Opened 10 years ago
Closed 7 years ago
#8992 closed defect (fixed)
Coercion of univariate quotient polynomial rings
Reported by: | SimonKing | Owned by: | robertwb |
---|---|---|---|
Priority: | major | Milestone: | sage-5.6 |
Component: | coercion | Keywords: | coercion quotient ring sd40.5 |
Cc: | Merged in: | sage-5.6.beta0 | |
Authors: | Simon King | Reviewers: | Mike Hansen, Travis Scrimshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Consider the following setting:
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: Q2 = P.quo([(x^2+1)^2*(x^5+3)])
The gcd of the moduli is (x^2+1)^2
, and so it should be true that the pushout of Q1 and Q2 is the quotient ring with this gcd as modulus. Currently, the pushout raises an error, but with #8800 one has:
sage: from sage.categories.pushout import pushout sage: Q = pushout(Q1,Q2); Q Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^4 + 2*x^2 + 1
However, there remain two bugs that are not covered in #8800 and that prevent a proper coercion of Q1 and Q2.
First bug:
sage: Q.has_coerce_map_from(Q1) False sage: Q.has_coerce_map_from(Q2) False
Second bug:
sage: Q(Q1.gen()) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (932, 0)) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (932, 0)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /home/king/SAGE/sage-4.3.1/devel/<ipython console> in <module>() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_quotient_ring.pyc in __call__(self, x) 272 return PolynomialQuotientRingElement(self, self.__ring(x.lift()), check=False) 273 return PolynomialQuotientRingElement( --> 274 self, self.__ring(x) , check=True) 275 276 def _is_valid_homomorphism_(self, codomain, im_gens): /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3108)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3010)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_ring.pyc in _element_constructor_(self, x, check, is_gen, construct, **kwds) 310 x = x.Polrev() 311 --> 312 return C(self, x, check, is_gen, construct=construct, **kwds) 313 314 def is_integral_domain(self, proof = True): /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_element_generic.pyc in __init__(self, parent, x, check, is_gen, construct) 654 655 if check: --> 656 x = [QQ(z) for z in x] 657 658 self.__list = list(x) /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3108)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3010)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/rational.so in sage.rings.rational.Rational.__init__ (sage/rings/rational.c:5781)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/rational.so in sage.rings.rational.Rational.__set_value (sage/rings/rational.c:7052)() TypeError: Unable to coerce xbar (<class 'sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement'>) to Rational sage: Q.gen() xbar
It could be that the following is an additional bug, but perhaps it is just a special case of the previous:
sage: Q(str(Q.gen())) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (932, 0)) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (932, 0)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /home/king/SAGE/sage-4.3.1/devel/<ipython console> in <module>() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_quotient_ring.pyc in __call__(self, x) 272 return PolynomialQuotientRingElement(self, self.__ring(x.lift()), check=False) 273 return PolynomialQuotientRingElement( --> 274 self, self.__ring(x) , check=True) 275 276 def _is_valid_homomorphism_(self, codomain, im_gens): /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3108)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3010)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_ring.pyc in _element_constructor_(self, x, check, is_gen, construct, **kwds) 297 R = self.base_ring() 298 p = Parser(Integer, R, LookupNameMaker({self.variable_name(): self.gen()}, R)) --> 299 return self(p.parse(x)) 300 except NameError: 301 raise TypeError,"Unable to coerce string" /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.parse (sage/misc/parser.c:3481)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.parse (sage/misc/parser.c:3345)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_eqn (sage/misc/parser.c:5136)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_expr (sage/misc/parser.c:5456)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_term (sage/misc/parser.c:5681)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_factor (sage/misc/parser.c:6044)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_power (sage/misc/parser.c:6158)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.Parser.p_atom (sage/misc/parser.c:6711)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/misc/parser.so in sage.misc.parser.LookupNameMaker.__call__ (sage/misc/parser.c:7653)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3108)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3010)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/rational.so in sage.rings.rational.Rational.__init__ (sage/rings/rational.c:5781)() /home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-packages/sage/rings/rational.so in sage.rings.rational.Rational.__set_value (sage/rings/rational.c:6517)() TypeError: unable to convert xbar to a rational
Attachments (3)
Change History (27)
comment:1 Changed 10 years ago by
comment:2 Changed 10 years ago by
I think I found one source of the problem. The call method (that will become an element_constructor method) says:
if isinstance(x, PolynomialQuotientRingElement): P = x.parent() if P is self: return x elif P == self: return PolynomialQuotientRingElement(self, self.__ring(x.lift()), check=False)
In other words: Only if the parent of x is equal to self, it is attempted to convert x into self via conversion in the polynomial ring. I think this condition should simply be dropped.
