A framework for discrete valuations in Sage

[saraedum]

Review

Please check off [x] the following when you think that a file is in good shape (modulo the comments that you made.) Or put a [-] if it needs substantial work. You can put your name next to file to tell others that you are already having a look at it.

[x] function_field/function_field_valuation.py (Stefan Wewers)
[x] padics/discrete_value_group.py
[x] padics/padic_valuation.py (David)
[x] valuation/README.md
[x] valuation/__init__.py
[x] valuation/all.py (David)
[x] valuation/augmented_valuation.py (David)
[x] valuation/developing_valuation.py (Shiva)
[x] valuation/gauss_valuation.py (Padmavathi)
[x] valuation/inductive_valuation.py (David)
[x] valuation/limit_valuation.py (David)
[x] valuation/mapped_valuation.py (David)
[x] valuation/scaled_valuation.py (David)
[x] valuation/trivial_valuation.py (David)
[x] valuation/valuation.py (David)
[x] valuation/valuation_space.py (David)
[x] valuation/valuations_catalog.py (David)
[x] valuation/value_group.py (Padmavathi)
[x] rings/function_field/function_field.py
[x] rings/integer_ring.pyx
[x] rings/number_field/number_field.py
[x] rings/number_field/order.py
[x] rings/padics/padic_generic.py
[x] rings/rational_field.py

Known Issues

sage -t --long src/sage/rings/valuation/augmented_valuation.py  # 21 doctests failed
sage -t --long src/sage/rings/padics/padic_valuation.py  # 5 doctests failed
sage -t --long src/sage/rings/valuation/inductive_valuation.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/limit_valuation.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/valuation.py  # 4 doctests failed
sage -t --long src/sage/rings/valuation/valuation_space.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/gauss_valuation.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/scaled_valuation.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/developing_valuation.py  # 1 doctest failed
sage -t --long src/sage/rings/valuation/trivial_valuation.py  # 3 doctests failed
sage -t --long src/sage/rings/function_field/function_field_valuation.py  # 11 doctests failed
sage -t --long src/sage/rings/valuation/mapped_valuation.py  # 4 doctests failed

Necessary changes

Fix bugs in Sage

There are a number of trivial bugs that get fixed by monkey-patches in ​https://github.com/saraedum/mac_lane/blob/master/__init__.py

1. Conversion from a Function Field to its Constant Field #21872
2. Conversion from a Function Field to its underlying Polynomial Ring #23166
3. Coercions between Function Fields #23167
4. Coercions are injective if the underlying map is #21879
5. Ring homomorphisms from Fields are injective #21879
6. Polynomial rings embed into their fraction fields #23185
7. The embedding of a ring into a polynomial ring over that ring is injective #23203, #23204, #23211
8. p-adic rings embed into their fraction fields #23188
9. Morphisms of number fields are injective #21879
10. ZZ into QQ is injective #21879
11. quotients of polynomial rings are injective/surjective #23190
12. ZZ into a Number Field is injective #21879
13. ZZ into an order of a Number Field is injective #21879
14. ZZ does not map onto QQ #23186
15. ZpCA shifts are broken
16. add default implementation of inverse_of_unit() #23191
17. R[x]→S[x] is injective/surjective if R→S is #23495

Add new features to Sage

New features that the code needs to work

1. Factorization over iterated extensions of finite fields. #21996
2. principal_part() and sides() of a Newton Polygon (patch this in the calling code instead.)
3. (cached_in_argument_method #22034)

Make tests non-trivial

1. (some_elements() should be non-trivial for number fields/orders) #23192
2. (some_elements() should be non-trivial/deterministic for rational function fields and their extensions) #23193
3. (some_elements() should be non-trivial for fraction_fields of polynomial rings) #23194

Add the valuation code to Sage

i.e., add these files ​https://github.com/saraedum/mac_lane to Sage.

