Re: [sage-devel] Re: Implementing rings of coordinates
There is now a ticket (#26741) ready for review in which the changes have been implemented. I decided not to refactor __call__ because the number of failing doctest was quite big. Maybe this is a project for a separate ticket. I have no idea on how to test reliably if the changes introduced any measurable slowdown. Can anyone chime in on how to do it? Thanks S. * Nils Bruin [2018-11-22 11:10:11]: Pay attention, though. There may be all kinds of guidelines about how to write sage code "appropriately", but in classes where performance is very important there may be shortcuts that violate the guidelines. That may very well be intentional. It may also be that it's legacy code and that rewriting it according to the latest trends does not particularly affect performance negatively. On Thursday, November 22, 2018 at 9:48:41 AM UTC-8, Salvatore Stella wrote: After a more accurate inspection, it appears that MPolynomialRing_polydict is in quite a bad shape. First of all it redefines __call__ which, if I read [1] correctly, should not be done. Second, within the many cases in __call__ one can find: {{{ 510 elif isinstance(x, dict): 511 K = self.base_ring() 512 return MPolynomial_polydict(self, {i: K(a) for i, a in iteritems(x)}) }}} and few lines below {{{ 561 if isinstance(x, dict): 562 return MPolynomial_polydict(self, x) }}} Clearly some housekeeping is in order. I'll try to do something about it and then post again. Any input is welcome S. [1] http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html#coercion-the-basics * Simon King > [2018-11-22 14:10:14]: >On 2018-11-22, Simon King > wrote: >> However, I believe it is bad usage to hard-code a certain class as >> output of arithmetic errors. > >Oops. "errors" is an error, it should be "operations". > >-- >You received this message because you are subscribed to the Google Groups "sage-devel" group. >To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+...@googlegroups.com . >To post to this group, send email to sage-...@googlegroups.com . >Visit this group at https://groups.google.com/group/sage-devel. >For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Implementing rings of coordinates
You make a very good point, I'll try to be careful. I doubt this is a case of efficiency since now __call__ goes through redundant cases and even has an argument that is not used anywhere. Anyway I will cobble together something and we can do speed testing before merging. * Nils Bruin [2018-11-22 11:10:11]: Pay attention, though. There may be all kinds of guidelines about how to write sage code "appropriately", but in classes where performance is very important there may be shortcuts that violate the guidelines. That may very well be intentional. It may also be that it's legacy code and that rewriting it according to the latest trends does not particularly affect performance negatively. On Thursday, November 22, 2018 at 9:48:41 AM UTC-8, Salvatore Stella wrote: After a more accurate inspection, it appears that MPolynomialRing_polydict is in quite a bad shape. First of all it redefines __call__ which, if I read [1] correctly, should not be done. Second, within the many cases in __call__ one can find: {{{ 510 elif isinstance(x, dict): 511 K = self.base_ring() 512 return MPolynomial_polydict(self, {i: K(a) for i, a in iteritems(x)}) }}} and few lines below {{{ 561 if isinstance(x, dict): 562 return MPolynomial_polydict(self, x) }}} Clearly some housekeeping is in order. I'll try to do something about it and then post again. Any input is welcome S. [1] http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html#coercion-the-basics * Simon King > [2018-11-22 14:10:14]: >On 2018-11-22, Simon King > wrote: >> However, I believe it is bad usage to hard-code a certain class as >> output of arithmetic errors. > >Oops. "errors" is an error, it should be "operations". > >-- >You received this message because you are subscribed to the Google Groups "sage-devel" group. >To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+...@googlegroups.com . >To post to this group, send email to sage-...@googlegroups.com . >Visit this group at https://groups.google.com/group/sage-devel. >For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Implementing rings of coordinates
Pay attention, though. There may be all kinds of guidelines about how to write sage code "appropriately", but in classes where performance is very important there may be shortcuts that violate the guidelines. That may very well be intentional. It may also be that it's legacy code and that rewriting it according to the latest trends does not particularly affect performance negatively. On Thursday, November 22, 2018 at 9:48:41 AM UTC-8, Salvatore Stella wrote: > > After a more accurate inspection, it appears that MPolynomialRing_polydict > is > in quite a bad shape. First of all it redefines __call__ which, if I read > [1] > correctly, should not be done. Second, within the many cases in __call__ > one > can find: > > {{{ > 510 elif isinstance(x, dict): > 511 K = self.base_ring() > 512 return MPolynomial_polydict(self, {i: K(a) for i, a in > iteritems(x)}) > }}} > > and few lines below > > {{{ > 561 if isinstance(x, dict): > 562 return MPolynomial_polydict(self, x) > }}} > > Clearly some housekeeping is in order. I'll try to do something about it > and > then post again. Any input is welcome > S. > > [1] > http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html#coercion-the-basics > > > > > > * Simon King > [2018-11-22 14:10:14]: > > >On 2018-11-22, Simon King > wrote: > >> However, I believe it is bad usage to hard-code a certain class as > >> output of arithmetic errors. > > > >Oops. "errors" is an error, it should be "operations". > > > >-- > >You received this message because you are subscribed to the Google Groups > "sage-devel" group. > >To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+...@googlegroups.com . > >To post to this group, send email to sage-...@googlegroups.com > . > >Visit this group at https://groups.google.com/group/sage-devel. > >For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Implementing rings of coordinates
