correctly handle exponential growth in asymptotic ring

[dkrenn]

The base of an exponential growth element can be any number, but indeed it should only be a positive number and its argument should be dealt with in a separate way (as this does not contribute to the growth, but still distinguishes different elements, e.g. (-2)^n and 2^n. As a consequence, the sorting of the terms in an asymptotic expansion is not correct and as one wanted.

E.g. one might get something

3/32*(-1)^n*n^(-4) + 3/8*(-1)^n*n^(-5) + O((-1)^n*n^(-6)) + (-1/27*I*sqrt(3) + 1/27)*(-zeta3 - 1)^n*n^(-3) + (-1/9*I*sqrt(3) + 1/3)*(-zeta3 - 1)^n*n^(-4) + O((-zeta3 - 1)^n*n^(-5)) + 133/72*n + 7/12*log(n) + 7/12*euler_gamma - 1/6*a0*(I*sqrt(3) + 1) - 1/6*a1*(-I*sqrt(3) + 1) - 1/4*a2 - 23/6 - 11/36*n^(-1) + O(n^(-2)) + (1/27*I*sqrt(3) + 1/27)*zeta3^n*n^(-3) + (1/9*I*sqrt(3) + 1/3)*zeta3^n*n^(-4) + O(zeta3^n*n^(-5))

(copied out of some larger computation)

[dkrenn]

Last 10 new commits:

​b71c441	extend element constructor for partial conversion elements
​79276e3	update doctests due to nonnegativity
​6950ea8	minor code simplification due to nonnegativity
​1cbad39	extend splitting of raw elements to all complex fields
​01b6403	extend growth group factory
​608c296	allow splitting of symbolic elements
​1a0f5a9	fix remaining doctests
​96de88a	ExponentialArgumentGrowthGroup
​a14dec4	...Functor
​ebf3d85	test category

[git]

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

​9200823	extend docstrings and complete them
​1a5fb6c	fixup conversion string to parent and fixup related doctests
​1ce1501	factor out NonGrowthGroup
​26eeca7	docstring of group_factory in exponential groups
​da51c19	refactor group_factory
​e13c97a	simplify a method
​35070e2	fixup classes
​4cd7643	set non_growth_group class
​711c61c	extend growth group factory to deal correctly with argument growth groups
​fa684a2	rename to _non_growth_group_class_

[git]

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

​d01abd4	move non_growth_group-methods to GenericGrowthGroup
​a4d2ec1	non_growth_group method for monimial groups
​c2a1859	fixup doctests
​67e0046	fix imports in doctest
​b6ffb11	add monomial non-growth groups
​3e96f9e	solve a minor bug in repr
​2e7bb26	extend growth group factory to monomial non-growth groups
​8e67f6c	add some more doctests to factory
​3247905	small update in docstring
​d1a0417	factory for monomial growth groups

[git]

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

​0e68723	I: add a doctest
​541148b	U: make the docs build
​ae99d04	Merge branch 'u/dkrenn/roots-of-unity-group' into u/dkrenn/asy-roots-of-unity-etc

[git]

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

​da0d3dc	U: index new groups
​3804f50	Merge branch 'u/dkrenn/roots-of-unity-group' into u/dkrenn/asy-roots-of-unity-etc

[git]

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

​9e05089	fix inversion bug in exponential growth group
​72bd4ea	whitespaces
​a2d2fcf	fix and extend doctests in asymptotic_ring
​d368958	helper function for stripping the symbolic part of exponents in pow
​ad7a216	solve bug on pow, rpow by dealing with symbolic exponents
​a563d8f	correct typo in docstring
​efd6443	fix doctests after last change (pow/exponents)
​3652b18	fix QQ_+ doctests on growth_group_cartesian
​8f69cce	fix one more doctest in term_monoid
​c3dcbe3	adapt growth group used in binomial generator

[git]

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

​2466bdc	implement _an_element_ for exponential growth groups
​3f0d5f6	check positivity wrt SR in __init__ of exponential growth groups
​cef2e5e	fix doctests by assumptions on SR
​d949a25	add an additional doctest
​f0e16c4	fix doctests (U --> S)
​3f78197	fix doctest (U-->S) for cartesian growth groups
​f1b4b0f	fix doctests (U-->S) for term monoids
​003cf78	fix doctests asymptotic ring (U-->S, assumptions SR)
​6b42bc8	extend repr_op to take care of operator '_'
​7810433	fix powers/rpow/cyclotomicfield conversion/coercion bug

[git]

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

​b2857e9	U: absolute value
​57b4a92	Merge branch 'u/dkrenn/roots-of-unity-group' into u/dkrenn/asy-roots-of-unity-etc
​cfc8b42	_an_element_base_ for ExponentialNonGrowthGroup
​182afd0	factor out additional check and skip it for ExponentialNonGrowthGroup
​fdfdb1a	extend error message for additional check
​0a100cc	py3-correctly handle exceptions
​3e7f385	py3: islice
​0780a3f	Merge tag '8.5.beta2' into u/dkrenn/asy-roots-of-unity-etc