[roed]

Last 10 new commits:

​925d8fa	fix typo in comment
​c4a7b1a	Added a tutorial in the README
​20e6110	move to subdirectory for merging with sage tree
​ed206ec	removing gitignore for merge with sage tree
​14799b0	Merge mac_lane infrastructure for discrete valuations into sage
​0767201	remove mac_lane LICENSE
​bd1dcbf	remove obsolete TODOs
​0eb3fff	remove monkey patches
​6c3a301	move valuation code to valuation/
​0f615c7	remove specific valuation code out of valuation/

[git]

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

​8afc361	remove standalone import commands
​4153ef9	Wired up valuations in the Sage library

[git]

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

​c0a81c8

fix function lookup

[saraedum]

New commits:

​c0a81c8

fix function lookup

[padma_sk]

I was reviewing gauss_valuation.py and tried reducing a polynomial using the Gauss valuation induced by the 2-adic valuation, and got an unexpected error message. I thought it would tell me that the polynomial wasn't integral, and instead it gave me a coercion error.

sage: v
Gauss valuation induced by 2-adic valuation
sage: v.domain()
Univariate Polynomial Ring in y over Integer Ring
sage: h
1/2*y^2
sage: v.reduce(h)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-108-4d78566b468b> in <module>()
----> 1 v.reduce(h)
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/gauss_valuation.py in reduce(self, f, check, degree_bound, coefficients, valuations)
    360
    361         """
--> 362         f = self.domain().coerce(f)
    363
    364         if degree_bound is not None:
 
/usr/local/sage/src/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (/usr/local/sage/src/build/cythonized/sage/structure/parent.c:11229)()
   1166             return False
   1167
-> 1168     cpdef coerce(self, x):
   1169         """
   1170         Return x as an element of self, if and only if there is a canonical
 
/usr/local/sage/src/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (/usr/local/sage/src/build/cythonized/sage/structure/parent.c:11158)()
   1193                 except Exception:
   1194                     _record_exception()
-> 1195             raise TypeError("no canonical coercion from %s to %s" % (parent(x), self))
   1196         else:
   1197             return (<map.Map>mor)._call_(x)
 
TypeError: no canonical coercion from Univariate Polynomial Ring in y over Rational Field to Univariate Polynomial Ring in y over Integer Ring

[padma_sk]

equivalence_unit from gauss_valuation.py isn't outputting the results shown in the example input -2 as shown in the file.

sage: v
Gauss valuation induced by 2-adic valuation
sage: v.domain()
Univariate Polynomial Ring in y over Integer Ring
sage: v.equivalence_unit(2)
4
sage: v.equivalence_unit(-2)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-128-71aadb857663> in <module>()
----> 1 v.equivalence_unit(-Integer(2))
 
/usr/local/sage/src/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller.__call__ (/usr/local/sage/src/build/cythonized/sage/misc/cachefunc.c:1079
2)()
   2036                 return cache[k]
   2037         except KeyError:
-> 2038             w = self._instance_call(*args, **kwds)
   2039             cache[k] = w
   2040             return w
 
/usr/local/sage/src/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller._instance_call (/usr/local/sage/src/build/cythonized/sage/misc/cachefunc.
c:10238)()
   1912             True
   1913         """
-> 1914         return self.f(self._instance, *args, **kwds)
   1915
   1916     cdef fix_args_kwds(self, tuple args, dict kwds):
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/gauss_valuation.py in equivalence_unit(self, s, reciprocal)
    474             return self.equivalence_reciprocal(self.equivalence_unit(-s))
    475
--> 476         ret = self._base_valuation.element_with_valuation(s)
    477         return self.domain()(ret)
    478
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/valuation_space.py in element_with_valuation(self, s)
    465             s = QQ.coerce(s)
    466             if s not in self.value_semigroup():
--> 467                 raise ValueError("s must be in the value semigroup of this valuation but %r is not in %r"%(s, self.value_semigroup()))
    468             if s == 0:
    469                 return self.domain().one()
 
ValueError: s must be in the value semigroup of this valuation but -2 is not in Additive Abelian Semigroup generated by 1

[saraedum]

Thanks for reporting this. I think this is ok. The problem here is not that the polynomial is not integral but that the polynomial is not in the domain.

