AsymptoticRing: exp & log, cleanup, some improvements, documentation

[dkrenn]

Logarithm and exponential function (both with arbitrary appropriate bases) of asymptotic expressions.

Cleanup, some improvements, documentation in the asymptotic ring framework (see also #17601).

Depends on #19073

CC: @behackl @cheuberg

Component: asymptotic expansions

Author: Benjamin Hackl, Daniel Krenn

Branch/Commit: f9fbccb

Reviewer: Daniel Krenn, Clemens Heuberger

Issue created by migration from https://trac.sagemath.org/ticket/19083

[dkrenn]

Branch: u/dkrenn/asy/prototype

[dkrenn]

Dependencies: #17600, #17693, #17715, #17716, #18182, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079

[dkrenn]

Commit: e9acd0e

[dkrenn]

Last 10 new commits:

a23d36e	construction and functor and doctests
3b49e70	pushout: correct str/repr (switch to be constistent with remaining Sage)
a3b2cc6	Merge branch 'pushout/functor-str' into u/dakrenn/asy/rings-coercion
19247a5	fix derived classes
dacbfcb	more replacements of `__str__` by _repr_
d1356e5	Merge branch 'pushout/functor-str' into u/dakrenn/asy/rings-coercion
27601ba	fix missing docs
e1acc40	improve docs (seealso, links, etc)
98e8860	make doctest coverage 100% (asymptotic_ring)
e9acd0e	cleanup (remove a comment)

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

9c1fc0e	cleanup documentation: strange 'exact removed
ddbd90a	collect asymptotic code in one directory
ae47bcb	Merge remote-tracking branch 'origin/u/behackl/asy/asymptoticExpression' into t/19048/asy/an_element
3a44a01	fix imports to make doctests pass
171d232	Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into asy/prototype
702527e	Merge commit '695f08d2dd5d98589dfc10b3f2da89ce4e7dd908' of trac.sagemath.org:sage into asy/prototype
3cacc52	change recursive pushout to common_parent (to take care of direct coercions)
4662eed	bug kind of solved (called now directly by cartesian_product); move doctest
23354db	add missing test and fix broken tests
078d327	Merge remote-tracking branch 'origin/u/dkrenn/18182-on-6.7' into asy/prototype

[sagetrac-git]

Changed commit from e9acd0e to 078d327

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Changed commit from 078d327 to 97cdf16

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

263598c	some doc fixes in term_moniod
a382656	add a link in growth_group_factory
c549344	some improvments in the module description of the asymptotic ring
45549cd	big_oh: some seealso
0bf9781	fix doctests
223c1e3	move parts in documentation-tree
adc9236	write doc on used data structures
42a5c1e	two more headlines
d1f4611	fix docbuild (wrong apostrophe)
97cdf16	small change in division example

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

d759c8e	allow O(0)
ab05e75	extend error messages in element_constructor and test for nonzeroness
4bb85a5	rewrite element_constructor of terms
da0a68a	term: rename base_ring to coefficient_ring
ffe1db8	make it working again and fix doctests
ff7fb30	change `_repr_` of monoids
29ed6b3	move element_construction to GenericTermMonoid
1ac20d7	rewrite element_constructor of AsymptoticRing to accept SR and polynomials
15ba65e	correct a bug in growth_group_cartesian._element_constructor_
4bbe5f3	add a doctest to convert from SR

[sagetrac-git]

Changed commit from 97cdf16 to 4bbe5f3

[sagetrac-git]

Changed commit from 4bbe5f3 to 8e0428e

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c958237	docs and doctests for 100%
b8ebe81	' * ' to '*' in elements
8e0428e	remove special treating of 1/x in `_repr_` (due to inconsitency)

[sagetrac-git]

Changed commit from 8e0428e to d59304b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

4115f61	add a pushout-doctest
ad1ca3f	extend and simplify element_constructor and use convert-flag everywhere
e05a7fb	categories and __classcall__
38075d0	__invert__: take care of changing parent
6d1f0c3	small changes in multiplication code
66948e2	rmul, lmul
f48f64a	doc
aad4bf7	convert NN in growth group factory doctest
b2753ed	change _an_element_: remove - to avoid infinite loop in get_action
d59304b	make AsymptoticRing derived from Algebra

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

57cd39f	doc of rmul
1e625e3	add a doctest for scalar multiplication
be23e63	fix bug with "is" and change_parameter
0c2b6e4	improves working with categories and use CommutativeAlgebras()
ee071a7	fix scalar multiplication by zero
f54e588	some checks on the given names of the generators (when using R.<....>)
92861ed	more on names/gens
18bc9e8	correct handling of parent in __invert__
d833544	minor rewrite of __pow__

