#19083: AsymptoticRing: exp & log, cleanup, some improvements, documentation
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: asymptotic | Resolution:
expansions | Merged in:
Keywords: | Reviewers: Daniel Krenn, Clemens
Authors: Benjamin Hackl, | Heuberger
Daniel Krenn | Work issues:
Report Upstream: N/A | Commit:
Branch: | e8ad893715b0dfc8a3907a05382b0c1cba57b818
u/dkrenn/asy/prototype | Stopgaps:
Dependencies: #19073 |
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Changes (by dkrenn):
* commit: 2c60570eb1755791db1a82aa3e3ab70ddbb505c0 =>
e8ad893715b0dfc8a3907a05382b0c1cba57b818
Comment:
Replying to [comment:60 cheuberg]:
> 1. `misc.split_str_by_op`:
> - parameter `op`: is special treatment of `^^` worthwhile when `op
='^'` or is that a special case for `*`?
The motivation comes, of course, from `*` and `**`. Since `^^` is not one
of Python's operators, it should not be interpreted as twice `^`. Thus, I
think this should be as it is.
> - parameter `strip_parentheses` not tested
> - document and test `op is None`. This is used in
`growth_group.Variable.__init__`
Added.
> 2. `misc.repr_op`: what about `-` and `/`? Why don't they also induce
parentheses?
> {{{
> sage: from sage.rings.asymptotic.misc import repr_op
> sage: repr_op('a-b', '^', 'c')
> 'a-b^c'
> sage: repr_op('a+b', '^', 'c')
> '(a+b)^c'
> }}}
Now included as well.
> 4. `growth_group.log`:
> - see comments on `growth_group.is_lt_one`.
Done.
> - error "results in a sum" is not tested.
Added.
> 5. `growth_group.log_factor`:
> - why `from growth_group import GenericGrowthGroup`?
Removed.
> - see comments on `growth_group.is_lt_one`
Done.
> 6. `GenericGrowthElement.__ne__`: is the "Note" box actually needed?
Not really; deleted.
> 7. `GenericGrowthElement._rpow_element_`:
> - when is the output `None`?
Removed output `None`.
> - I do not understand "it lives (in contrast to rpow) in its own
group".
Rewritten.
> 8. `GenericGrowthGroup._create_element_via_parent_`: I do not understand
the explanation.
Rewritten.
> Is "via" a good part of the name of the method?
Renamed to `_create_element_in_extension_`.
> 9. `GenericGrowthGroup.gens`:
> - why "monomial" growth group in the generic group?
> - why `MonomialGrowthElement`?
Cut and paste problem; changed.
> 10. `MonomialGrowthElement.__pow__`: Is the following intentional:
> {{{
> sage: P = GrowthGroup('x^ZZ')
> sage: x = P.gen()
> sage: a = x^7; a
> x^7
> sage: a^(1/7)
> x
> sage: (a^(1/7)).parent()
> Growth Group x^QQ
> }}}
> I understand that `((1/7)*7).parent()` is `QQ`, but in that case,
the user explicitly left the integers. It is not clear to me whether this
is also the case here.
`(a^7)^(1/7)` is calculated as `a^(7*(1/7))`, thus the same phenomenon as
with `((1/7)*7).parent()` appears.
> 11. `MonomialGrowthElement._log_factor_`:
> - The parameter `base` is ignored in the second `if`:
> {{{
> sage: G = GrowthGroup('exp(x)^ZZ*x^ZZ')
> sage: e1 = G('exp(x)'); e1
> exp(x)
> sage: log(e1, base=2)
> x
Corrected.
> }}}
> - In some cases, computation fails although it would be feasible:
> {{{
> sage: G = GrowthGroup('(e^x)^ZZ*x^ZZ')
> sage: e1 = G('e^x'); e1
> e^x
> sage: var('e')
> sage: log(e1^2, base=e^2)
> Traceback (most recent call last):
> ...