This works:

sage: R.<x> = QQ[]
sage: v = valuations.GaussValuation(R, QQ.valuation(2))
sage: v.reduce(x + 1/2)
ValueError: reduction not defined for non-integral elements and x + 1/2 is not integral over Gauss valuation induced by 2-adic valuation

This does not:

sage: R.<x> = ZZ[]
sage: v = valuations.GaussValuation(R, ZZ.valuation(2))
sage: v.reduce(x + 1/2)
TypeError: no canonical coercion from Univariate Polynomial Ring in x over Rational Field to Univariate Polynomial Ring in x over Integer Ring

Replying to padma_sk:

I was reviewing gauss_valuation.py and tried reducing a polynomial using the Gauss valuation induced by the 2-adic valuation, and got an unexpected error message. I thought it would tell me that the polynomial wasn't integral, and instead it gave me a coercion error.

sage: v
Gauss valuation induced by 2-adic valuation
sage: v.domain()
Univariate Polynomial Ring in y over Integer Ring
sage: h
1/2*y^2
sage: v.reduce(h)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-108-4d78566b468b> in <module>()
----> 1 v.reduce(h)
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/gauss_valuation.py in reduce(self, f, check, degree_bound, coefficients, valuations)
    360
    361         """
--> 362         f = self.domain().coerce(f)
    363
    364         if degree_bound is not None:
 
/usr/local/sage/src/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (/usr/local/sage/src/build/cythonized/sage/structure/parent.c:11229)()
   1166             return False
   1167
-> 1168     cpdef coerce(self, x):
   1169         """
   1170         Return x as an element of self, if and only if there is a canonical
 
/usr/local/sage/src/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (/usr/local/sage/src/build/cythonized/sage/structure/parent.c:11158)()
   1193                 except Exception:
   1194                     _record_exception()
-> 1195             raise TypeError("no canonical coercion from %s to %s" % (parent(x), self))
   1196         else:
   1197             return (<map.Map>mor)._call_(x)
 
TypeError: no canonical coercion from Univariate Polynomial Ring in y over Rational Field to Univariate Polynomial Ring in y over Integer Ring

[saraedum]

You are in the wrong domain in this example I think: This is the error you are seeing because there is no element of valuation -2 in ZZ[x].

sage: R.<x> = ZZ[]
sage: v = valuations.GaussValuation(R, ZZ.valuation(2))
sage: v.element_with_valuation(-2)
ValueError: s must be in the value semigroup of this valuation but -2 is not in Additive Abelian Semigroup generated by 1

However, this works in QQ[x].

sage: sage: R.<x> = QQ[]
sage: v = valuations.GaussValuation(R, QQ.valuation(2))
sage: v.element_with_valuation(-2)
1/4

Does that make sense? (Should it be documented more explicitly?)

Replying to padma_sk:

equivalence_unit from gauss_valuation.py isn't outputting the results shown in the example input -2 as shown in the file.

sage: v
Gauss valuation induced by 2-adic valuation
sage: v.domain()
Univariate Polynomial Ring in y over Integer Ring
sage: v.equivalence_unit(2)
4
sage: v.equivalence_unit(-2)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-128-71aadb857663> in <module>()
----> 1 v.equivalence_unit(-Integer(2))
 
/usr/local/sage/src/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller.__call__ (/usr/local/sage/src/build/cythonized/sage/misc/cachefunc.c:1079
2)()
   2036                 return cache[k]
   2037         except KeyError:
-> 2038             w = self._instance_call(*args, **kwds)
   2039             cache[k] = w
   2040             return w
 
/usr/local/sage/src/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller._instance_call (/usr/local/sage/src/build/cythonized/sage/misc/cachefunc.
c:10238)()
   1912             True
   1913         """
-> 1914         return self.f(self._instance, *args, **kwds)
   1915
   1916     cdef fix_args_kwds(self, tuple args, dict kwds):
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/gauss_valuation.py in equivalence_unit(self, s, reciprocal)
    474             return self.equivalence_reciprocal(self.equivalence_unit(-s))
    475
--> 476         ret = self._base_valuation.element_with_valuation(s)
    477         return self.domain()(ret)
    478
 
