Skip to content
This repository has been archived by the owner on Jan 30, 2023. It is now read-only.

Commit

Permalink
src/sage/geometry/polyhedron/backend_normaliz.py: Mark non-rational e…
Browse files Browse the repository at this point in the history 
…xamples # optional - sage.rings.number_field
  • Loading branch information
Matthias Koeppe committed Oct 8, 2021
1 parent c0e73d8 commit 49658e0
Showing 1 changed file with 57 additions and 57 deletions.
114 changes: 57 additions & 57 deletions src/sage/geometry/polyhedron/backend_normaliz.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -47,12 +47,12 @@ def _number_field_elements_from_algebraics_list_of_lists_of_lists(listss, **kwds
EXAMPLES::
sage: rt2 = AA(sqrt(2)); rt2
sage: rt2 = AA(sqrt(2)); rt2 # optional - sage.rings.number_field
1.414213562373095?
sage: rt3 = AA(sqrt(3)); rt3
sage: rt3 = AA(sqrt(3)); rt3 # optional - sage.rings.number_field
1.732050807568878?
sage: from sage.geometry.polyhedron.backend_normaliz import _number_field_elements_from_algebraics_list_of_lists_of_lists
sage: K, results, hom = _number_field_elements_from_algebraics_list_of_lists_of_lists([[[rt2], [1]], [[rt3]], [[1], []]]); results
sage: K, results, hom = _number_field_elements_from_algebraics_list_of_lists_of_lists([[[rt2], [1]], [[rt3]], [[1], []]]); results # optional - sage.rings.number_field
[[[-a^3 + 3*a], [1]], [[-a^2 + 2]], [[1], []]]
"""
from sage.rings.qqbar import number_field_elements_from_algebraics
Expand Down Expand Up @@ -171,7 +171,7 @@ class Polyhedron_normaliz(Polyhedron_base):
Algebraic polyhedra::
sage: P = Polyhedron(vertices=[[1], [sqrt(2)]], backend='normaliz', verbose=True) # optional - pynormaliz
sage: P = Polyhedron(vertices=[[1], [sqrt(2)]], backend='normaliz', verbose=True) # optional - pynormaliz # optional - sage.rings.number_field
# ----8<---- Equivalent Normaliz input file ----8<----
amb_space 1
number_field min_poly (a^2 - 2) embedding [1.414213562373095 +/- 2.99e-16]
Expand All @@ -182,16 +182,16 @@ class Polyhedron_normaliz(Polyhedron_base):
(a) 1
# ----8<-------------------8<-------------------8<----
# Calling PyNormaliz.NmzCone(cone=[], number_field=['a^2 - 2', 'a', '[1.414213562373095 +/- 2.99e-16]'], subspace=[], vertices=[[1, 1], [[[0, 1], [1, 1]], 1]])
sage: P # optional - pynormaliz
sage: P # optional - pynormaliz # optional - sage.rings.number_field
A 1-dimensional polyhedron in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
sage: P.vertices() # optional - pynormaliz
sage: P.vertices() # optional - pynormaliz # optional - sage.rings.number_field
(A vertex at (1), A vertex at (sqrt(2)))
sage: P = polytopes.icosahedron(exact=True, backend='normaliz') # optional - pynormaliz
sage: P # optional - pynormaliz
sage: P = polytopes.icosahedron(exact=True, backend='normaliz') # optional - pynormaliz # optional - sage.rings.number_field
sage: P # optional - pynormaliz # optional - sage.rings.number_field
A 3-dimensional polyhedron in (Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?)^3 defined as the convex hull of 12 vertices
sage: x = polygen(ZZ); P = Polyhedron(vertices=[[sqrt(2)], [AA.polynomial_root(x^3-2, RIF(0,3))]], backend='normaliz', verbose=True) # optional - pynormaliz
