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sagemathgh-39438: enhanced details in link.py
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In particular, using `next` a few times.

Also some code formatting (pycodestyle)

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#39438
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert
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Release Manager committed Feb 4, 2025
2 parents 17e144f + bc0ad12 commit 9e086c2
Showing 1 changed file with 47 additions and 47 deletions.
94 changes: 47 additions & 47 deletions src/sage/knots/link.py
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Original file line number Diff line number Diff line change
Expand Up @@ -515,9 +515,9 @@ def fundamental_group(self, presentation='wirtinger'):
F = FreeGroup(len(arcs))
rels = []
for crossing, orientation in zip(self.pd_code(), self.orientation()):
a = arcs.index([i for i in arcs if crossing[0] in i][0])
b = arcs.index([i for i in arcs if crossing[3] in i][0])
c = arcs.index([i for i in arcs if crossing[2] in i][0])
a = next(idx for idx, i in enumerate(arcs) if crossing[0] in i)
b = next(idx for idx, i in enumerate(arcs) if crossing[3] in i)
c = next(idx for idx, i in enumerate(arcs) if crossing[2] in i)
ela = F.gen(a)
elb = F.gen(b)
if orientation < 0:
Expand All @@ -526,7 +526,7 @@ def fundamental_group(self, presentation='wirtinger'):
rels.append(ela * elb / elc / elb)
return F.quotient(rels)

def _repr_(self):
def _repr_(self) -> str:
r"""
Return a string representation.
Expand Down Expand Up @@ -705,9 +705,8 @@ def idx(cross, edge):
"""
i = cross.index(edge)
if cross.count(edge) > 1:
return cross.index(edge, i+1)
else:
return i
return cross.index(edge, i + 1)
return i

seifert_circles = self.seifert_circles()
newedge = max(flatten(pd_code)) + 1
Expand Down Expand Up @@ -740,8 +739,8 @@ def idx(cross, edge):
C1[idx(C1, a)] = newedge + 1
C2 = newPD[newPD.index(tails[b])]
C2[idx(C2, b)] = newedge + 2
newPD.append([newedge + 3, newedge, b, a]) # D
newPD.append([newedge + 2, newedge, newedge + 3, newedge + 1]) # E
newPD.append([newedge + 3, newedge, b, a]) # D
newPD.append([newedge + 2, newedge, newedge + 3, newedge + 1]) # E
self._braid = Link(newPD).braid(remove_loops=remove_loops)
return self._braid
else:
Expand All @@ -761,21 +760,21 @@ def idx(cross, edge):
C1[idx(C1, -a)] = newedge + 1
C2 = newPD[newPD.index(tails[-b])]
C2[idx(C2, -b)] = newedge + 2
newPD.append([newedge + 2, newedge + 1, newedge + 3, newedge]) # D
newPD.append([newedge + 3, -a, -b, newedge]) # E
newPD.append([newedge + 2, newedge + 1, newedge + 3, newedge]) # D
newPD.append([newedge + 3, -a, -b, newedge]) # E
self._braid = Link(newPD).braid(remove_loops=remove_loops)
return self._braid

# We are in the case where no Vogel moves are necessary.
G = DiGraph()
G.add_vertices([tuple(c) for c in seifert_circles])
for i,c in enumerate(pd_code):
for i, c in enumerate(pd_code):
if self.orientation()[i] == 1:
a = [x for x in seifert_circles if c[3] in x][0]
b = [x for x in seifert_circles if c[0] in x][0]
a = next(x for x in seifert_circles if c[3] in x)
b = next(x for x in seifert_circles if c[0] in x)
else:
a = [x for x in seifert_circles if c[0] in x][0]
b = [x for x in seifert_circles if c[1] in x][0]
a = next(x for x in seifert_circles if c[0] in x)
b = next(x for x in seifert_circles if c[1] in x)
G.add_edge(tuple(a), tuple(b))

# Get a simple path from a source to a sink in the digraph
Expand All @@ -785,7 +784,7 @@ def idx(cross, edge):
B = BraidGroup(len(ordered_cycles))
available_crossings = copy(pd_code)
oc_set = set(ordered_cycles[0])
for i,x in enumerate(pd_code):
for i, x in enumerate(pd_code):
if any(elt in oc_set for elt in x):
crossing = x
crossing_index = i
Expand Down Expand Up @@ -903,7 +902,7 @@ def _directions_of_edges(self):
heads[a] = next_crossing[0]
tails[a] = D
D = next_crossing[0]
a = D[(D.index(a)+2) % 4]
a = D[(D.index(a) + 2) % 4]