/projects/da1818ed-996d-4de6-acc6-361415b7725d/user/padma_sk/mac_lane/valuation_space.py in element_with_valuation(self, s)
    465             s = QQ.coerce(s)
    466             if s not in self.value_semigroup():
--> 467                 raise ValueError("s must be in the value semigroup of this valuation but %r is not in %r"%(s, self.value_semigroup()))
    468             if s == 0:
    469                 return self.domain().one()
 
ValueError: s must be in the value semigroup of this valuation but -2 is not in Additive Abelian Semigroup generated by 1

[gpark]

Ran the test and found the error:

sage -t src/sage/rings/function_field/function_field.py # 7 doctests failed

[saraedum]

Replying to gpark:

Ran the test and found the error:

sage -t src/sage/rings/function_field/function_field.py # 7 doctests failed

Did you run the tests with all the dependencies applied? About 50 tests fail for me. That's expected (since the dependencies are not in yet.)

[saraedum]

The following errors are expected. I am working on them.

----------------------------------------------------------------------
sage -t --warn-long 39.1 src/sage/rings/valuation/limit_valuation.py  # 52 doctests failed
sage -t --warn-long 39.1 src/sage/rings/valuation/gauss_valuation.py  # 1 doctest failed
sage -t --warn-long 39.1 src/sage/rings/valuation/valuation_space.py  # 2 doctests failed
sage -t --warn-long 39.1 src/sage/rings/valuation/mapped_valuation.py  # 42 doctests failed
sage -t --warn-long 39.1 src/sage/rings/valuation/valuation.py  # 9 doctests failed
sage -t --warn-long 39.1 src/sage/rings/valuation/inductive_valuation.py  # 13 doctests failed
sage -t --warn-long 39.1 src/sage/rings/valuation/augmented_valuation.py  # 16 doctests failed
----------------------------------------------------------------------

[saraedum]

Sorry, I somehow reverted some changes to the ticket description. Not sure how this happened.

[swewers]

I have had a look at function_field_valuation. I have already worked with the code a lot, and it is working fine, and the documentation is extensive and clear. But I have only tested the latest standalone version.

[git]

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

​9fd8733

fix import

[git]

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

​e1e65a5

fixed typo

[git]

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

​9c16a1b

undo .valuation() shortcut

[git]

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

​119f245

It is not relevant whether a valuation converts into the valuation space but whether it is already in the valuation space

[git]

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

​7ea9874

fix doctests

[saraedum]

New commits:

​9fd8733	fix import
​e1e65a5	fixed typo
​9c16a1b	undo .valuation() shortcut
​119f245	It is not relevant whether a valuation converts into the valuation space but whether it is already in the valuation space
​7ea9874	fix doctests

[git]

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

​3fd4140	add doctest output
​0c60cb7	fix valuation parameters

[git]

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

​2010014

restricting to ZZ, we need to know the prime

[saraedum]

New commits:

​3fd4140	add doctest output
​0c60cb7	fix valuation parameters
​2010014	restricting to ZZ, we need to know the prime

[git]

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

​e5ef4d8	do not catch everything
​efe2490	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[roed]

New commits:

​e5ef4d8	do not catch everything
​9fd8733	fix import
​e1e65a5	fixed typo
​9c16a1b	undo .valuation() shortcut
​119f245	It is not relevant whether a valuation converts into the valuation space but whether it is already in the valuation space
​7ea9874	fix doctests
​3fd4140	add doctest output
​0c60cb7	fix valuation parameters
​2010014	restricting to ZZ, we need to know the prime
​efe2490	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[roed]

Oops. Reverting.

