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sagemathgh-39298: small cleanup in tropical files
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just minor fixes after ruff suggestions in tropical files

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#39298
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert
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Release Manager committed Jan 9, 2025
2 parents 51d8c1e + 298de9b commit 63f8189
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Showing 3 changed files with 52 additions and 59 deletions.
23 changes: 12 additions & 11 deletions src/sage/rings/semirings/tropical_mpolynomial.py
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Original file line number Diff line number Diff line change
Expand Up @@ -33,9 +33,9 @@
# ****************************************************************************

from sage.misc.cachefunc import cached_method
from sage.rings.polynomial.multi_polynomial_element import MPolynomial_polydict
from sage.structure.parent import Parent
from sage.structure.unique_representation import UniqueRepresentation
from sage.rings.polynomial.multi_polynomial_element import MPolynomial_polydict


class TropicalMPolynomial(MPolynomial_polydict):
Expand Down Expand Up @@ -286,8 +286,9 @@ def plot3d(self, color='random'):
multivariate polynomial in two variables
"""
from random import random
from sage.plot.graphics import Graphics

from sage.geometry.polyhedron.constructor import Polyhedron
from sage.plot.graphics import Graphics
from sage.sets.real_set import RealSet
from sage.symbolic.relation import solve

Expand Down Expand Up @@ -399,7 +400,11 @@ def tropical_variety(self):
sage: p1.tropical_variety()
Tropical surface of 1*x*y + (-1/2)*x*z + 4*z^2
"""
from sage.rings.semirings.tropical_variety import TropicalCurve, TropicalSurface, TropicalVariety
from sage.rings.semirings.tropical_variety import (
TropicalCurve,
TropicalSurface,
TropicalVariety,
)

if self.parent().ngens() == 2:
return TropicalCurve(self)
Expand Down Expand Up @@ -617,8 +622,8 @@ def dual_subdivision(self):
A vertex at (1, 0, 1, 0),
A vertex at (1, 1, 0, 0))]
"""
from sage.geometry.polyhedron.constructor import Polyhedron
from sage.geometry.polyhedral_complex import PolyhedralComplex
from sage.geometry.polyhedron.constructor import Polyhedron

TV = self.tropical_variety()
cycles = []
Expand All @@ -627,18 +632,14 @@ def dual_subdivision(self):
for indices in TV._vertices_components().values():
cycle = []
for index in indices:
vertices = TV._keys[index[0]]
for v in vertices:
cycle.append(v)
cycle.extend(TV._keys[index[0]])
cycles.append(cycle)
else:
line_comps = TV.weight_vectors()[1]
for indices in line_comps.values():
cycle = []
for index in indices:
vertices = TV._keys[index]
for v in vertices:
cycle.append(v)
cycle.extend(TV._keys[index])
cycles.append(cycle)

polyhedron_lst = []
Expand Down Expand Up @@ -729,8 +730,8 @@ def __init__(self, base_semiring, n, names, order):
sage: R = PolynomialRing(T, 5, 'x')
sage: TestSuite(R).run()
"""
from sage.rings.semirings.tropical_semiring import TropicalSemiring
from sage.categories.semirings import Semirings
from sage.rings.semirings.tropical_semiring import TropicalSemiring
if not isinstance(base_semiring, TropicalSemiring):
raise ValueError(f"{base_semiring} is not a tropical semiring")
Parent.__init__(self, base=base_semiring, names=names, category=Semirings())
Expand Down
6 changes: 3 additions & 3 deletions src/sage/rings/semirings/tropical_polynomial.py
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Original file line number Diff line number Diff line change
Expand Up @@ -35,9 +35,9 @@
# ****************************************************************************

from sage.misc.cachefunc import cached_method
from sage.structure.unique_representation import UniqueRepresentation
from sage.structure.parent import Parent
from sage.rings.polynomial.polynomial_element_generic import Polynomial_generic_sparse
from sage.structure.parent import Parent
from sage.structure.unique_representation import UniqueRepresentation


class TropicalPolynomial(Polynomial_generic_sparse):
Expand Down Expand Up @@ -371,9 +371,9 @@ def piecewise_function(self):
sage: p3.piecewise_function()
3*x + 1
"""
from sage.symbolic.ring import SR
from sage.functions.piecewise import piecewise
from sage.sets.real_set import RealSet
from sage.symbolic.ring import SR

