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Trac #32652: sage.geometry.polyhedron: Mark doctests # optional - sage.rings.number_field
(cherry-picked from #32432) URL: https://trac.sagemath.org/32652 Reported by: mkoeppe Ticket author(s): Matthias Koeppe Reviewer(s): Jonathan Kliem
2 parents 5c0ceda + 1400654 commit 4f73d49

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‎src/sage/geometry/polyhedron/backend_field.py

+42-42
Original file line numberDiff line numberDiff line change
@@ -9,13 +9,13 @@
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sage: p0 = (0, 0)
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sage: p1 = (1, 0)
12-
sage: p2 = (1/2, AA(3).sqrt()/2)
13-
sage: equilateral_triangle = Polyhedron([p0, p1, p2])
14-
sage: equilateral_triangle.vertices()
12+
sage: p2 = (1/2, AA(3).sqrt()/2) # optional - sage.rings.number_field
13+
sage: equilateral_triangle = Polyhedron([p0, p1, p2]) # optional - sage.rings.number_field
14+
sage: equilateral_triangle.vertices() # optional - sage.rings.number_field
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(A vertex at (0, 0),
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A vertex at (1, 0),
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A vertex at (0.500000000000000?, 0.866025403784439?))
18-
sage: equilateral_triangle.inequalities()
18+
sage: equilateral_triangle.inequalities() # optional - sage.rings.number_field
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(An inequality (-1, -0.5773502691896258?) x + 1 >= 0,
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An inequality (1, -0.5773502691896258?) x + 0 >= 0,
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An inequality (0, 1.154700538379252?) x + 0 >= 0)
@@ -46,22 +46,22 @@ class Polyhedron_field(Polyhedron_base):
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EXAMPLES::
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49-
sage: p = Polyhedron(vertices=[(0,0),(AA(2).sqrt(),0),(0,AA(3).sqrt())],
49+
sage: p = Polyhedron(vertices=[(0,0),(AA(2).sqrt(),0),(0,AA(3).sqrt())], # optional - sage.rings.number_field
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....: rays=[(1,1)], lines=[], backend='field', base_ring=AA)
51-
sage: TestSuite(p).run()
51+
sage: TestSuite(p).run() # optional - sage.rings.number_field
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TESTS::
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sage: K.<sqrt3> = QuadraticField(3)
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sage: p = Polyhedron([(0,0), (1,0), (1/2, sqrt3/2)])
57-
sage: TestSuite(p).run()
55+
sage: K.<sqrt3> = QuadraticField(3) # optional - sage.rings.number_field
56+
sage: p = Polyhedron([(0,0), (1,0), (1/2, sqrt3/2)]) # optional - sage.rings.number_field
57+
sage: TestSuite(p).run() # optional - sage.rings.number_field
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Check that :trac:`19013` is fixed::
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sage: K.<phi> = NumberField(x^2-x-1, embedding=1.618)
62-
sage: P1 = Polyhedron([[0,1],[1,1],[1,-phi+1]])
63-
sage: P2 = Polyhedron(ieqs=[[-1,-phi,0]])
64-
sage: P1.intersection(P2)
61+
sage: K.<phi> = NumberField(x^2-x-1, embedding=1.618) # optional - sage.rings.number_field
62+
sage: P1 = Polyhedron([[0,1],[1,1],[1,-phi+1]]) # optional - sage.rings.number_field
63+
sage: P2 = Polyhedron(ieqs=[[-1,-phi,0]]) # optional - sage.rings.number_field
64+
sage: P1.intersection(P2) # optional - sage.rings.number_field
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The empty polyhedron in (Number Field in phi with defining polynomial x^2 - x - 1 with phi = 1.618033988749895?)^2
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Check that :trac:`28654` is fixed::
@@ -83,10 +83,10 @@ def _is_zero(self, x):
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EXAMPLES::
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86-
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
87-
sage: p._is_zero(0)
86+
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
87+
sage: p._is_zero(0) # optional - sage.rings.number_field
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True
89-
sage: p._is_zero(1/100000)
89+
sage: p._is_zero(1/100000) # optional - sage.rings.number_field
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False
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"""
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return x == 0
@@ -105,10 +105,10 @@ def _is_nonneg(self, x):
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EXAMPLES::
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sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
109-
sage: p._is_nonneg(1)
108+
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
109+
sage: p._is_nonneg(1) # optional - sage.rings.number_field
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True
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sage: p._is_nonneg(-1/100000)
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sage: p._is_nonneg(-1/100000) # optional - sage.rings.number_field
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False
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"""
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return x >= 0
@@ -127,10 +127,10 @@ def _is_positive(self, x):
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EXAMPLES::
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sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
131-
sage: p._is_positive(1)
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sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
131+
sage: p._is_positive(1) # optional - sage.rings.number_field
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True
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sage: p._is_positive(0)
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sage: p._is_positive(0) # optional - sage.rings.number_field
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False
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"""
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return x > 0
@@ -150,12 +150,12 @@ def _init_from_Vrepresentation_and_Hrepresentation(self, Vrep, Hrep):
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sage: from sage.geometry.polyhedron.parent import Polyhedra_field
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sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
153-
sage: parent = Polyhedra_field(AA, 1, 'field')
153+
sage: parent = Polyhedra_field(AA, 1, 'field') # optional - sage.rings.number_field