[git]

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

​1eace28	Update valuation_space.py
​21b0f68	Update valuation_space.py
​38f3815	Update valuation_space.py
​7c57f68	Update valuation_space.py
​d90afa8	Update valuation_space.py
​1cb8178	Update valuation_space.py
​39cb55b	Update valuation_space.py
​a474ed5	Update valuation_space.py
​ca2089f	Update valuation_space.py
​0fd986f	Merge remote-tracking branch 'remotes/github/sage' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​bcb78f3	Update scaled_valuation.py
​be4daab	Update valuation.py
​7a95a9d	Update augmented_valuation.py
​dbf7791	Update augmented_valuation.py
​58bb2bc	Update developing_valuation.py
​e1c8bd5	Update limit_valuation.py
​a0f6bd3	Update mapped_valuation.py
​33aa99f	Update padic_valuation.py

[git]

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

​b90ba64	Fix doctest for left action
​37d7187	Remove absolute_import

[roed]

New commits:

​b90ba64	Fix doctest for left action
​37d7187	Remove absolute_import

[git]

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

​8da1ceb

Clarify semigroup construction

[git]

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

​07e40b9

add shifting doctest

[roed]

New commits:

​07e40b9

add shifting doctest

[git]

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

​021b188

improve error message

[git]

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

​a6a798f

Clarified the notion of minimality

[git]

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

​ee0db31

clarify meaning of effective_degree

[git]

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

​e9243b8

bring residue into the right residue ring

[git]

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

​24e68ec

add to/from residue ring tests

[git]

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

​791879a	use more robust r strings
​2bed311	No workaround for number field equality necessary

[git]

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

​c02de30	Added an example of a p-adic valuation in an order
​e3fb245	trivial extensions are totally ramified
​e959a8b	check for subrings so extensions() is not bound to fail
​544977a	add doctest to element_with_valuation

[git]

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

​a0880bd

Fix bug in p-adic shift

[git]

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

​e9eddbd

better size estimate for large primes

[git]

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

​6a1e0f1	fixed docstring
​45286d7	Update function_field.py
​d0ebc9b	Merge branch 'sage' of github.com:saraedum/mac_lane into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​7c1bf02

Key has changed

[git]

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

​a93ce9a

Some examples that came up at Sage Days 87

[saraedum]

New commits:

​a93ce9a

Some examples that came up at Sage Days 87

[git]

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

​709e7f6	GaussValuation is available on the global scope
​a86ed5e	added introductory examples for developing valuations
​f305a7f	Update inductive_valuation.py
​b86ddd7	Merge branch 'sage' of github.com:saraedum/mac_lane into t/21869/a_framework_for_discrete_valuations_in_sage
​7bc7f17	Improved intro sections of valuation files

[saraedum]

New commits:

​709e7f6	GaussValuation is available on the global scope
​a86ed5e	added introductory examples for developing valuations
​f305a7f	Update inductive_valuation.py
​b86ddd7	Merge branch 'sage' of github.com:saraedum/mac_lane into t/21869/a_framework_for_discrete_valuations_in_sage
​7bc7f17	Improved intro sections of valuation files

[git]

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

​62134d8

move README to the reference manual

[saraedum]

New commits:

​62134d8

move README to the reference manual

[git]

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

​39ee4e9

Move p-adic valuation factory documentation

[saraedum]

New commits:

​39ee4e9

Move p-adic valuation factory documentation

---

New commits:

​39ee4e9

Move p-adic valuation factory documentation

[git]

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

​d893c55

remove completed TODO

[saraedum]

New commits:

​d893c55

remove completed TODO

[git]

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

​e318075

value_group has moved

[git]

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

​a2d1091

fix toctree formatting

[git]

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

​9b02800

fix docbuild

[git]

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

​735cd8d

fix typo

[git]

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

​04dd395

fix reference link

[git]

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

​75ccb0e	fix typo
​36f33e6	remove commented out code

[git]

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

​13f7d6c	fix grammar
​39b0792	Fix MacLane references
​4630b93	fix LaTeX

[git]

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

​cc9607f

fix docbuild

[git]

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

​2b767b7

fix reference key

[git]