Furthermore, after the above code block
return PolynomialQuotientRingElement(self, self.__ring(x) , check=True)
Hence, it is again tried to interprete x in the polynomial ring of self. But the problem is that the variable names in self and in self.__ring
are usually different. So, conversion of strings must fail.
comment:3 Changed 10 years ago by
A side remark: I just noticed that univariate quotient rings have no representation in Singular. I guess this will be on a different ticket, though.
Changed 10 years ago by
_element_constructor_ and _coerce_map_from_ for polynomial quotient rings; may depend on #8800
comment:4 Changed 10 years ago by
OK, I have a ticket. I worked on top of my patches for #8807 and #8800, but if this new patch applies then it should be stand-alone (simply try).
What does it provide?
- Polynomial quotient rings had a call method instead of an _element_constructor_. My patch provides one.
- Previously, a coercion between polynomial quotient rings was not used, even though it clearly should exist when the modulus of the codomain divides the modulus of the domain. This is now solved, by adding a _coerce_map_from_ method.
- The old call method relied on the variable names of the underlying polynomial ring, when processing a string. That's obviously wrong, because the variable names of the quotient ring may be different.
- String evaluation is possible even when one has a polynomial quotient ring over a polynomial ring (example below). This is possible by using
GenDictWithBasering
, which I had originally introduced for infinite polynomial rings.
Examples
Conversion between two quotient rings (coercion exists only in one direction):
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: Q2 = P.quo([(x^2+1)^2]) sage: Q2(Q1.gen()) xbar sage: Q1(Q2.gen()) xbar sage: Q1.has_coerce_map_from(Q2) False sage: Q2.has_coerce_map_from(Q1) True
Here the underlying polynomial ring has a basering that by itself is a polynomial ring:
sage: R.<y> = P[] sage: Q3 = R.quo([(y^2+1)]); Q3 Univariate Quotient Polynomial Ring in ybar over Univariate Polynomial Ring in x over Rational Field with modulus y^2 + 1 sage: Q3(Q1.gen()) # this uses the lift into the underlying polynomial ring x
String evaluation works (if you think about it, this is non-trivial, since it involves generator names of both Q3 and R):
sage: Q3('x*ybar^2') -x
Now, back to the example from the ticket description. If #8807 and #8800 are used as well, one obtains:
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: Q2 = P.quo([(x^2+1)^2*(x^5+3)]) sage: Q1.gen()^2*Q2.gen()^2 + 2*Q1.gen()^2 + 1 0 sage: (Q1.gen()^2*Q2.gen()^2 + 2*Q1.gen()^2 + 1).parent() Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^4 + 2*x^2 + 1
I just realise that I forgot to provide a doc test for _coerce_map_from_. I will post it in a few minutes, and then it's ready for review!
comment:5 Changed 10 years ago by
- Status changed from new to needs_review
OK, the doc test is added (testing coercion from a polynomial ring to a quotient ring and between two quotient rings). Ready for review!
comment:6 Changed 8 years ago by
- Reviewers set to PatchBot
- Status changed from needs_review to needs_work
- Work issues set to rebase
Afraid this one has bitrotted -- it needs a rebase.
comment:7 Changed 8 years ago by
- Work issues changed from rebase to rewrite
Apparently, all but the last problem mentioned in the ticket description have already been fixed in other tickets. Namely, with vanilla sage-5.0.beta7, one has
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: Q2 = P.quo([(x^2+1)^2*(x^5+3)]) sage: from sage.categories.pushout import pushout sage: Q = pushout(Q1,Q2); Q Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^4 + 2*x^2 + 1 sage: Q.has_coerce_map_from(Q1) True sage: Q.has_coerce_map_from(Q2) True sage: Q(Q1.gen()) xbar sage: Q(str(Q.gen())) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (2068, 0)) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (2068, 0)) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (2068, 0)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) ... TypeError: unable to convert xbar to a rational
Also, the __call__
method of quotient rings has already been replaced by an _element_constructor_
, as it should.
