():
Expand Down
2 changes: 1 addition & 1 deletion src/sage/geometry/linear_expression.py
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Expand Up @@ -440,7 +440,7 @@ def evaluate(self, point):
9
sage: ex([1,1]) # syntactic sugar
9
sage: ex([pi, e])
sage: ex([pi, e]) # optional - sage.symbolic
2*pi + 3*e + 4
"""
try:
Expand Down
2 changes: 1 addition & 1 deletion src/sage/geometry/polyhedral_complex.py
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@@ -1,4 +1,4 @@
# -*- coding: utf-8 -*-
# sage.doctest: optional - sage.graphs
r"""
Finite polyhedral complexes

Expand Down
6 changes: 3 additions & 3 deletions src/sage/geometry/polyhedron/backend_number_field.py
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Expand Up @@ -119,11 +119,11 @@ def _init_from_Vrepresentation(self, vertices, rays, lines,

Check that the coordinates of a vertex get simplified in the Symbolic Ring::

sage: p = Polyhedron(ambient_dim=2, base_ring=SR, backend='number_field')
sage: p = Polyhedron(ambient_dim=2, base_ring=SR, backend='number_field') # optional - sage.symbolic
sage: from sage.geometry.polyhedron.backend_number_field import Polyhedron_number_field
sage: Polyhedron_number_field._init_from_Vrepresentation(p, [(0,1/2),(sqrt(2),0),(4,5/6)], [], []); p
sage: Polyhedron_number_field._init_from_Vrepresentation(p, [(0,1/2),(sqrt(2),0),(4,5/6)], [], []); p # optional - sage.symbolic
A 2-dimensional polyhedron in (Symbolic Ring)^2 defined as the convex hull of 3 vertices
sage: p.vertices()[0][0]
sage: p.vertices()[0][0] # optional - sage.symbolic
0
"""
(vertices, rays, lines), internal_base_ring \
Expand Down
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