x = SR.var('x')
data = self.monomial_coefficients()
Expand Down
82 changes: 37 additions & 45 deletions src/sage/rings/semirings/tropical_variety.py
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Original file line number Diff line number Diff line change
Expand Up @@ -26,12 +26,11 @@
# https://www.gnu.org/licenses/
# ****************************************************************************

from sage.rings.infinity import infinity
from sage.rings.rational_field import QQ
from sage.structure.sage_object import SageObject
from sage.structure.unique_representation import UniqueRepresentation

from sage.rings.rational_field import QQ
from sage.rings.infinity import infinity


class TropicalVariety(UniqueRepresentation, SageObject):
r"""
Expand Down Expand Up @@ -188,10 +187,11 @@ def __init__(self, poly):
"""
import operator
from itertools import combinations
from sage.symbolic.ring import SR
from sage.symbolic.relation import solve

from sage.arith.misc import gcd
from sage.rings.semirings.tropical_mpolynomial import TropicalMPolynomial
from sage.symbolic.relation import solve
from sage.symbolic.ring import SR

if not isinstance(poly, TropicalMPolynomial):
raise ValueError(f"{poly} is not a multivariate tropical polynomial")
Expand Down Expand Up @@ -448,9 +448,10 @@ def _components_intersection(self):
5: [((0, t2, 0), {0 <= t2}), ((1/2*t2, t2, t2), {t2 <= 0})]}
"""
import operator

from sage.functions.min_max import max_symbolic, min_symbolic
from sage.symbolic.relation import solve
from sage.sets.set import Set
from sage.symbolic.relation import solve

def update_result(result):
sol_param = solve(new_expr, vars)
Expand Down Expand Up @@ -592,19 +593,20 @@ def weight_vectors(self):
sage: all(a == vector([0,0,0,0]) for a in [sum(lst) for lst in vec])
True
"""
from sage.symbolic.ring import SR
from sage.symbolic.relation import solve
from sage.calculus.functional import diff
from itertools import combinations

from sage.arith.misc import gcd
from sage.calculus.functional import diff
from sage.matrix.constructor import matrix
from sage.modules.free_module_element import vector, zero_vector
from itertools import combinations
from sage.symbolic.relation import solve
from sage.symbolic.ring import SR

dim = self.dimension()
t = SR.var('t')
t_vars = [SR.var('t{}'.format(i)) for i in range(dim)]
u_vars = [SR.var('u{}'.format(i)) for i in range(dim)]
convert_tu = {ti: ui for ti, ui in zip(t_vars, u_vars)}
t_vars = [SR.var(f't{i}') for i in range(dim)]
u_vars = [SR.var(f'u{i}') for i in range(dim)]
convert_tu = dict(zip(t_vars, u_vars))
CI = self._components_intersection()
unique_line = set()
index_line = {}
Expand Down Expand Up @@ -657,9 +659,9 @@ def weight_vectors(self):
if is_unique:
new_eqn = tuple([eq.subs(convert_tu) for eq in eqn])
cdns = line[1]
new_cdn = set([cdn.subs(convert_tu) for cdn in cdns])
new_cdn = {cdn.subs(convert_tu) for cdn in cdns}
unique_line.add(new_eqn)
index_line[index] = tuple([new_eqn, new_cdn])
index_line[index] = (new_eqn, new_cdn)
line_comps[index] = [i]
index += 1
else:
Expand All @@ -676,9 +678,7 @@ def weight_vectors(self):
for v in l.variables():
all_var.add(v)
for vpar in all_var:
par_drv = []
for l in line:
par_drv.append(QQ(diff(l, vpar)))
par_drv = [QQ(diff(l, vpar)) for l in line]
par_drv = vector(par_drv)
dir_vecs.append(par_drv)

Expand All @@ -688,32 +688,24 @@ def weight_vectors(self):
surface = self._hypersurface[i][0]
drv_vectors = []
for vpar in self._vars:
temp_vec = []
for s in surface:
temp_vec.append(QQ(diff(s, vpar)))
temp_vec = [QQ(diff(s, vpar)) for s in surface]
temp_vec = vector(temp_vec)
drv_vectors.append(temp_vec)
temp = [t_vars]
for vec in drv_vectors:
temp.append(vec)
temp.extend(drv_vectors)
vec_matrix = matrix(SR, temp)
normal_vec = vec_matrix.det()
temp_nor = []
for tvar in t_vars:
temp_nor.append(QQ(diff(normal_vec, tvar)))
temp_nor = [QQ(diff(normal_vec, tvar)) for tvar in t_vars]
normal_vec = vector(temp_nor)
normal_vec *= 1/gcd(normal_vec)