unassigned = set(flatten(pd_code)).difference(set(tails))
while unassigned:
Expand All @@ -920,7 +919,7 @@ def _directions_of_edges(self):
break
heads[a] = next_crossing
D = next_crossing
a = D[(D.index(a)+2) % 4]
a = D[(D.index(a) + 2) % 4]
if a in unassigned:
unassigned.remove(a)
return tails, heads
Expand Down Expand Up @@ -1110,7 +1109,7 @@ def _enhanced_states(self):
nmax = max(flatten(crossings)) + 1
for i in range(2 ** ncross):
v = Integer(i).bits()
v = v + (ncross - len(v))*[0]
v = v + (ncross - len(v)) * [0]
G = Graph()
for j, cr in enumerate(crossings):
n = nmax + j
Expand All @@ -1134,7 +1133,7 @@ def _enhanced_states(self):
smoothings.append((tuple(v), sm, iindex, jmin, jmax))
states = [] # we got all the smoothings, now find all the states
for sm in smoothings:
for k in range(len(sm[1])+1):
for k in range(len(sm[1]) + 1):
for circpos in combinations(sorted(sm[1]), k): # Add each state
circneg = sm[1].difference(circpos)
j = writhe + sm[2] + len(circpos) - len(circneg)
Expand Down Expand Up @@ -1197,13 +1196,13 @@ def _khovanov_homology_cached(self, height, ring=ZZ):
difs = [index for index, value in enumerate(V1[0])
if value != V20[index]]
if len(difs) == 1 and not (V2[2].intersection(V1[1]) or V2[1].intersection(V1[2])):
m[ii, jj] = (-1)**sum(V2[0][x] for x in range(difs[0]+1, ncross))
m[ii, jj] = (-1)**sum(V2[0][x] for x in range(difs[0] + 1, ncross))
# Here we have the matrix constructed, now we have to put it in the dictionary of complexes
else:
m = matrix(ring, len(bij), 0)
complexes[i] = m.transpose()
if (i-1, j) not in bases:
complexes[i-1] = matrix(ring, len(bases[(i,j)]), 0)
if (i - 1, j) not in bases:
complexes[i - 1] = matrix(ring, len(bases[(i, j)]), 0)
homologies = ChainComplex(complexes).homology()
return tuple(sorted(homologies.items()))

Expand Down Expand Up @@ -1457,7 +1456,7 @@ def pd_code(self):
for i, j in zip(last_component, first_component):
d_dic[i][1] = d_dic[j][0]
crossing_dic = {}
for i,x in enumerate(oriented_gauss_code[1]):
for i, x in enumerate(oriented_gauss_code[1]):
if x == -1:
crossing_dic[i + 1] = [d_dic[-(i + 1)][0], d_dic[i + 1][0],
d_dic[-(i + 1)][1], d_dic[i + 1][1]]
Expand Down Expand Up @@ -1611,7 +1610,7 @@ def _braid_word_components(self):

missing = sorted(missing1)
x = [[] for i in range(len(missing) + 1)]
for i,a in enumerate(missing):
for i, a in enumerate(missing):
for j, mlj in enumerate(ml):
if mlj != 0 and abs(mlj) < a:
x[i].append(mlj)
Expand Down Expand Up @@ -2108,7 +2107,7 @@ def khovanov_polynomial(self, var1='q', var2='t', base_ring=ZZ):
gens = [g for g in H.gens() if g.order() == infinity or ch.divides(g.order())]
l = len(gens)
if l:
coeff[(h,d)] = l
coeff[(h, d)] = l
return L(coeff)

def determinant(self):
Expand Down Expand Up @@ -2826,7 +2825,7 @@ def jones_polynomial(self, variab=None, skein_normalization=False, algorithm='jo
if variab is None:
variab = 't'
# We force the result to be in the symbolic ring because of the expand
return jones(SR(variab)**(ZZ(1)/ZZ(4))).expand()
return jones(SR(variab)**(ZZ.one() / ZZ(4))).expand()
elif algorithm == 'jonesrep':
braid = self.braid()
# Special case for the trivial knot with no crossings
Expand Down Expand Up @@ -3084,14 +3083,14 @@ def homfly_polynomial(self, var1=None, var2=None, normalization='lm'):
L = LaurentPolynomialRing(ZZ, [var1, var2])
if len(self._isolated_components()) > 1:
if normalization == 'lm':
fact = L({(1, -1):-1, (-1, -1):-1})
fact = L({(1, -1): -1, (-1, -1): -1})
elif normalization == 'az':
fact = L({(1, -1):1, (-1, -1):-1})
fact = L({(1, -1): 1, (-1, -1): -1})
elif normalization == 'vz':
fact = L({(1, -1):-1, (-1, -1):1})
fact = L({(1, -1): -1, (-1, -1): 1})
else:
raise ValueError('normalization must be either `lm`, `az` or `vz`')
fact = fact ** (len(self._isolated_components())-1)
fact = fact ** (len(self._isolated_components()) - 1)
for i in self._isolated_components():
fact = fact * Link(i).homfly_polynomial(var1, var2, normalization)
return fact
Expand All @@ -3102,7 +3101,7 @@ def homfly_polynomial(self, var1=None, var2=None, normalization='lm'):
for comp in ogc[0]:
s += ' {}'.format(len(comp))
for cr in comp:
s += ' {} {}'.format(abs(cr)-1, sign(cr))
s += ' {} {}'.format(abs(cr) - 1, sign(cr))
for i, cr in enumerate(ogc[1]):
s += ' {} {}'.format(i, cr)
from sage.libs.homfly import homfly_polynomial_dict
Expand All @@ -3124,7 +3123,7 @@ def homfly_polynomial(self, var1=None, var2=None, normalization='lm'):
h_az = self.homfly_polynomial(var1=var1, var2=var2, normalization='az')
a, z = h_az.parent().gens()
v = ~a
return h_az.subs({a:v})
return h_az.subs({a: v})
else:
raise ValueError('normalization must be either `lm`, `az` or `vz`')

