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lines changed Original file line number Diff line number Diff line change @@ -633,10 +633,9 @@ def _frobenius_charpoly_gekeler(self):
633633 # The system is solved over K, but the coefficients should all
634634 # be in Fq We project back into Fq here.
635635 sol_Fq = [K (x ).vector ()[0 ] for x in sol ]
636- char_poly = []
637- for i in range (r ):
638- char_poly .append ([sol_Fq [block_shifts [i ] + j ]
639- for j in range (shifts [i ])])
636+ char_poly = [[sol_Fq [block_shifts [i ] + j ]
637+ for j in range (shifts [i ])]
638+ for i in range (r )]
640639 return PolynomialRing (A , name = 'X' )(char_poly + [1 ])
641640
642641 def _frobenius_charpoly_motive (self ):
@@ -651,8 +650,9 @@ def _frobenius_charpoly_motive(self):
651650 Instead, use :meth:`frobenius_charpoly` with the option
652651 `algorithm='motive'`.
653652
654- OUTPUT: a univariate polynomial with coefficients in the
655- function ring
653+ OUTPUT:
654+
655+ a univariate polynomial with coefficients in the function ring
656656
657657 EXAMPLES::
658658
Original file line number Diff line number Diff line change @@ -273,11 +273,11 @@ def gens_reduced(self):
273273 gens = self .gens ()
274274 if len (gens ) == 1 :
275275 return gens
276- candidate_gensets = []
277- for genset in powerset ( gens ):
278- if self . parent ()( genset ) == self :
279- candidate_gensets . append ( genset )
280- candidate_gensets . sort ( key = lambda item : ( len ( item ), len ( repr ( item )), item ))
276+ candidate_gensets = [genset for genset in powerset ( gens )
277+ if self . parent ()( genset ) == self ]
278+ candidate_gensets . sort ( key = lambda item : ( len ( item ),
279+ len ( repr ( item )),
280+ item ))
281281 return candidate_gensets [0 ]
282282
283283 def ring (self ):
Original file line number Diff line number Diff line change @@ -1251,9 +1251,8 @@ def _gens_two(self) -> tuple:
12511251
12521252 R = hnf .base_ring ()
12531253
1254- basis = []
1255- for row in hnf :
1256- basis .append (sum ([c1 * c2 for c1 , c2 in zip (row , O .basis ())]))
1254+ basis = [sum (c1 * c2 for c1 , c2 in zip (row , O .basis ()))
1255+ for row in hnf ]
12571256
12581257 n = len (basis )
12591258 alpha = None
Original file line number Diff line number Diff line change @@ -540,7 +540,7 @@ def order(self, algorithm='numeric'):
540540
541541 return sum (bs )
542542
543- def get_points (self , n ):
543+ def get_points (self , n ) -> list :
544544 """
545545 Return `n` points of the Jacobian group.
546546
Original file line number Diff line number Diff line change @@ -510,13 +510,12 @@ def to_V(e):
510510 v = O ._coordinate_vector (e )
511511 vec = []
512512 for i in reversed (range (n )):
513- q ,r = v [i ].quo_rem (M [i ,i ])
513+ q , r = v [i ].quo_rem (M [i , i ])
514514 v -= q * M [i ]
515- for j in range (degs [i ]):
516- vec .append (r [j ])
515+ vec .extend (r [j ] for j in range (degs [i ]))
517516 return vector (vec )
518517
519- def fr_V (vec ): # to_O
518+ def fr_V (vec ): # to_O
520519 vec = vec .list ()
521520 pos = 0
522521 e = F (0 )
Original file line number Diff line number Diff line change @@ -715,8 +715,7 @@ def _add_(self, other):
715715 G = []
716716 for n in range (self ._prec ):
717717 G_n = [self [n ], other [n ]]
718- for i in range (n ):
719- G_n .append (P ._eta_bar (G [i ], n - i ))
718+ G_n .extend (P ._eta_bar (G [i ], n - i ) for i in range (n ))
720719 G .append (G_n )
721720 sum_vec = tuple (sum (G [i ]) for i in range (self ._prec ))
722721
@@ -753,8 +752,7 @@ def _mul_(self, other):
753752 G_n .extend (fast_char_p_power (self [i ], p ** (n - i ))
754753 * fast_char_p_power (other [n - i ], p ** i )
755754 for i in range (1 , n ))
756- for i in range (n ):
757- G_n .append (P ._eta_bar (G [i ], n - i ))
755+ G_n .extend (P ._eta_bar (G [i ], n - i ) for i in range (n ))
758756 G .append (G_n )
759757 prod_vec = tuple (sum (G [i ]) for i in range (self ._prec ))
760758
Original file line number Diff line number Diff line change @@ -488,13 +488,10 @@ def __call__(self, *args):
488488 initial = 0 ))
489489
490490 # gens from self
491- gens = []
492- for gen in G .gens ():
493- newgen = []
494- for cyc in gen .cycle_tuples ():
495- for k in range (1 , sum (Mlist [cyc [0 ] - 1 ].grade ()) + 1 ):
496- newgen .append (tuple ([k + starts [i - 1 ] for i in cyc ]))
497- gens .append (newgen )
491+ gens = [[tuple ([k + starts [i - 1 ] for i in cyc ])
492+ for cyc in gen .cycle_tuples ()
493+ for k in range (1 , sum (Mlist [cyc [0 ] - 1 ].grade ()) + 1 )]
494+ for gen in G .gens ()]
498495
499496 # gens from M_i and dompart
500497 P = args [0 ].parent ()
@@ -503,9 +500,9 @@ def __call__(self, *args):
503500 K , K_dompart = M .permutation_group ()
504501 for i , v in enumerate (K_dompart ):
505502 pi [i ].extend ([start + k for k in v ])
506- for gen in K . gens ():
507- gens . append ([ tuple ([ start + k for k in cyc ])
508- for cyc in gen . cycle_tuples ()] )
503+ gens . extend ([ tuple ([ start + k for k in cyc ])
504+ for cyc in gen . cycle_tuples ()]
505+ for gen in K . gens () )
509506
510507 H = PermutationGroup (gens , domain = range (1 , starts [- 1 ] + 1 ))
511508 return P ._indices (H , pi , check = False )
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