sage: x = polygen(ZZ); P = Polyhedron(vertices=[[sqrt(2)], [AA.polynomial_root(x^3-2, RIF(0,3))]], backend='normaliz', verbose=True) # optional - pynormaliz # optional - sage.rings.number_field
# ----8<---- Equivalent Normaliz input file ----8<----
amb_space 1
number_field min_poly (a^6 - 2) embedding [1.122462048309373 +/- 5.38e-16]
Expand All @@ -202,9 +202,9 @@ class Polyhedron_normaliz(Polyhedron_base):
(a^2) 1
# ----8<-------------------8<-------------------8<----
# Calling PyNormaliz.NmzCone(cone=[], number_field=['a^6 - 2', 'a', '[1.122462048309373 +/- 5.38e-16]'], subspace=[], vertices=[[[[0, 1], [0, 1], [0, 1], [1, 1], [0, 1], [0, 1]], 1], [[[0, 1], [0, 1], [1, 1], [0, 1], [0, 1], [0, 1]], 1]])
sage: P # optional - pynormaliz
sage: P # optional - pynormaliz # optional - sage.rings.number_field
A 1-dimensional polyhedron in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
sage: P.vertices() # optional - pynormaliz
sage: P.vertices() # optional - pynormaliz # optional - sage.rings.number_field
(A vertex at (2^(1/3)), A vertex at (sqrt(2)))
"""
Expand Down Expand Up @@ -255,20 +255,20 @@ def _nmz_result(self, normaliz_cone, property):
NormalizError: Some error in the normaliz input data detected: Unknown ConeProperty...
sage: x = polygen(QQ, 'x')
sage: K.<a> = NumberField(x^3 - 3, embedding=AA(3)**(1/3))
sage: p = Polyhedron(vertices=[(0,0),(1,1),(a,3),(-1,a**2)], rays=[(-1,-a)], backend='normaliz') # optional - pynormaliz
sage: sorted(p._nmz_result(p._normaliz_cone, 'VerticesOfPolyhedron')) # optional - pynormaliz
sage: K.<a> = NumberField(x^3 - 3, embedding=AA(3)**(1/3)) # optional - sage.rings.number_field
sage: p = Polyhedron(vertices=[(0,0),(1,1),(a,3),(-1,a**2)], rays=[(-1,-a)], backend='normaliz') # optional - pynormaliz # optional - sage.rings.number_field
sage: sorted(p._nmz_result(p._normaliz_cone, 'VerticesOfPolyhedron')) # optional - pynormaliz # optional - sage.rings.number_field
[[-1, a^2, 1], [1, 1, 1], [a, 3, 1]]
sage: triangulation_generators = p._nmz_result(p._normaliz_cone, 'Triangulation')[1] # optional - pynormaliz
sage: sorted(triangulation_generators) # optional - pynormaliz
sage: triangulation_generators = p._nmz_result(p._normaliz_cone, 'Triangulation')[1] # optional - pynormaliz # optional - sage.rings.number_field
sage: sorted(triangulation_generators) # optional - pynormaliz # optional - sage.rings.number_field
[[-a^2, -3, 0], [-1, a^2, 1], [0, 0, 1], [1, 1, 1], [a, 3, 1]]
sage: p._nmz_result(p._normaliz_cone, 'AffineDim') == 2 # optional - pynormaliz
sage: p._nmz_result(p._normaliz_cone, 'AffineDim') == 2 # optional - pynormaliz # optional - sage.rings.number_field
True
sage: p._nmz_result(p._normaliz_cone, 'EmbeddingDim') == 3 # optional - pynormaliz
sage: p._nmz_result(p._normaliz_cone, 'EmbeddingDim') == 3 # optional - pynormaliz # optional - sage.rings.number_field
True
sage: p._nmz_result(p._normaliz_cone, 'ExtremeRays') # optional - pynormaliz
sage: p._nmz_result(p._normaliz_cone, 'ExtremeRays') # optional - pynormaliz # optional - sage.rings.number_field
[[-1/3*a^2, -1, 0]]
sage: p._nmz_result(p._normaliz_cone, 'MaximalSubspace') # optional - pynormaliz
sage: p._nmz_result(p._normaliz_cone, 'MaximalSubspace') # optional - pynormaliz # optional - sage.rings.number_field
[]
"""
def rational_handler(list):
