Opened 5 years ago
Last modified 3 years ago
#21869 closed enhancement
A framework for discrete valuations in Sage — at Version 40
Reported by:  saraedum  Owned by:  

Priority:  major  Milestone:  sage7.5 
Component:  commutative algebra  Keywords:  discrete valuations, valuations, padics, function fields, number fields, smooth projective curves, Mac Lane algorithm, Montes algorithm, sd87 
Cc:  Merged in:  
Authors:  Julian Rüth  Reviewers:  
Report Upstream:  N/A  Work issues:  move references to references file, move README to sage documentation, make sure that valuation() has a lot of the documentation and the factory just references it, remove optional: integrated bits 
Branch:  u/saraedum/a_framework_for_discrete_valuations_in_sage (Commits, GitHub, GitLab)  Commit:  c0a81c8285b47f6fc89aa34bc125ac474c75f2e9 
Dependencies:  Stopgaps: 
Description (last modified by )
This is a metaticket to keep track of the progress of integrating https://github.com/saraedum/mac_lane into Sage.
Review
For your convenience you can review this ticket at https://github.com/saraedum/mac_lane/pull/4 (and leave inline comments.)
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.
[ ] function_field/function_field_valuation.py [ ] padics/discrete_value_group.py [ ] padics/padic_valuation.py [] valuation/README.md [x] valuation/__init__.py [ ] valuation/all.py [ ] valuation/augmented_valuation.py [ ] valuation/developing_valuation.py [ ] valuation/gauss_valuation.py (Padmavathi) [ ] valuation/inductive_valuation.py [ ] valuation/limit_valuation.py [ ] valuation/mapped_valuation.py [ ] valuation/scaled_valuation.py [ ] valuation/trivial_valuation.py [ ] valuation/valuation.py [ ] valuation/valuation_space.py [ ] valuation/valuations_catalog.py [ ] valuation/value_group.py (Padmavathi)
Necessary changes
Fix bugs in Sage
There are a number of trivial bugs that get fixed by monkeypatches in https://github.com/saraedum/mac_lane/blob/master/__init__.py
 Conversion from a Function Field to its Constant Field #21872
 Conversion from a Function Field to its underlying Polynomial Ring #23166
 Coercions between Function Fields #23167
 Coercions are injective if the underlying map is #21879
 Ring homomorphisms from Fields are injective #21879
 Polynomial rings embed into their fraction fields #23185
 The embedding of a ring into a polynomial ring over that ring is injective #23203, #23204, #23211
 padic rings embed into their fraction fields #23188
 Morphisms of number fields are injective #21879
 ZZ into QQ is injective #21879
 quotients of polynomial rings are injective/surjective #23190
 ZZ into a Number Field is injective #21879
 ZZ into an order of a Number Field is injective #21879
 ZZ does not map onto QQ #23186
ZpCA shifts are broken add default implementation of inverse_of_unit() #23191
Add new features to Sage
New features that the code needs to work
 Factorization over iterated extensions of finite fields. #21996
principal_part() and sides() of a Newton Polygon(patch this in the calling code instead.) (cached_in_argument_method #22034)
Make tests nontrivial
 (some_elements() should be nontrivial for number fields/orders) #23192
 (some_elements() should be nontrivial/deterministic for rational function fields and their extensions) #23193
 (some_elements() should be nontrivial 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.
Change History (40)
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comment:27 Changed 4 years ago by
 Branch set to u/saraedum/a_framework_for_discrete_valuations_in_sage
comment:28 Changed 4 years ago by
 Commit set to 0f615c771cac39a2cce4d54b4fd190f1c84992de
 Keywords sd87 added
comment:29 Changed 4 years ago by
 Commit changed from 0f615c771cac39a2cce4d54b4fd190f1c84992de to 4153ef9b3a920d079437825960d904205fc2ae53
comment:30 Changed 4 years ago by
 Commit changed from 4153ef9b3a920d079437825960d904205fc2ae53 to c0a81c8285b47f6fc89aa34bc125ac474c75f2e9
Branch pushed to git repo; I updated commit sha1. New commits:
c0a81c8  fix function lookup

comment:31 Changed 4 years ago by
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New commits:
c0a81c8  fix function lookup

comment:32 Changed 4 years ago by
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 Work issues set to move references to references file, move README to sage documentation, make sure that valuation() has a lot of the documentation and the factory just references it, remove optional: integrated bits
comment:33 Changed 4 years ago by
 Status changed from new to needs_review
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comment:36 followup: ↓ 38 Changed 4 years ago by
I was reviewing gauss_valuation.py and tried reducing a polynomial using the Gauss valuation induced by the 2adic 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 2adic 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) <ipythoninput1084d78566b468b> in <module>() > 1 v.reduce(h) /projects/da1818ed996d4de6acc6361415b7725d/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
comment:37 followup: ↓ 39 Changed 4 years ago by
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 2adic 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) <ipythoninput12871aadb857663> 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/da1818ed996d4de6acc6361415b7725d/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/da1818ed996d4de6acc6361415b7725d/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
comment:38 in reply to: ↑ 36 Changed 4 years ago by
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 nonintegral elements and x + 1/2 is not integral over Gauss valuation induced by 2adic 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 2adic 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 2adic 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) <ipythoninput1084d78566b468b> in <module>() > 1 v.reduce(h) /projects/da1818ed996d4de6acc6361415b7725d/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
comment:39 in reply to: ↑ 37 Changed 4 years ago by
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 2adic 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) <ipythoninput12871aadb857663> 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/da1818ed996d4de6acc6361415b7725d/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/da1818ed996d4de6acc6361415b7725d/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
comment:40 Changed 4 years ago by
 Description modified (diff)
Last 10 new commits:
fix typo in comment
Added a tutorial in the README
move to subdirectory for merging with sage tree
removing gitignore for merge with sage tree
Merge mac_lane infrastructure for discrete valuations into sage
remove mac_lane LICENSE
remove obsolete TODOs
remove monkey patches
move valuation code to valuation/
remove specific valuation code out of valuation/