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

​cdf89ae

renamed reference manual section

[saraedum]

Last 10 new commits:

​735cd8d	fix typo
​04dd395	fix reference link
​75ccb0e	fix typo
​36f33e6	remove commented out code
​13f7d6c	fix grammar
​39b0792	Fix MacLane references
​4630b93	fix LaTeX
​cc9607f	fix docbuild
​2b767b7	fix reference key
​cdf89ae	renamed reference manual section

[git]

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

​c011093

reformat headers for reference manual

[saraedum]

New commits:

​c011093

reformat headers for reference manual

[git]

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

​8022ed1

fix docbuild

[git]

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

​14e034e

fix value_group documentation

[git]

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

​3bff1b9

fix documentation in valuation

[git]

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

​ed13821	fix documentation of valuation_space
​7db0f05	fix documentation of gauss_valuation

[git]

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

​2f6dd58

fix MacLane references

[git]

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

​738904b	trying to fix augmented valuation links
​007499e	shorten links

[git]

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

​a105a8f

fixed links in documentation

[git]

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

​3b91735

fixing links in developing valuation

[git]

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

​ee5abb2

Fix links in developing valuation

[git]

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

​51e89db	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​0f66745	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​984cc75	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​35b62e6	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​c50f6ec	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​93757ef	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​5c62063	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​f173caf	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​013292f	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​548e879	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​6da7536	fix broken documentation links
​6aa9f65	Fixed documentation
​d27262a	Fix _richcmp_
​6509f94	Merge remote-tracking branch 'trac/u/saraedum/23190' into t/21869/a_framework_for_discrete_valuations_in_sage
​fb66f9f	Fix richcmp
​e3fb631	Merge branch 'u/saraedum/a_polynomial_ring_embeds_into_its_fraction_field' of git://trac.sagemath.org/sage into t/23185/a_polynomial_ring_embeds_into_its_fraction_field
​f3ecd0e	added missing doctest
​5093894	Merge remote-tracking branch 'trac/u/saraedum/a_polynomial_ring_embeds_into_its_fraction_field' into t/21869/a_framework_for_discrete_valuations_in_sage
​2ca7a7c	fix pickling of valuations

[saraedum]

New commits:

​6da7536	fix broken documentation links
​6aa9f65	Fixed documentation
​d27262a	Fix _richcmp_
​6509f94	Merge remote-tracking branch 'trac/u/saraedum/23190' into t/21869/a_framework_for_discrete_valuations_in_sage
​fb66f9f	Fix richcmp
​e3fb631	Merge branch 'u/saraedum/a_polynomial_ring_embeds_into_its_fraction_field' of git://trac.sagemath.org/sage into t/23185/a_polynomial_ring_embeds_into_its_fraction_field
​f3ecd0e	added missing doctest
​5093894	Merge remote-tracking branch 'trac/u/saraedum/a_polynomial_ring_embeds_into_its_fraction_field' into t/21869/a_framework_for_discrete_valuations_in_sage
​2ca7a7c	fix pickling of valuations

[git]

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

​b105f14	Disable function field test
​50d6090	fix _relative_size output
​9bf9e75	fill in missing doctest output
​45e0e8f	fix copy&paste error

[saraedum]

New commits:

​b105f14	Disable function field test
​50d6090	fix _relative_size output
​9bf9e75	fill in missing doctest output
​45e0e8f	fix copy&paste error

[git]

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

​a4ac152	Call pAdicValuation instead of .valuation
​6de2868	fix _relative_size output

[saraedum]

New commits:

​a4ac152	Call pAdicValuation instead of .valuation
​6de2868	fix _relative_size output

[git]

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

​cf61932	Fix doctest
​1329738	Allow p-adic rings
​249bdc0	Update doctest output

[saraedum]

New commits:

​cf61932	Fix doctest
​1329738	Allow p-adic rings
​249bdc0	Update doctest output

[git]