Expand Down Expand Up @@ -313,7 +313,7 @@ def _convert_to_pynormaliz(x):
TESTS::
sage: K.<sqrt2> = QuadraticField(2)
sage: K.<sqrt2> = QuadraticField(2) # optional - sage.rings.number_field
sage: from sage.geometry.polyhedron.backend_normaliz import Polyhedron_normaliz as Pn
sage: Pn._convert_to_pynormaliz(17)
17
Expand All @@ -325,18 +325,18 @@ def _convert_to_pynormaliz(x):
[[28, 5]]
sage: Pn._convert_to_pynormaliz(28901824309821093821093812093810928309183091832091/5234573685674784567853456543456456786543456765)
[[28901824309821093821093812093810928309183091832091, 5234573685674784567853456543456456786543456765]]
sage: Pn._convert_to_pynormaliz(7 + sqrt2)
sage: Pn._convert_to_pynormaliz(7 + sqrt2) # optional - sage.rings.number_field
[[7, 1], [1, 1]]
sage: Pn._convert_to_pynormaliz(7/2 + sqrt2)
sage: Pn._convert_to_pynormaliz(7/2 + sqrt2) # optional - sage.rings.number_field
[[7, 2], [1, 1]]
sage: Pn._convert_to_pynormaliz([[1, 2], (3, 4)])
[[1, 2], [3, 4]]
Check that :trac:`29836` is fixed::
sage: P = polytopes.simplex(backend='normaliz') # optional - pynormaliz
sage: K.<sqrt2> = QuadraticField(2) # optional - pynormaliz
sage: P.dilation(sqrt2) # optional - pynormaliz
sage: K.<sqrt2> = QuadraticField(2) # optional - pynormaliz # optional - sage.rings.number_field
sage: P.dilation(sqrt2) # optional - pynormaliz # optional - sage.rings.number_field
A 3-dimensional polyhedron in (Number Field in sqrt2 with defining polynomial x^2 - 2 with sqrt2 = 1.41...)^4 defined as the convex hull of 4 vertices
"""
def _QQ_pair(x):
Expand Down Expand Up @@ -369,16 +369,16 @@ def _init_from_normaliz_data(self, data, normaliz_field=None, verbose=False):
[[0, -1, 2], [0, 2, -1]]
sage: from sage.geometry.polyhedron.backend_normaliz import Polyhedron_normaliz # optional - pynormaliz
sage: from sage.rings.qqbar import AA # optional - pynormaliz
sage: from sage.rings.number_field.number_field import QuadraticField # optional - pynormaliz
sage: from sage.rings.qqbar import AA # optional - pynormaliz # optional - sage.rings.number_field
sage: from sage.rings.number_field.number_field import QuadraticField # optional - pynormaliz # optional - sage.rings.number_field
sage: data = {'number_field': ['a^2 - 2', 'a', '[1.4 +/- 0.1]'], # optional - pynormaliz
....: 'inhom_inequalities': [[-1, 2, 0], [0, 0, 1], [2, -1, 0]]}
sage: from sage.geometry.polyhedron.parent import Polyhedra_normaliz # optional - pynormaliz
sage: parent = Polyhedra_normaliz(AA, 2, 'normaliz') # optional - pynormaliz
sage: Polyhedron_normaliz(parent, None, None, normaliz_data=data, # indirect doctest, optional - pynormaliz
sage: parent = Polyhedra_normaliz(AA, 2, 'normaliz') # optional - pynormaliz # optional - sage.rings.number_field
sage: Polyhedron_normaliz(parent, None, None, normaliz_data=data, # indirect doctest, optional - pynormaliz # optional - sage.rings.number_field
....: normaliz_field=QuadraticField(2))
A 2-dimensional polyhedron in AA^2 defined as the convex hull of 1 vertex and 2 rays
sage: _.inequalities_list() # optional - pynormaliz
sage: _.inequalities_list() # optional - pynormaliz # optional - sage.rings.number_field
[[0, -1/2, 1], [0, 2, -1]]
"""
if normaliz_field is None:
Expand Down Expand Up @@ -433,10 +433,10 @@ def _is_zero(self, x):
EXAMPLES::