[git]

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

​8d05984	Trac #26146 (py3): avoid comparison of NoneType and tuple
​9e1bedb	Trac #26146 (py3): fix escape in re.sub
​1b73a77	Trac #26146 (py3): handle raised exceptions properly
​2b124c5	Trac #26146 (py3): fix Heisenbug due to non-sorting of subsets
​05f0844	Merge branch 'u/dkrenn/asy-py3' of git://trac.sagemath.org/sage into u/dkrenn/asy-roots-of-unity-etc

[dkrenn]

Some small update to take care of a trivial merge conflict in the current 8.5.beta2 and make everything Python3-compatible.

[git]

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

​f82c1a2	Trac #26587: fix doctests other than sage.rings.asymptotic
​4059d0d	Merge branch 'u/dkrenn/asy-roots-of-unity-etc-8.4' into u/dkrenn/asy-roots-of-unity-etc

[dkrenn]

Ok, patchbot was not happy; changed, so let's give it another try...

---

New commits:

​f82c1a2	Trac #26587: fix doctests other than sage.rings.asymptotic
​4059d0d	Merge branch 'u/dkrenn/asy-roots-of-unity-etc-8.4' into u/dkrenn/asy-roots-of-unity-etc

---

New commits:

​f82c1a2	Trac #26587: fix doctests other than sage.rings.asymptotic
​4059d0d	Merge branch 'u/dkrenn/asy-roots-of-unity-etc-8.4' into u/dkrenn/asy-roots-of-unity-etc

[git]

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

​c994b45	Merge tag '8.7' into u/dkrenn/asy-roots-of-unity-etc
​6b50c47	Trac #26587: rename variable in doctest
​01aef0f	Merge tag '8.7' into u/dkrenn/roots-of-unity-group
​48523ad	extend conversion repr<-->parent (cherry-pick)
​9aab729	remove import
​a5fefd2	Merge branch 'u/dkrenn/roots-of-unity-group' into HEAD

[dkrenn]

Merged in 8.7.

[behackl]

Merged changes from #26588 and fixed one failing doctest. I'll have a look at this now.

---

New commits:

​980825c	abs(AbstractArgument) should not return Python int
​c3d5c15	additional doctests w.r.t. normalization
​7c7eb1f	test that global methods real_part and imag_part also work
​a193018	Merge branch 'asy/roots-of-unity-group' into asy/roots-of-unity-etc
​7c1a021	fix failing doctest (QQ^y --> (QQ_+)^y)

[behackl]

These changes look good and produce a working version of the creation of the AsymptoticRing. I only have minor remarks, namely:

• growth_group.py
  1. L2855: str(self.exponent).isalpha() can probably even be str(self.exponent).isidentifier().
  2. L5348: I'd suggest trimming multiple spaces such that not only 'ZZ * I' or 'ZZ *I', but maybe also 'ZZ * I' and friends are recognized.

---

New commits:

​8a6b4ca	Trac #26587: use isidentifier
​7620a4f	Trac #26588: kwds passed on to element during construction
​3d72ec3	Trac #26588: return type of __abs__
​31668d6	Trac #26588: move exactly_one_is_true to sage.misc.misc
​9d7173d	Trac #26588: add doctest for normalize=False
​1c3e52f	Merge branch 't/26588/asy/roots-of-unity-groups' into t/26587/asy/roots-of-unity-etc
​22e2957	Trac #26587: handle multiple spaces in growth group string

[dkrenn]

Replying to behackl:

These changes look good and produce a working version of the creation of the AsymptoticRing. I only have minor remarks, namely:

• growth_group.py
  1. L2855: str(self.exponent).isalpha() can probably even be str(self.exponent).isidentifier().

Done in

​8a6b4ca

Trac #26587: use isidentifier

1. L5348: I'd suggest trimming multiple spaces such that not only 'ZZ * I' or 'ZZ *I', but maybe also 'ZZ * I' and friends are recognized.

Done in

​22e2957

Trac #26587: handle multiple spaces in growth group string

[behackl]

Replying to dkrenn:

• growth_group.py
  1. L2855: str(self.exponent).isalpha() can probably even be str(self.exponent).isidentifier().

Done in

​8a6b4ca

Trac #26587: use isidentifier

LGTM

1. L5348: I'd suggest trimming multiple spaces such that not only 'ZZ * I' or 'ZZ *I', but maybe also 'ZZ * I' and friends are recognized.

Done in

​22e2957

Trac #26587: handle multiple spaces in growth group string

LGTM.

Thank you.

[behackl]

... waiting for the patchbot before setting this to positive_review.