[sagetrac-git]

Changed commit from d59304b to d833544

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

caef9ea	term: is_same --> __eq__
5618385	rewrite has_same_summands to use iterators efficiently
51cfce6	adapt doc
ef4160e	Merge branch 'asy/inversion' into asy/prototype
e4bf138	fix failing doctest after merge

[sagetrac-git]

Changed commit from d833544 to e4bf138

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a13f6cb	write map and mapped
6b747e6	mapping argument for .copy()
edfd1b8	bring map and mapped back to work and use new copy-construction
4a33e4f	fix bug in merge
7680531	make truncate faster
c7c02b0	element.__init__: check if summands are of correct type
4659972	rewrite `__init__` of element to use new feature of MutablePoset
7287ca1	make `_mul_term_` faster

[sagetrac-git]

Changed commit from e4bf138 to 7287ca1

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Changed commit from 7287ca1 to 6c04529

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2863321	allow merge to go over all elements
9391c78	derive MutablePoset from object (instead of SageObject)
70859d7	cleanup: delete toset since not yet implemented
d647d95	write map and mapped
e64cbd8	mapping argument for .copy()
c28749c	bring map and mapped back to work and use new copy-construction
ceb0b37	fix bug in merge
123d0c8	Merge branch 'u/dkrenn/asy/mutable-poset' into asy/prototype
6c04529	fix lazy import problem when using short representations

[sagetrac-git]

Changed commit from 6c04529 to 5068df9

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1d023c6	import AsymptoticRing lazy
e02895f	remove some empty lines
738f4ed	explicitly use coefficient_ring(-1) in subtraction
ecf5ba8	use simplify/convert everywhere explicit
55d6ad3	restructure and rewrite classcall and init of growth group
3e449df	solve non-uniquenessbug by rewriting classcall and init of term
5068df9	rewrite classcall and init of asymptotic ring

[sagetrac-git]

Changed commit from 5068df9 to 93b8e0b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

25231e1	rewrite `__pow__` of asymptotic ring
5408f6d	Asymptotic Term with ... --> Term with ...
8730ab8	creation of element via parent method for ring
ac3d1ec	adapt __pow__
fff27da	fix FloatingPointException (vs. ZeroDivisonError)
1097dee	create misc.py and move functions from other files to this file
8bae4a9	change imports to make everything running again
184ead8	use relative imports where possible
ed536a1	use asymptotic_ring option when calling factory TermMonoid
93b8e0b	correct thing reported by pyflakes

[dkrenn]

comment:86

Replying to @cheuberg:

31. AsymptoticExpansion.__init__:
    • parameter convert is neither documented nor tested.

Now it is.

• test error "Cannot include ..."

Doctest added.

32. AsymptoticExpansion._mul_term_: I'd prefer to say simplify = not isinstance(term, ExactTerm) because this seems to be more robust with respect to future extensions.

True, good idea; changed.

33. AsymptoticExpansion.__invert__:
    • test errors

Done.

[dkrenn]

comment:87

33. AsymptoticExpansion.__invert__:
    • I think that there is shared code between __invert__, __log__, __exp__ and powers with rational exponents. In all those cases, it is important to split into main term and renormalized remainder. The main term is then processed according to the respective method, the remainder is inserted into a converging taylor series with certain coefficients (this could be handeled by one method getting the sequence of taylor coefficients as an argument). Possibly in a follow-up ticket.

Yes, I've noticed this as well. I have it on my local todo list. Now this is #19423

[dkrenn]

comment:88

34. AsymptoticExpansion.__pow__:
    • why is (y^2 + O(y))^(1/2) not tested (add a comment?)

I've refered to #19316.

• test error: "Cannot take ... to the negative exponent"
• test error: "Taking ... to the exponent ... not implemented"

Added tests.

• rational exponents could be implemented via binomial series (follow-up ticket?)

A ticket (#19316) already exists.

35. AsymptoticExpansion.log:
    • test error ("several maximal elements")

Added.

• I am not convinced that having k as an AsymptoticExpansion is very efficient (let the division be in QQ and convert later?, cf. rpow.)

Changed and made some tests: I could save about 15% cputime :)

Rest will follow later today.