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
sage: p._is_zero(0)
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
sage: p._is_zero(0) # optional - sage.rings.number_field
True
sage: p._is_zero(1/100000)
sage: p._is_zero(1/100000) # optional - sage.rings.number_field
False
"""
return x == 0
Expand All @@ -455,10 +455,10 @@ def _is_nonneg(self, x):
EXAMPLES::
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
sage: p._is_nonneg(1)
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
sage: p._is_nonneg(1) # optional - sage.rings.number_field
True
sage: p._is_nonneg(-1/100000)
sage: p._is_nonneg(-1/100000) # optional - sage.rings.number_field
False
"""
return x >= 0
Expand All @@ -477,10 +477,10 @@ def _is_positive(self, x):
EXAMPLES::
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA)
sage: p._is_positive(1)
sage: p = Polyhedron([(sqrt(3),sqrt(2))], base_ring=AA) # optional - sage.rings.number_field
sage: p._is_positive(1) # optional - sage.rings.number_field
True
sage: p._is_positive(0)
sage: p._is_positive(0) # optional - sage.rings.number_field
False
"""
return x > 0
Expand Down Expand Up @@ -595,14 +595,14 @@ def _init_from_Hrepresentation(self, ieqs, eqns, minimize=True, verbose=False):
Check that :trac:`30248` is fixed, that maps as input works::
sage: q = Polyhedron(backend='normaliz', base_ring=AA, # optional - pynormaliz
sage: q = Polyhedron(backend='normaliz', base_ring=AA, # optional - pynormaliz # optional - sage.rings.number_field
....: rays=[(0, 0, 1), (0, 1, -1), (1, 0, -1)])
sage: make_new_Hrep = lambda h: tuple(x if i == 0 else -1*x for i, x in enumerate(h._vector))
sage: new_inequalities = map(make_new_Hrep, q.inequality_generator()) # optional - pynormaliz
sage: new_equations = map(make_new_Hrep, q.equation_generator()) # optional - pynormaliz
sage: parent = q.parent() # optional - pynormaliz
sage: new_q = parent.element_class(parent,None,[new_inequalities,new_equations]) # optional - pynormaliz
sage: new_q # optional - pynormaliz
sage: new_inequalities = map(make_new_Hrep, q.inequality_generator()) # optional - pynormaliz # optional - sage.rings.number_field
sage: new_equations = map(make_new_Hrep, q.equation_generator()) # optional - pynormaliz # optional - sage.rings.number_field
sage: parent = q.parent() # optional - pynormaliz # optional - sage.rings.number_field
sage: new_q = parent.element_class(parent,None,[new_inequalities,new_equations]) # optional - pynormaliz # optional - sage.rings.number_field
sage: new_q # optional - pynormaliz # optional - sage.rings.number_field
A 3-dimensional polyhedron in AA^3 defined as the convex hull of 1 vertex and 3 rays
"""

Expand Down Expand Up @@ -928,26 +928,26 @@ def _compute_nmz_data_lists_and_field(self, data_lists, convert_QQ, convert_NF):
sage: p._compute_nmz_data_lists_and_field([[[AA(1)]], [[1/2]]], # optional - pynormaliz
....: convert_QQ, convert_NF)
(([[1000]], [[500]]), Rational Field)
sage: p._compute_nmz_data_lists_and_field([[[AA(sqrt(2))]], [[1/2]]], # optional - pynormaliz
sage: p._compute_nmz_data_lists_and_field([[[AA(sqrt(2))]], [[1/2]]], # optional - pynormaliz # optional - sage.rings.number_field
....: convert_QQ, convert_NF)
([[[a]], [[1/2]]],
Number Field in a with defining polynomial y^2 - 2 with a = 1.414213562373095?)