So, I wouldn't say that the patch needs to be rebased: It has to be rewritten, or better, it needs to be reduced to those parts that are responsible for making a quotient ring understand the string representation of its generators.
comment:8 Changed 8 years ago by
- Work issues changed from rewrite to rewrite, make polynomial division work
Currently, I can not produce patch that would cover all examples from this ticket. The reason is another bug:
sage: P.<y> = QQ['x'][] sage: y.divides(y) --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) /home/simon/SAGE/sage-5.0.beta7/<ipython console> in <module>() /home/simon/SAGE/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.CommutativeRingElement.divides (sage/structure/element.c:14887)() /home/simon/SAGE/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.so in sage.rings.polynomial.polynomial_element.Polynomial.__mod__ (sage/rings/polynomial/polynomial_element.c:15562)() /home/simon/SAGE/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.Element.__getattr__ (sage/structure/element.c:2919)() /home/simon/SAGE/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.getattr_from_other_class (sage/structure/parent.c:3302)() AttributeError: 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense' object has no attribute 'quo_rem'
That bug also exists in sage-4.6.2, but apparently it has not been present when I wrote the old patch.
Anyway, I think that bug could be fixed here, I see no need to open yet another ticket.
comment:9 Changed 8 years ago by
The reason for my complaint about y.divides(y)
is that the following example from a comment above would not work with the patch that I am now preparing:
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: R.<y> = P[] sage: Q3 = R.quo([(y^2+1)]); Q3 Univariate Quotient Polynomial Ring in ybar over Univariate Polynomial Ring in x over Rational Field with modulus y^2 + 1 sage: Q3(Q1.gen()) # uses the lift from Q1 to P, which is the base ring of Q3 x
The problem is that the coercion framework is not able to find out whether Q3
has a coerce map from Q1
.
So, I guess I should add a "try-except" clause in Q3._coerce_map_from_
, so that an error in division is caught and results in the answer "no, there is no coerce map".
comment:10 Changed 8 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
- Work issues rewrite, make polynomial division work deleted
I have produced a new patch.
Recall that most problems mentioned in the ticket description have already been solved in sage-5.0.beta7. The only remaining was conversion from strings.
Here, I suggest to use a tool that I have introduced in my code for infinite polynomial rings: It is a generalisation of the gens_dict of polynomial rings. In contrast to gens_dict, it not only considers the generator names of the ring, but it also considers (recursively) the generator names of the base ring. This recursive version of gens_dict is then passed to sage_eval.
Hence, if Q has generator 'xbar' and is the quotient ring of some polynomial ring P with generator 'x', then Q('x*xbar')
will be correctly evaluated as P.gen()*Q.gen()
, which in turn evaluates as Q(P.gen())*Q.gen()
.
Concerning the problem with y.divides(...)
: The problem can arise, if Q1 and Q2 are two polynomial quotient rings and one asks Q1.has_coerce_map_from(Q2)
. It will try to divide the moduli of Q1 and Q2. My suggestion is: If that division fails with an error, then there is no coerce map.
After these changes, the tests in sage/rings/polynomial/polynomial_quotient_ring.py and .../polynomial_quotient_ring_element.py pass.
Let's see if the patchbot finds a reason to complain...
Apply trac8992_conversion_polynomial_quotient_ring.patch
comment:11 Changed 8 years ago by
Sorry, I should have mentioned that the patch is for 5.0.beta7, not for 4.8.
comment:12 Changed 8 years ago by
Findings of the patchbot: It does apply to 5.0.beta7, the tests pass (except for one test that seems unrelated with my patch).
Nevertheless, I had to modify my patch, because it has added trailing white space. It should be fixed now.
Apply trac8992_conversion_polynomial_quotient_ring.patch
comment:13 Changed 8 years ago by
There are a few typos in your patch: "are no unique", "my lift an", "in principal".
comment:14 Changed 8 years ago by
Typos corrected, I hope!