[sagetrac-git]

Changed commit from 44b52d6 to 8006837

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2522bd0	Trac #19094/#19083 comment 66, 36: add error test
8cbacdf	Trac #19094/#19083 comment 66, 37: refer to #19424 in not tested doctest
ec10395	Trac #19094/#19083 comment 66, 39: extend description of old_parent (in
36a48e4	Trac #19094/#19083 comment 66, 39: `_create_element_in_extension_` rewrite doctests and rename parameter to old_term_parent
38a597b	Trac #19094/#19083 comment 66, 40: remove outdated NOTE block
b927671	Trac #19094/#19083 comment 66, 40: complete doctests of AsymptoticRing._element_constructor_
7624627	Trac #19094/#19083 comment 66, 40: refer to trac tickets at O-Term from SR todo
1ceba10	Trac #19094/#19083 comment 66, 40: test conversion from multivariate polynomial ring
8006837	Trac #19094/#19083 comment 66, 40: simplify test for empty data

[dkrenn]

comment:90

Replying to @cheuberg:

36. AsymptoticExpansion.rpow:
    • Decrease indentation of ALGORITHM block

Done.

• Test error "Cannot construct the power ..."

Added test.

37. AsymptoticRing: Add some comment on the "TESTS" section which is currently inactive.

Added (#19424).

38. AsymptoticRing.change_parameter: is this a good name (the method sounds like an inplace change, but usually returns a new parent instead)

True, but consistent with

sage: R.<z> = ZZ[]
sage: R.change_ring(QQ)
Univariate Polynomial Ring in z over Rational Field
sage: R
Univariate Polynomial Ring in z over Integer Ring

39. AsymptoticRing._create_element_via_parent_:
    • I do not like the name and the description of the method.

Changed earlier already.

• The role of old_parent is not documented

Extended doc.

• In all uses of the method in this module, old_parent is set and is a term monoid. In the example of this method, it is an asymptotic ring.

Uuups...changed.

• I do not understand why old_parent is needed: if term.parent() is old_parent, then self.change_parameter will probably not change the parent anyway.

E.g. when inverting, then the term parameter will be the already inverted term and old_parent the parent of the original term.

40. AsymptoticRing._element_constructor_:
    • The note box seems to be outdated, as the parameter summands no longer exists.

Deleted.

• test error "Not all list entries ..."
• test error "Symbolic expression ... is not in ..."

Added.

• Why not data or data == 0 instead of not data?

Changed.

• What happens with an O-Term in SR?

There seems to be a bug in SR: #19425. Opened follow up #19426.

• conversion of multivariate polynomial ring is not tested.

Now it is.

43. Delete the following in src/doc/en/reference/rings/index.rst

.. toctree::
   :hidden:

   asymptotic_expansions_index

Not possible, since in src/doc/en/reference/index.rst all indices are included
via :doc: which seems not to add them to any toctree.

[sagetrac-git]

Changed commit from 8006837 to a848139

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

4e5af11	Trac #19094/#19083 comment 66, 36: delete ALGORITHM block
cb083d4	Trac #19094/#19083 comment 66, 41: delete `_create_exact_summands_` since not needed
cf228bb	Trac #19094/#19083 comment 66, 42: make creating of exact summand with growth but without coefficient impossible
a848139	Trac #19094/#19083 comment 66, 42: create_summands: add doctests for interesting `data`

[dkrenn]

comment:92

Replying to @cheuberg:

36. AsymptoticExpansion.rpow:
    • The algorithm given in the documentation seems to be quite obvious
    • I do not like "the rest", "the remaining part": those are actually the asymptotic main parts.
    • Why is the algorithm described in that much detail here and nowhere (log, exp, pow) else?

Block deleted.

40. AsymptoticRing._element_constructor_:
    • I do not understand the sentence "If set, then it is assured that the terms belong to this asymptotic ring (by converting them if needed)." Who does the converting?

Meanwhile the convert parameter in AsymptoticExpansion has a better description.

41. AsymptoticRing._create_exact_summand_: Why is this needed and not handeled by .create_summand?

Deleted and remaining code adapted.

42. AsymptoticRing.create_summand:
    • doctest case of interesting data (i.e. with coefficient and growth element).

Added.

• The following is surprising:

sage: AR.<z> = AsymptoticRing('z^QQ', QQ)
sage: AR.create_summand('exact', growth='z^2')
z^2

I'd rather expect an error or zero than using an implicit coefficient of `1`

Changed; now there is an error.

[cheuberg]

Changed branch from u/dkrenn/asy/prototype to u/cheuberg/asy/prototype

[sagetrac-git]

Changed commit from a848139 to f9fbccb

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

de137d1	Trac #19083: fix one ReSt error
f9fbccb	Trac #19083: expand description of parameter "convert"

[cheuberg]

comment:95

I checked the changes again, added two trivial commits. Doctests pass, documentation builds, trac's automerge fails for unknown reasons, but branch merges cleanly into 6.10.beta0.

[vbraun]

Changed branch from u/cheuberg/asy/prototype to f9fbccb