Expand Down Expand Up @@ -3313,8 +3312,8 @@ def colorings(self, n=None):
M = self._coloring_matrix(n=n)
KM = M.right_kernel_matrix()
F = FreeModule(M.base_ring(), KM.dimensions()[0])
K = [v*KM for v in F]
res = set([])
K = [v * KM for v in F]
res = set()
arcs = self.arcs('pd')
for coloring in K:
colors = sorted(set(coloring))
Expand Down Expand Up @@ -3408,7 +3407,7 @@ def coloring_maps(self, n=None, finitely_presented=False):
maps = []
for c in cols:
t = list(c.values())
ims = [b*a**i for i in t]
ims = [b * a**i for i in t]
maps.append(gr.hom(ims))
return maps

Expand Down Expand Up @@ -3627,7 +3626,7 @@ def plot(self, gap=0.1, component_gap=0.5, solver=None,

# Special case for the unknot
if not pd_code:
return circle((0,0), ZZ(1)/ZZ(2), color=color, **kwargs)
return circle((0, 0), ZZ.one() / ZZ(2), color=color, **kwargs)

# The idea is the same followed in spherogram, but using MLP instead of
# network flows.
Expand All @@ -3653,9 +3652,9 @@ def flow_from_source(e):
Return the flow variable from the source.
"""
if e > 0:
return v[2*edges.index(e)]
return v[2 * edges.index(e)]
else:
return v[2*edges.index(-e)+1]
return v[2 * edges.index(-e) + 1]

def flow_to_sink(e):
r"""
Expand All @@ -3680,9 +3679,10 @@ def flow_to_sink(e):
MLP.solve()
# we store the result in a vector s packing right bends as negative left ones
values = MLP.get_values(v, convert=ZZ, tolerance=1e-3)
s = [values[2*i] - values[2*i + 1] for i in range(len(edges))]
s = [values[2 * i] - values[2 * i + 1] for i in range(len(edges))]
# segments represents the different parts of the previous edges after bending
segments = {e: [(e,i) for i in range(abs(s[edges.index(e)])+1)] for e in edges}
segments = {e: [(e, i) for i in range(abs(s[edges.index(e)]) + 1)]
for e in edges}
pieces = {tuple(i): [i] for j in segments.values() for i in j}
nregions = []
for r in regions[:-1]: # interior regions
Expand Down Expand Up @@ -3711,7 +3711,7 @@ def flow_to_sink(e):
c = -1
b = a
while c != 2:
if b == len(badregion)-1:
if b == len(badregion) - 1:
b = 0
else:
b += 1
Expand Down Expand Up @@ -3739,15 +3739,15 @@ def flow_to_sink(e):

if a < b:
r1 = badregion[:a] + [[badregion[a][0], 0], [N1, 1]] + badregion[b:]
r2 = badregion[a + 1:b] + [[N2, 1],[N1, 1]]
r2 = badregion[a + 1:b] + [[N2, 1], [N1, 1]]
else:
r1 = badregion[b:a] + [[badregion[a][0], 0], [N1, 1]]
r2 = badregion[:b] + [[N2, 1],[N1, 1]] + badregion[a + 1:]
r2 = badregion[:b] + [[N2, 1], [N1, 1]] + badregion[a + 1:]

if otherregion:
c = [x for x in otherregion if badregion[b][0] == x[0]]
c = otherregion.index(c[0])
otherregion.insert(c + 1, [N2,otherregion[c][1]])
otherregion.insert(c + 1, [N2, otherregion[c][1]])
otherregion[c][1] = 0
nregions.remove(badregion)
nregions.append(r1)
Expand Down Expand Up @@ -3805,7 +3805,7 @@ def flow_to_sink(e):
turn = -1
else:
turn = 1
lengthse = [lengths[(e,k)] for k in range(abs(s[edges.index(e)])+1)]
lengthse = [lengths[(e, k)] for k in range(abs(s[edges.index(e)]) + 1)]
if c.index(e) == 0 or (c.index(e) == 3 and orien == 1) or (c.index(e) == 1 and orien == -1):
turn = -turn
lengthse.reverse()
Expand Down

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