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sage: Vrep = [[[0], [1]], [], []]
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sage: Hrep = [[[0, 1], [1, -1]], []]
156-
sage: p = Polyhedron_field(parent, Vrep, Hrep,
157-
....: Vrep_minimal=True, Hrep_minimal=True) # indirect doctest
158-
sage: p
156+
sage: p = Polyhedron_field(parent, Vrep, Hrep, # indirect doctest # optional - sage.rings.number_field
157+
....: Vrep_minimal=True, Hrep_minimal=True)
158+
sage: p # optional - sage.rings.number_field
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A 1-dimensional polyhedron in AA^1 defined as the convex hull of 2 vertices
160160
"""
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self._init_Vrepresentation(*Vrep)
@@ -234,12 +234,12 @@ def _init_Vrepresentation(self, vertices, rays, lines):
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sage: from sage.geometry.polyhedron.parent import Polyhedra_field
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sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
237-
sage: parent = Polyhedra_field(AA, 1, 'field')
237+
sage: parent = Polyhedra_field(AA, 1, 'field') # optional - sage.rings.number_field
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sage: Vrep = [[[0], [1]], [], []]
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sage: Hrep = [[[0, 1], [1, -1]], []]
240-
sage: p = Polyhedron_field(parent, Vrep, Hrep, # indirect doctest
240+
sage: p = Polyhedron_field(parent, Vrep, Hrep, # indirect doctest # optional - sage.rings.number_field
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....: Vrep_minimal=True, Hrep_minimal=True)
242-
sage: p.vertices_list()
242+
sage: p.vertices_list() # optional - sage.rings.number_field
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[[0], [1]]
244244
"""
245245
self._Vrepresentation = []
@@ -258,13 +258,13 @@ def _init_Vrepresentation_backend(self, Vrep):
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EXAMPLES::
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261-
sage: p = Polyhedron(vertices=[(0,1/sqrt(2)),(sqrt(2),0),(4,sqrt(5)/6)],
261+
sage: p = Polyhedron(vertices=[(0,1/sqrt(2)),(sqrt(2),0),(4,sqrt(5)/6)], # optional - sage.rings.number_field
262262
....: base_ring=AA, backend='field') # indirect doctest
263-
sage: p.Hrepresentation()
263+
sage: p.Hrepresentation() # optional - sage.rings.number_field
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(An inequality (-0.1582178750233332?, 1.097777812326429?) x + 0.2237538646678492? >= 0,
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An inequality (-0.1419794359520263?, -1.698172434277148?) x + 1.200789243901438? >= 0,
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An inequality (0.3001973109753594?, 0.600394621950719?) x - 0.4245431085692869? >= 0)
267-
sage: p.Vrepresentation()
267+
sage: p.Vrepresentation() # optional - sage.rings.number_field
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(A vertex at (0.?e-15, 0.707106781186548?),
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A vertex at (1.414213562373095?, 0),
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A vertex at (4.000000000000000?, 0.372677996249965?))
@@ -279,12 +279,12 @@ def _init_Hrepresentation(self, inequalities, equations):
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sage: from sage.geometry.polyhedron.parent import Polyhedra_field
281281
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
282-
sage: parent = Polyhedra_field(AA, 1, 'field')
282+
sage: parent = Polyhedra_field(AA, 1, 'field') # optional - sage.rings.number_field
283283
sage: Vrep = [[[0], [1]], [], []]
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sage: Hrep = [[[0, 1], [1, -1]], []]
285-
sage: p = Polyhedron_field(parent, Vrep, Hrep, # indirect doctest
285+
sage: p = Polyhedron_field(parent, Vrep, Hrep, # indirect doctest # optional - sage.rings.number_field
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....: Vrep_minimal=True, Hrep_minimal=True)
287-
sage: p.inequalities_list()
287+
sage: p.inequalities_list() # optional - sage.rings.number_field
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[[0, 1], [1, -1]]
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"""
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self._Hrepresentation = []
@@ -301,13 +301,13 @@ def _init_Hrepresentation_backend(self, Hrep):
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EXAMPLES::
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sage: p = Polyhedron(vertices=[(0,1/sqrt(2)),(sqrt(2),0),(4,sqrt(5)/6)],
304+
sage: p = Polyhedron(vertices=[(0,1/sqrt(2)),(sqrt(2),0),(4,sqrt(5)/6)], # optional - sage.rings.number_field
305305
....: base_ring=AA, backend='field') # indirect doctest
306-
sage: p.Hrepresentation()
306+
sage: p.Hrepresentation() # optional - sage.rings.number_field
307307
(An inequality (-0.1582178750233332?, 1.097777812326429?) x + 0.2237538646678492? >= 0,
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An inequality (-0.1419794359520263?, -1.698172434277148?) x + 1.200789243901438? >= 0,
309309
An inequality (0.3001973109753594?, 0.600394621950719?) x - 0.4245431085692869? >= 0)
310-
sage: p.Vrepresentation()
310+
sage: p.Vrepresentation() # optional - sage.rings.number_field
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(A vertex at (0.?e-15, 0.707106781186548?),
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A vertex at (1.414213562373095?, 0),
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A vertex at (4.000000000000000?, 0.372677996249965?))
@@ -320,13 +320,13 @@ def _init_empty_polyhedron(self):
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TESTS::
322322
323-
sage: empty = Polyhedron(backend='field', base_ring=AA); empty
323+
sage: empty = Polyhedron(backend='field', base_ring=AA); empty # optional - sage.rings.number_field
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The empty polyhedron in AA^0
325-
sage: empty.Vrepresentation()
325+
sage: empty.Vrepresentation() # optional - sage.rings.number_field
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()
327-
sage: empty.Hrepresentation()
327+
sage: empty.Hrepresentation() # optional - sage.rings.number_field
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(An equation -1 == 0,)
329-
sage: Polyhedron(vertices = [], backend='field')
329+
sage: Polyhedron(vertices=[], backend='field')
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The empty polyhedron in QQ^0
331331
sage: Polyhedron(backend='field')._init_empty_polyhedron()
332332
"""

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