74
74
from sage .structure .sequence import Sequence
75
75
from sage .modules .free_module_element import vector
76
76
77
- from sage .misc .superseded import deprecated_function_alias
78
-
79
77
80
78
class UnwrappingMorphism (Morphism ):
81
79
r"""
@@ -324,8 +322,6 @@ def discrete_exp(self, v):
324
322
# DUMB IMPLEMENTATION!
325
323
return sum ([self ._gen_elements [i ] * ZZ (v [i ]) for i in range (len (v ))], self .universe ()(0 ))
326
324
327
- _discrete_exp = deprecated_function_alias (32384 , discrete_exp )
328
-
329
325
def discrete_log (self , x , gens = None ):
330
326
r"""
331
327
Given an element of the ambient group, attempt to express it in terms
@@ -421,8 +417,6 @@ def discrete_log(self, x, gens=None):
421
417
assert x == sum (r * g for r , g in zip (res , gens ))
422
418
return res
423
419
424
- _discrete_log = deprecated_function_alias (32384 , discrete_log )
425
-
426
420
def torsion_subgroup (self , n = None ):
427
421
r"""
428
422
Return the `n`-torsion subgroup of this additive abelian group
@@ -594,7 +588,7 @@ def _base(j, k, c):
594
588
595
589
assert k - j == 1
596
590
aajk = subbasis (j , k )
597
- assert not any (p * a for a in aajk ) # orders are in {1,p}
591
+ assert not any (p * a for a in aajk ) # orders are in {1,p}
598
592
idxs = [i for i , a in enumerate (aajk ) if a ]
599
593
600
594
rs = [([0 ], [0 ]) for i in range (len (aajk ))]
@@ -627,18 +621,18 @@ def _rec(j, k, c):
627
621
return _base (j , k , c )
628
622
629
623
w = 2
630
- js = list (range (j , k , (k - j + w - 1 ) // w )) + [k ]
624
+ js = list (range (j , k , (k - j + w - 1 ) // w )) + [k ]
631
625
assert len (js ) == w + 1
632
626
633
627
x = vector ([0 ] * len (aa ))
634
628
for i in reversed (range (w )):
635
629
636
630
gamma = p ** (js [i ] - j ) * c - dotprod (x , subbasis (js [i ], k ))
637
631
638
- v = _rec (js [i ], js [i + 1 ], gamma )
632
+ v = _rec (js [i ], js [i + 1 ], gamma )
639
633
640
- assert not any (q1 % q2 for q1 , q2 in zip (qq (js [i ], js [i + 1 ]), qq (js [i ], k )))
641
- x += vector (q1 // q2 * r for q1 , q2 , r in zip (qq (js [i ], js [i + 1 ]), qq (js [i ], k ), v ))
634
+ assert not any (q1 % q2 for q1 , q2 in zip (qq (js [i ], js [i + 1 ]), qq (js [i ], k )))
635
+ x += vector (q1 // q2 * r for q1 , q2 , r in zip (qq (js [i ], js [i + 1 ]), qq (js [i ], k ), v ))
642
636
643
637
return x
644
638
@@ -700,7 +694,7 @@ def _expand_basis_pgroup(p, alphas, vals, beta, h, rel):
700
694
701
695
# step 1
702
696
min_r = rel [- 1 ] or float ('inf' )
703
- for i in range (k - 1 ):
697
+ for i in range (k - 1 ):
704
698
if not rel [i ]:
705
699
continue
706
700
if rel [i ] < 0 :
@@ -712,16 +706,16 @@ def _expand_basis_pgroup(p, alphas, vals, beta, h, rel):
712
706
if min_r == float ('inf' ):
713
707
raise ValueError ('rel must have at least one nonzero entry' )
714
708
val_rlast = rel [- 1 ].valuation (p )
715
- # assert rel[-1] == p ** val_rlast
716
- # assert not sum(r*a for r,a in zip(rel, alphas+[beta]))
709
+ # assert rel[-1] == p ** val_rlast
710
+ # assert not sum(r*a for r,a in zip(rel, alphas+[beta]))
717
711
718
712
# step 2
719
713
if rel [- 1 ] == min_r :
720
- for i in range (k - 1 ):
721
- beta += alphas [i ] * (rel [i ]// rel [- 1 ])
714
+ for i in range (k - 1 ):
715
+ beta += alphas [i ] * (rel [i ] // rel [- 1 ])
722
716
alphas .append (beta )
723
717
vals .append (val_rlast )
724
- # assert alphas[-1].order() == p**vals[-1]
718
+ # assert alphas[-1].order() == p**vals[-1]
725
719
return
726
720
727
721
# step 3
0 commit comments