TESTS::
sage: K.<a> = QuadraticField(-5)
sage: p = Polyhedron(vertices=[(a,1/2),(2,0),(4,5/6)], # indirect doctest # optional - pynormaliz
sage: K.<a> = QuadraticField(-5) # optional - sage.rings.number_field
sage: p = Polyhedron(vertices=[(a,1/2),(2,0),(4,5/6)], # indirect doctest # optional - pynormaliz # optional - sage.rings.number_field
....: base_ring=K, backend='normaliz')
Traceback (most recent call last):
...
ValueError: invalid base ring: Number Field in a ... is not real embedded
Checks that :trac:`30248` is fixed::
sage: q = Polyhedron(backend='normaliz', base_ring=AA, # indirect doctest # optional - pynormaliz
sage: q = Polyhedron(backend='normaliz', base_ring=AA, # indirect doctest # optional - pynormaliz # optional - sage.rings.number_field
....: rays=[(0, 0, 1), (0, 1, -1), (1, 0, -1)]); q
A 3-dimensional polyhedron in AA^3 defined as the convex hull of 1 vertex and 3 rays
sage: -q # optional - pynormaliz
sage: -q # optional - pynormaliz # optional - sage.rings.number_field
A 3-dimensional polyhedron in AA^3 defined as the convex hull of 1 vertex and 3 rays
"""
from sage.categories.number_fields import NumberFields
Expand Down Expand Up @@ -1078,7 +1078,7 @@ def _number_field_triple(normaliz_field):
sage: from sage.geometry.polyhedron.backend_normaliz import Polyhedron_normaliz as Pn
sage: Pn._number_field_triple(QQ) is None
True
sage: Pn._number_field_triple(QuadraticField(5))
sage: Pn._number_field_triple(QuadraticField(5)) # optional - sage.rings.number_field
['a^2 - 5', 'a', '[2.236067977499789 +/- 8.06e-16]']
"""
from sage.rings.real_arb import RealBallField
Expand Down Expand Up @@ -1327,10 +1327,10 @@ def __setstate__(self, state):
sage: P2 == P # optional - pynormaliz
True
sage: P = polytopes.dodecahedron(backend='normaliz') # optional - pynormaliz
sage: P1 = loads(dumps(P)) # optional - pynormaliz
sage: P2 = Polyhedron_normaliz(P1.parent(), None, None, P1._normaliz_cone, normaliz_field=P1._normaliz_field) # optional - pynormaliz
sage: P == P2 # optional - pynormaliz
sage: P = polytopes.dodecahedron(backend='normaliz') # optional - pynormaliz # optional - sage.rings.number_field
sage: P1 = loads(dumps(P)) # optional - pynormaliz # optional - sage.rings.number_field
sage: P2 = Polyhedron_normaliz(P1.parent(), None, None, P1._normaliz_cone, normaliz_field=P1._normaliz_field) # optional - pynormaliz # optional - sage.rings.number_field
sage: P == P2 # optional - pynormaliz # optional - sage.rings.number_field
True
Test that :trac:`31820` is fixed::
Expand Down Expand Up @@ -1496,8 +1496,8 @@ def _volume_normaliz(self, measure='euclidean'):
Check that :trac:`28872` is fixed::
sage: P = polytopes.dodecahedron(backend='normaliz') # optional - pynormaliz
sage: P.volume(measure='induced_lattice') # optional - pynormaliz
sage: P = polytopes.dodecahedron(backend='normaliz') # optional - pynormaliz # optional - sage.rings.number_field
sage: P.volume(measure='induced_lattice') # optional - pynormaliz # optional - sage.rings.number_field
-1056*sqrt5 + 2400
Some sanity checks that the ambient volume works correctly::
Expand Down

0 comments on commit 49658e0

Please sign in to comment.