groups for handling arguments

[dkrenn]

Implement groups that handle complex arguments, points on the unit circle, roots of unit etc.

These groups are needed for growth groups of asymptotic rings in relation to #26587.

[git]

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

​02eef7b	U: more imports cleanup in doctests
​db30a45	U: implement __pow__
​3b7b75c	U: major restructuring of classes (factor out AbstractArgumentGroup)
​1bfff61	U: ArgumentByElementGroup
​2fbf67e	U: ArgumentGroupFactory
​e03bd7f	U: fixup: spaces
​adbeca0	U: fixup imports
​51e5ee6	U: update copyright
​b3c17bf	U: module description

[git]

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

​1d7098e	U: cleanup
​7627b79	U: simplify repr-code (by using existing stuff)
​24dd452	U: extend error message in ArgumentGroup-factory
​4087aba	U: rename to argument_groups
​b429e37	I: imaginary groups initial commit
​99c7af7	I: imaginary elements
​d60a1a5	I: imaginary group
​b07eb40	U: extend error message for conversion
​27ec542	U: fix imports in doctests after previous move/rename

[git]

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

​0e68723	I: add a doctest
​541148b	U: make the docs build

[git]

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

​da0d3dc

U: index new groups

[git]

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

​3817de0	U: extend __pow__ to take care of extensions
​d788f68	U: simplify element_constructor
​333411b	U: methods for conversion to symbolic
​fe54d42	U: use new _symbolic_
​dc3ae71	U: Action of RootsOfUnityGroup
​ce8b438	U: implement SignGroup
​11df6a0	U: is_one, is_minus_one for Sign
​72fc938	U: Action of Sign
​4b87cb4	U: doctests and docstrings (minor)

[git]

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

​83c8114	U: use sign group in factory
​029ce0a	U: fix doctests
​9fa8cec	U: implement coercion
​c31cfcd	U: extend element construction (related to coercion(
​07a3988	U: coercion for argument by element groups

[git]

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

​b2857e9

U: absolute value

[dkrenn]

Small Python3-related update concerning #26587.

[behackl]

I have started to look at your changes. It seems that the patchbot is unhappy:

sage -t --long src/sage/groups/misc_gps/argument_groups.py
**********************************************************************
File "src/sage/groups/misc_gps/argument_groups.py", line 658, in sage.groups.misc_gps.argument_groups.UnitCircleGroup._repr_short_
Failed example:
    UnitCircleGroup(RR)._repr_short_()
Expected:
    'U_RR'
Got:
    'U_(Real Field with 53 bits of precision)'
**********************************************************************
File "src/sage/groups/misc_gps/argument_groups.py", line 1253, in sage.groups.misc_gps.argument_groups.ArgumentByElementGroup._repr_short_
Failed example:
    ArgumentByElementGroup(CC)._repr_short_()
Expected:
    'Arg_CC'
Got:
    'Arg_Complex Field with 53 bits of precision'
**********************************************************************
2 items had failures:
   1 of   3 in sage.groups.misc_gps.argument_groups.ArgumentByElementGroup._repr_short_
   1 of   3 in sage.groups.misc_gps.argument_groups.UnitCircleGroup._repr_short_
    [336 tests, 2 failures, 0.13 s]

[git]

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

​01aef0f

Merge tag '8.7' into u/dkrenn/roots-of-unity-group

[git]

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

​48523ad	extend conversion repr<-->parent (cherry-pick)
​9aab729	remove import

[dkrenn]

Replying to behackl:

I have started to look at your changes. It seems that the patchbot is unhappy:

sage -t --long src/sage/groups/misc_gps/argument_groups.py
[...]

Indeed there was a commit missing; now cherry-picked.

[behackl]

Added two commits. Some further comments:

• argument_groups.py
  1. L67: What is the intention of the normalize-keyword and how should it be used? Currently, only for UnitCirclePoint the argument is normalized to be contained within the interval [0,1). For ArgumentByElement the element is not changed. Both of that is fine, however: the keyword is not respected by any of the _element_constructor_ methods. Is it only there for potential future groups inheriting from AbstractArgumentGroup?
  2. L297: __abs__ returns the Python int 1. (Fixed via 980825c561)
  3. I wanted to have some additional doctests where normalization is involved (c3d5c15f47).
  4. L1713: I think that exactly_one_is_true is quite useful and should maybe live in misc/misc.py.

• imaginary_groups.py:
  1. After implementing imag and real, also the global methods real_part and imag_part can be called; this should be tested (7c7eb1fcf6)

Other than that, I have no further comments and am happy with the code. Having these rather basic groups allows to build a solution regarding the handling of the (incomparable) asymptotic growth elements in an AsymptoticRing -- which we desire a lot.

---

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

[dkrenn]

Replying to behackl:

Added two commits.

LGTM, thanks.

• argument_groups.py
  1. L67: What is the intention of the normalize-keyword and how should it be used? Currently, only for UnitCirclePoint the argument is normalized to be contained within the interval [0,1). For ArgumentByElement the element is not changed. Both of that is fine, however: the keyword is not respected by any of the _element_constructor_ methods. Is it only there for potential future groups inheriting from AbstractArgumentGroup?

kwds are now passed on the element during construction.

1. L297: __abs__ returns the Python int 1. (Fixed via 980825c561)

sage: type(exp(QQ(0)))
<type 'sage.rings.integer.Integer'>

so I've changed it to have the same behavior.

1. I wanted to have some additional doctests where normalization is involved (c3d5c15f47).

LGTM

1. L1713: I think that exactly_one_is_true is quite useful and should maybe live in misc/misc.py.

Done.

• imaginary_groups.py:
  1. After implementing imag and real, also the global methods real_part and imag_part can be called; this should be tested (7c7eb1fcf6)

LGTM

Needs small cross review of changes.

---

New commits:

​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

[git]

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

​9d7173d

Trac #26588: add doctest for normalize=False

[behackl]

I am happy with all changes.

[mmezzarobba]

Can you please explain what this doctest is for?

sage: i = CIF(I)
sage: J(3*i)
Traceback (most recent call last):
...
ValueError: 3 (Real Interval Field with 53 bits of precision)
is not in Integer Ring
> *previous* TypeError: unable to coerce
<type 'sage.rings.real_mpfi.RealIntervalFieldElement'> to an integer

I don't understand why this needs to fail while, according to a very similar test a few lines above, J(3*CBF(i)) is supposed to succeed.

After #28517, J(3*CIF(i)) would return 3*I as well. Is that acceptable?

Thanks!

[dkrenn]

Replying to mmezzarobba:

Can you please explain what this doctest is for? [...] I don't understand why this needs to fail while, according to a very similar test a few lines above, J(3*CBF(i)) is supposed to succeed.

After #28517, J(3*CIF(i)) would return 3*I as well. Is that acceptable?

Indeed, this should not fail and is therefore very acceptable. (Not sure why I did not open a ticket for this or wrote at least some kind of remark.)

Thanks for catching this and also for asking back to me; very much appreciated. :)