#15393: compute the automorphism group of a morphism of P1
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Reporter: bhutz | Owner: bhutz
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: sage-days55 | Reviewers: Grayson Jorgenson
Authors: bhutz, bthompson, | Work issues:
jdefaria | Commit:
Report Upstream: N/A | 88ad7deca2fadbb8b70ed82baf43f61e748d78d1
Branch: | Stopgaps:
u/bhutz/ticket/15393 |
Dependencies: |
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Changes (by gjorgenson):
* status: needs_review => needs_work
* reviewer: => Grayson Jorgenson
Comment:
Reviewed code and came up with a list of minor changes and some questions
about the functionality:
- Add comment before use of Subset stating that unordered subset
selection works for QQ
- In the rational fixed points function, add example demonstrating the
iso_type parameter
- Elaborate on the set W referenced from ln 134 onwards in comments
- ln 126, 259, change ZZ to F
- ln 237, 253, 269, change K(s) to s when appending
- ln 287: 'We have proved that to In [FMV] it is proven that'
- ln 332: remove "an automorphism of P^1"
- ln 385: B=copy(A)
- ln 394: remove 'multiplicative'
- remove 'get_orders'. Change 'PGL_order' to be 'order' and have it call
'PGL_repn'. Fix ln 775 where 'getorders' is called (don't forget to sort
by order)
- import 'CRT' -> 'from sage.rings.arith import CRT'
- ln 464: Integers in not imported
- ln 498: describe 'moduli' as integer prime powers
- in CRT_automorphisms: define M (see CRT_helper ln 430). Output also
includes M
- 'd' is not needed
- 'CRT_automorphisms' can pass an empty list ot CRT_helper if there are
no degree 'd' automorphisms. If it does encounter an empty list it needs
to not pass it (or its moduli) to CRT_helper.open (maybe not since the map
is injective)
- ln 521: 'automorphim'
- ln 534: ending comma not needed. add defaults. add that automorphisms
are matrices. Deleted commented out code
- ln 532: 'M' is an integer (product of prime powers)
- ln 563: comment explaining 'scalar*a - (scalar*a/M).round()*M' instead
of (scalar*a).lift()
- ln 568: condense 'if' use max(abs(aa),abs(bb),abs(cc),abs(dd)), from
previous change don't need absolute value.
- ln 664: comment about del needs to start at the end not to have issues
automorphism_group_QQ_CRT
- defaults for keywords
- OUTPUT: remove 'as linear fraction transformations'
- line 735: h=h/(gcd(h,h.derivative())), Actually do this as done on line
1260
- line 738: points -> point
- line 766 Q -> QQ
- line 772: not needed comment line
- line 788-789: A or [B and (C1 or C2)], missing []
- line 797: QQ
- line 805: extra line
- line 815: extra line
- line 827: QQ
- line 178, 851, 852: k in never incremented
- CRT does not seem to actually be used very well. It checks all lifts
for one prime (which sine the reduction map is injective should find all
the maps). This is highly inefficient when the height bound is high.
automorphism_group_FF
- remove authors part to top of file
- algoritm -> use citation
- default for return_functions
- examples, add keywords
- line 920 938, 941 extra line
- line 948: determines
- line 949 yy has wrong number quotes
- 972: no need for y
- 983: X is not used
- 1006: use sigma not ssigma, delete 1045
- 1057: just use poly_ring not R
- 1052-1053: why scaling to have constant term of numerator be 1
- 1059-60 could use poly constructor R(ff), R(gg)
- 1131: use citation
- 1149: no 'phi' no 'E'
- line 1205 extra line
- line 1215 no 'F'
- line 1268, 1275, 1324 extra line
- order_p_automorphism, cite algorithm 4 in FMV
- 1396 means we don't need pre_data
- extra line 1451, 1462, 1474, 1485, 1489, 1501
- line 1523 - Boolean type
- line 1527: automorphisms with order prime to $p$.
- 1549 get rid of 'T'
- 1559 - assume 2nd coordinate of point is 1 (i.e. normalized
- extra line 1565
- line 1568: sqrt to get cardinality of the field and not the degree 2
extension
- line 1595 : citation
- line 1675: remove ???
- line 1760-1765 delete
- line 1797 should raise and error
--
Ticket URL: <http://trac.sagemath.org/ticket/15393#comment:11>
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