Apply trac8992_conversion_polynomial_quotient_ring.patch
comment:15 follow-up: ↓ 17 Changed 8 years ago by
This looks pretty good to me. The one things I worry about is that the result of sage_eval may not actually belong to the correct parent. I would put a check to make sure that it actually does. Then, I think we can mark this as positive review.
comment:16 Changed 8 years ago by
- Keywords sd40.5 added
- Reviewers changed from PatchBot to Mike Hansen
comment:17 in reply to: ↑ 15 ; follow-up: ↓ 18 Changed 8 years ago by
- Status changed from needs_review to needs_work
- Work issues set to Convert string into base ring as a fail safe
Replying to mhansen:
This looks pretty good to me. The one things I worry about is that the result of sage_eval may not actually belong to the correct parent. I would put a check to make sure that it actually does. Then, I think we can mark this as positive review.
At the moment, we have some problem with converting a string that defines an element of the base ring:
sage: P.<x> = QQ[] sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)]) sage: Q2 = P.quo([(x^2+1)^2*(x^5+3)]) sage: from sage.categories.pushout import pushout sage: Q = pushout(Q1,Q2); Q Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^4 + 2*x^2 + 1 sage: Q(Q1.gen()) xbar sage: sage: Q(str(Q.gen())) xbar sage: Q1(x) xbar sage: Q1('x') ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (2061, 0)) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (818, 0)) --------------------------------------------------------------------------- NameError Traceback (most recent call last) /home/simon/SAGE/sage-5.0/devel/sage-main/<ipython console> in <module>() /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:7941)() /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3345)() /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3248)() /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_quotient_ring.pyc in _element_constructor_(self, x) 419 # Interpretation in self has priority over interpretation in self.__ring 420 try: --> 421 return sage_eval(x, GenDictWithBasering(self,self.gens_dict())) 422 except TypeError, NameError: 423 pass /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/misc/sage_eval.pyc in sage_eval(source, locals, cmds, preparse) 197 return locals['_sage_eval_returnval_'] 198 else: --> 199 return eval(source, sage.all.__dict__, locals) 200 201 /home/simon/SAGE/sage-5.0/local/lib/python2.7/site-packages/sage/all.pyc in <module>() NameError: name 'x' is not defined
I'd like to make that work as well, and then add a test for the correct parent.
comment:18 in reply to: ↑ 17 Changed 8 years ago by
- Work issues changed from Convert string into base ring as a fail safe to Convert string into cover ring as a fail safe
Replying to SimonKing:
At the moment, we have some problem with converting a string that defines an element of the base ring
Sorry, I meant "cover ring".
comment:19 Changed 8 years ago by
- Work issues changed from Convert string into cover ring as a fail safe to Test that the result of conversion lives in the correct ring.
Funny. The code was an attempt to convert into the cover ring. But it says
try: return sage_eval(x, GenDictWithBasering(self,self.gens_dict())) except TypeError, NameError: pass try: return PolynomialQuotientRingElement(self, self.__ring(x), check=False) except TypeError: raise TypeError, "unable to convert %s into an element of %s"%(x,repr(self))
In the third line, the NameError
raised by sage_eval is not caught, because I forgot brackets. Arrgh.
comment:20 Changed 8 years ago by
Mike, you are right, the wrong parent can occur:
sage: Q1('1') 1 sage: _.parent() Integer Ring
comment:21 Changed 8 years ago by
- Status changed from needs_work to needs_review
OK, the two issues discussed in the previous posts are fixed and became doc tests. Needs review.
Apply trac8992_conversion_polynomial_quotient_ring.patch
comment:22 Changed 7 years ago by
- Reviewers changed from Mike Hansen to Mike Hansen, Travis Scrimshaw
- Status changed from needs_review to positive_review
- Work issues Test that the result of conversion lives in the correct ring. deleted
Looks good to me.
comment:23 Changed 7 years ago by
- Status changed from positive_review to needs_work
comment:24 Changed 7 years ago by
- Merged in set to sage-5.6.beta0
- Resolution set to fixed
- Status changed from needs_work to closed
The quotient rings implement their own call method, instead of implementing _element_constructor_. I guess this is where I should start.