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

​a92f47f	make sure that arguments to add_bigoh are correctly normalized
​aa1709d	comment on stagnating degrees
​005e7ab	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​bd15d71	add exact keyword
​99dccf6	Merge branch 't/23331/allow_exact_defining_polynomials_for_p_adic_extensions' into t/20310/change_precision
​ef4ed33	Fix SEEALSO:
​1754b44	Fix exact=True errors in the right branch
​7926b41	Moving code for fraction_field and integer_ring, and enabling fraction fields for fixed-mod
​7712a86	Merge remote-tracking branch 'trac/u/roed/fixed_mod_frac_field' into t/21869/a_framework_for_discrete_valuations_in_sage
​276e4f7	fix and fill in doctest output
​9b03cf8	compute fraction field only when necessary
​a886c42	fix pickling of nodes
​2d1cb90	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[saraedum]

Last 10 new commits:

​1754b44	Fix exact=True errors in the right branch
​7926b41	Moving code for fraction_field and integer_ring, and enabling fraction fields for fixed-mod
​7712a86	Merge remote-tracking branch 'trac/u/roed/fixed_mod_frac_field' into t/21869/a_framework_for_discrete_valuations_in_sage
​276e4f7	fix and fill in doctest output
​9b03cf8	compute fraction field only when necessary
​a886c42	fix pickling of nodes
​a92f47f	make sure that arguments to add_bigoh are correctly normalized
​aa1709d	comment on stagnating degrees
​005e7ab	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage
​2d1cb90	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​282c95e

Remove "not slopes"

[roed]

Doesn't seem "minor"....

[git]

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

​7b44fb3	A test case that failed in an older version
​ad9adb1	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​28fbf35	Check that extensions are computed correctly in towers of number fields
​101502e	Merge branch 'develop' into t/21869/a_framework_for_discrete_valuations_in_sage
​1221125	remove TABs
​7660eab	Mapped valuations should know whether they are discrete

[git]

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

​4e46d34	Added another failing case
​2bbcbb9	Merge branch 't/23525/implement_is_squarefree_for_p_adic_rings' into t/21869/a_framework_for_discrete_valuations_in_sage
​51f7ed0	Add test case

[git]

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

​7c915f1

Merge branch 'develop' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​82338dc	Fix factorization over fraction fields that are isomorphic to function fields
​64e6546	Merge branch 'develop' into t/23642/factorization_over_some_quotient_rings_incorrect
​f6dd0cd	Better isomorphisms between fraction fields and function fields
​38f18b8	minor docstring change
​8bfe326	Merge branch 'develop' into t/23660/better_isomorphisms_between_function_fields_and_fraction_fields
​746eac0	fix docstring
​4bddab1	Merge branch 't/23660/better_isomorphisms_between_function_fields_and_fraction_fields' into t/23642/factorization_over_some_quotient_rings_incorrect
​29feccb	Merge branch 't/23642/factorization_over_some_quotient_rings_incorrect' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​7e62f70	Fixing errors in the coercion to the fraction field for fixed-mod p-adics
​1a4333a	Merge branch 't/13591/add_bigoh' into t/23510/fixed_mod_frac_field
​cdeb376	Merge branch 't/13591/add_bigoh' into t/23510/fixed_mod_frac_field
​cb882fd	Update add_bigoh to account for fixed-mod having a fraction field
​a826978	Fix _tester_add_bigoh
​883e6b5	Fix doctest in local_generic_element.pyx
​52cbd2a	Merge branch 'u/roed/fixed_mod_frac_field' of git://trac.sagemath.org/sage into t/23510/fixed_mod_frac_field
​bc59ffa	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/23510/fixed_mod_frac_field
​3292259	Merge branch 'u/saraedum/fixed_mod_frac_field' of git://trac.sagemath.org/sage into t/23510/fixed_mod_frac_field
​b3c8ac3	Merge branch 't/23510/fixed_mod_frac_field' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​608c5c3

Use names for richcmp operators

[saraedum]

David: I made a trivial change. I don't think it needs review.

[roed]

Yeah, that change seems fine.