> ArithmeticError: Cannot build log((e^x)^2) since log(e^x) is not in
Growth Group (e^x)^ZZ * x^ZZ.
> }}}
This is now #19420.
> 12. `MonomialGrowthElement._rpow_element_`:
> - I do not understand "it lives (in contrast to rpow()) in its own
group."
Changed.
> - Parameter `base` is not tested (with an actual result).
Doctest added.
> - The documentation does not explain why `2^x` is illegal here (it
seems that this method operates only if the result can be a monomial
growth group element, not necessarily in the same growth group as `self`).
Example explained.
> 13. `ExponentialGrowthElement._repr_`: what is the motivation behind
checking for `-/^`? This leads to the following (perhaps stupid) example:
> {{{
> sage: from sage.rings.asymptotic.growth_group import
ExponentialGrowthGroup
> sage: G = ExponentialGrowthGroup(ZZ['x'], 'y'); G
> Growth Group ZZ[x]^y
> sage: G('(1-x)^y')
> (-x + 1)^y
> sage: G('(1+x)^y')
> x + 1^y
> }}}
Seems to be code from before `repr_op` and then just inserting it. Now
rewritten.
> 14. `GrowthGroupFactory`: the documentation sounds like
`ignore_variables=('e',)` would only be set when no keywords are given.
However, this applies even if only `ignore_variables` is not set.
Rewritten.
----
Last 10 new commits:
||[http://git.sagemath.org/sage.git/commit/?id=0ca6efda638f8a5819577629d3c360fcfd4a2f3c
0ca6efd]||{{{Trac #19094/#19083 comment 60, 11: correct wrong log and give
log in errors a base}}}||
||[http://git.sagemath.org/sage.git/commit/?id=71802dac512847136a46cf7a0f261e4240d44589
71802da]||{{{Trac #19094/#19083 comment 60, 8: rename to
_create_element_in_extension_}}}||
||[http://git.sagemath.org/sage.git/commit/?id=e2285e7012435f27c5ed0d2dfab34db255912244
e2285e7]||{{{Trac #19094/#19083 comment 60, 8: rewrite description of
_create_element_in_extension_}}}||
||[http://git.sagemath.org/sage.git/commit/?id=4cb775fbe20b1e44f5db2bef973f1763c80c6e35
4cb775f]||{{{Trac #19094/#19083 comment 60, 12: add doctest in
_rpow_element to test parameter base}}}||
||[http://git.sagemath.org/sage.git/commit/?id=51f796c2470150834d6949e408e257469f18afbd
51f796c]||{{{Trac #19094/#19083 comment 60, 12: document _rpow_element
2^x}}}||
||[http://git.sagemath.org/sage.git/commit/?id=2f110dbcba55c31032663e2b66a3d118abed3226
2f110db]||{{{Trac #19094/#19083 comment 60, 13: simplify
ExponentialGrowthElement._repr_}}}||
||[http://git.sagemath.org/sage.git/commit/?id=4c49d029e7a7998190c8d0c7409ebec79ece56af
4c49d02]||{{{Trac #19094/#19083 comment 60, 14: rewrite keyword arguments
documentation of GrowthGroupFactory}}}||
||[http://git.sagemath.org/sage.git/commit/?id=d2cc73a4aa79c5d27b888502026b44f90e751755
d2cc73a]||{{{add forgotten "EXAMPLES::" line}}}||
||[http://git.sagemath.org/sage.git/commit/?id=498dbad4ca50f6b4f6b87e2cd8d85543253c2f09
498dbad]||{{{Trac #19094/#19083 comment 60, 15: add a doctest to
GenericProduct._create_element_via_parent_}}}||
||[http://git.sagemath.org/sage.git/commit/?id=e8ad893715b0dfc8a3907a05382b0c1cba57b818
e8ad893]||{{{Trac #19094/#19083 comment 60, 16: delte misplaced statement
in docstring}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/19083#comment:69>
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