# Calculate the weight vector
temp_final = [t_vars]
for v in dir_vecs:
temp_final.append(v)
temp_final.extend(dir_vecs)
temp_final.append(normal_vec)
vec_matrix = matrix(SR, temp_final)
weight_vec = vec_matrix.det()
temp_weight = []
for tvar in t_vars:
temp_weight.append(QQ(diff(weight_vec, tvar)))
temp_weight = [QQ(diff(weight_vec, tvar)) for tvar in t_vars]
weight_vec = vector(temp_weight)
order = self._hypersurface[i][2]
weight_vec *= order
Expand All @@ -722,7 +714,7 @@ def weight_vectors(self):
balance = False
for i in range(1, len(WV[k])+1):
for j in combinations(range(len(WV[k])), i):
test_vectors = [v for v in WV[k]]
test_vectors = list(WV[k])
for idx in j:
test_vectors[idx] = -test_vectors[idx]
if sum(test_vectors) == zero_vector(QQ, dim):
Expand Down Expand Up @@ -791,8 +783,8 @@ def _axes(self):
sage: p2.tropical_variety()._axes()
[[-1, 2], [-1, 2], [-1, 2]]
"""
from sage.symbolic.relation import solve
from sage.arith.srange import srange
from sage.symbolic.relation import solve

if not self._hypersurface:
return [[-1, 1], [-1, 1], [-1, 1]]
Expand Down Expand Up @@ -911,8 +903,8 @@ def _polygon_vertices(self):
7: {(-1/2, -1, -1), (-1/2, 2, -1), (0, 0, 0), (0, 2, 0)},
8: {(1, 1, 1), (1, 2, 1), (2, 1, 1), (2, 2, 1)}}
"""
from sage.symbolic.relation import solve
from sage.sets.real_set import RealSet
from sage.symbolic.relation import solve

poly_verts = {i: set() for i in range(self.number_of_components())}
axes = self._axes()
Expand Down Expand Up @@ -1057,8 +1049,9 @@ def plot(self, color='random'):
sphinx_plot(p2.tropical_variety().plot())
"""
from random import random
from sage.plot.graphics import Graphics

from sage.geometry.polyhedron.constructor import Polyhedron
from sage.plot.graphics import Graphics

if color == 'random':
colors = []
Expand Down Expand Up @@ -1283,17 +1276,17 @@ def _vertices_components(self):
if lower != -infinity:
x = parametric_function[0].subs(**{str(v): lower})
y = parametric_function[1].subs(**{str(v): lower})
if (x,y) not in comp_vert:
comp_vert[(x,y)] = [(i, 1)]
if (x, y) not in comp_vert:
comp_vert[(x, y)] = [(i, 1)]
else:
comp_vert[(x,y)].append((i, 1))
comp_vert[(x, y)].append((i, 1))
if upper != infinity:
x = parametric_function[0].subs(**{str(v): upper})
y = parametric_function[1].subs(**{str(v): upper})
if (x,y) not in comp_vert:
comp_vert[(x,y)] = [(i, -1)]
if (x, y) not in comp_vert:
comp_vert[(x, y)] = [(i, -1)]
else:
comp_vert[(x,y)].append((i, -1))
comp_vert[(x, y)].append((i, -1))
return comp_vert

def weight_vectors(self):
Expand Down Expand Up @@ -1334,9 +1327,9 @@ def weight_vectors(self):
(-1, 0): [(-1, 0), (0, -1), (1, 1)],
(3, 4): [(-1, -1), (0, 1), (1, 0)]}
"""
from sage.arith.misc import gcd
from sage.calculus.functional import diff
from sage.modules.free_module_element import vector
from sage.arith.misc import gcd

if not self._vertices_components():
return {}
Expand Down Expand Up @@ -1636,10 +1629,9 @@ def plot(self):
+ R(4)*x**3*y + x**2*y**2 + R(2)*x*y**3 + y**4)
sphinx_plot(p3.tropical_variety().plot())
"""
from sage.plot.plot import plot
from sage.plot.text import text
from sage.plot.graphics import Graphics
from sage.plot.plot import parametric_plot
from sage.plot.plot import parametric_plot, plot
from sage.plot.text import text

if not self._hypersurface:
return plot(lambda x: float('nan'), {-1, 1})
Expand Down

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