[git]

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

​b81b722	Remove use of depraceted list()
​2904b76	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/21869/a_framework_for_discrete_valuations_in_sage
​5739955	Base change factorization to the right parent
​c17adf7	Merge branch 'u/saraedum/factorization_over_some_quotient_rings_incorrect' of git://trac.sagemath.org/sage into t/23642/factorization_over_some_quotient_rings_incorrect
​a63c1ff	Merge branch 't/23642/factorization_over_some_quotient_rings_incorrect' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​28b36f8	Fix ScaleAction
​b6c62d0	Fix doctests
​99b3ab2	Merge branch 't/23642/factorization_over_some_quotient_rings_incorrect' into t/21869/a_framework_for_discrete_valuations_in_sage
​dad02c7	Merge branch 'u/saraedum/fixed_mod_frac_field' of git://trac.sagemath.org/sage into t/23510/fixed_mod_frac_field
​189ac2b	Add _test_fraction_field to the coercion tutorial
​9ecff79	Merge branch 't/23510/fixed_mod_frac_field' into t/21869/a_framework_for_discrete_valuations_in_sage
​226518c	Merge remote-tracking branch 'trac/develop' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​271f6ec

Use a more specialized class for non-classical discrete valuations on function fields

[saraedum]

New commits:

​271f6ec

Use a more specialized class for non-classical discrete valuations on function fields

[git]

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

​bbca3ce	fill in doctest output
​20868e9	bring equivalence_decompositions back to non-fields

[saraedum]

New commits:

​bbca3ce	fill in doctest output
​20868e9	bring equivalence_decompositions back to non-fields

---

New commits:

​bbca3ce	fill in doctest output
​20868e9	bring equivalence_decompositions back to non-fields

[git]

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

​27351d9

Bring back equivalence_decompositions into local rings

[saraedum]

New commits:

​27351d9

Bring back equivalence_decompositions into local rings

[git]

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

​55b33e4	Coercions to the fraction field are injective
​ac081b0	Merge branch 't/23965/coercion_to_fraction_field_is_injective' into t/21869/a_framework_for_discrete_valuations_in_sage
​76df690	Fill in doctest output

[saraedum]

New commits:

​55b33e4	Coercions to the fraction field are injective
​ac081b0	Merge branch 't/23965/coercion_to_fraction_field_is_injective' into t/21869/a_framework_for_discrete_valuations_in_sage
​76df690	Fill in doctest output

---

New commits:

​55b33e4	Coercions to the fraction field are injective
​ac081b0	Merge branch 't/23965/coercion_to_fraction_field_is_injective' into t/21869/a_framework_for_discrete_valuations_in_sage
​76df690	Fill in doctest output

[git]

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

​87c900c	normalize() FP elements
​c7ac632	Merge branch 't/23966/conversion_from_zpfm_to_its_fraction_field_incorrect' into t/21869/a_framework_for_discrete_valuations_in_sage

[git]

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

​a29d30a	Fill in correct doctest output
​d9b9487	Fix computations in iterated extensions of number fields

[git]

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

​6c5c12b

fill in doctest output

[git]

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

​41277b3

Fix factorization doctests

[saraedum]

New commits:

​6c5c12b	fill in doctest output
​41277b3	Fix factorization doctests

---

New commits:

​6c5c12b	fill in doctest output
​41277b3	Fix factorization doctests

[git]

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

​09b6402

stable factorization output

[git]

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

​dfad6f4

Fix valuation.lift(report_coefficients=True)

[saraedum]

New commits:

​dfad6f4

Fix valuation.lift(report_coefficients=True)

---

New commits:

​dfad6f4

Fix valuation.lift(report_coefficients=True)

[git]

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

​8767fdc

fix docbuild

[git]

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

​ecfe1bc

fix doc references

[saraedum]

New commits:

​ecfe1bc

fix doc references

---

New commits:

​ecfe1bc

fix doc references

[git]

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

​775e093

Remove Python2 code from valuations

[saraedum]

New commits:

​775e093

Remove Python2 code from valuations