After a more accurate inspection, it appears that MPolynomialRing_polydict is in quite a bad shape. First of all it redefines __call__ which, if I read [1] correctly, should not be done. Second, within the many cases in __call__ one can find: {{{ 510 elif isinstance(x, dict): 511 K = self.base_ring() 512 return MPolynomial_polydict(self, {i: K(a) for i, a in iteritems(x)}) }}} and few lines below {{{ 561 if isinstance(x, dict): 562 return MPolynomial_polydict(self, x) }}} Clearly some housekeeping is in order. I'll try to do something about it and then post again. Any input is welcome S. [1] http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html#coercion-the-basics * Simon King [2018-11-22 14:10:14]: On 2018-11-22, Simon King wrote: However, I believe it is bad usage to hard-code a certain class as output of arithmetic errors. Oops. "errors" is an error, it should be "operations". -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Implementing rings of coordinates
Done: https://trac.sagemath.org/ticket/26741 It appears that the change messes up with coercions. More details in the ticket description. S. * Simon King [2018-11-22 14:10:14]: On 2018-11-22, Simon King wrote: However, I believe it is bad usage to hard-code a certain class as output of arithmetic errors. Oops. "errors" is an error, it should be "operations". -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Implementing rings of coordinates
Dear All, I decided to try inheriting from polynomials, specifically from `MPolynomialRing_polydict` and `MPolynomial_polydict`, but I noticed something strange: is there any reason why `MPolynomialRing_polydict` hardcodes `MPolynomial_polydict` as its element class? I would have expected something like ``` class MPolynomialRing_polydict( MPolynomialRing_macaulay2_repr, PolynomialRing_singular_repr, MPolynomialRing_base): Element = MPolynomial_polydict ``` followed by the use of `Element` whenever this was needed. Instead this class defines a method `_poly_class` which is only used once in `__init__` to define generators (at line 142). Afterwards, every method that needs to build elements imports again MPolynomial_polydict. This happens for example at line 437 for `__call__` and again at line 646 for `monomial_quotient`. This obviously makes it complicated to add funtionality to the elements. Thanks S. * Simon King [2018-11-21 12:03:24]: Dear S., On 2018-11-20, VulK wrote: I am trying to implement the ring of coordinates of a Lie group in the perspective of Peter-Weyl theorem. Concretely I would like to define a polynomial ring with infinitely many generators each depending on two points on a lattice. These generators satisfy many relations but, for the moment, I am happy to forget this fact. Is this possible in the current sage framework? Which are the classes I should inherit from? From a quick look at available classes it looks like InfinitePolynomialRing and InfinitePolynomial might be the one I am after but I do not see how to change the indexing sets as I need apart from brute force: I could keep a dictionary and hack _repr_ accordingly. Any better idea? I guess as the author of InfinitePolynomial*, I should chime in. Unfortunately I don't know the background of what you want to achieve. In particular, I don't know what indexing set you need. Of course, changing _repr_ in a sub-class is not a hack but common usage. Perhaps I should try to explain the purpose of InfinitePolynomial: You have a finite list of symbols and for each symbol you have a family of generators indexed by natural numbers. Together, they generate a free commutative K-algebra R (an "infinite polynomial ring"), where K is a field. Then, the symmetric group S of the natural numbers acts on each family of generators by permuting indices. Any ideal J in R that is (as a set) invariant under the S-action is finitely generated in the sense that there is a finite list of elements g1,...,gn of J such that the union of the S-orbits of g1,...,gn generates J as an R-ideal. Moreover, ideal containment can be effectively tested by some flavour of Gröbner basis theory ("symmetric Gröbner bases"). The purpose of my implementation is to compute symmetric Gröbner bases and test ideal containment. Is any of that useful for your application? Or do you just need an algebra with an indexed family of generators? Then, I suppose it is possible to implement it using the stuff in sage.sets.family, together with sage.combinat.free_module.CombinatorialFreeModule Inspite of its name, CombinatorialFreeModule can be used to implement an algebra. Beware, however, that it is all a very *general* implementation in *Python* (not Cython) and (I think) quite convoluted and indirect [e.g., apparently one is supposed to implement multiplication of elements not by providing _mul_ for the elements but by providing a method product_on_basis for the ring, which is then used in a multiplication method (again not of the elements but of the ring) that is provided by the category of AlgebrasWithBasis that is then finally used in a multiplication method for elements that (if I recall correctly) also is implemented in Python and is inherited from the category framework]. So, my impression has been that CombinatorialFreeModule is by design not to be competitive in terms of speed. But I am sure that other people will disagree with me on that point. I would recommend to find an appropriate Cython base class for your elements. You'd sub-class it (in Cython, if you care for speed), by providing _mul_ and _lmul_ for the elements. The parent (i.e., ring) can very well be implemented in Python, as typically speed matters less for the ring than for its elements. I could actually imagine to use CombinatorielFreeModule to implement the ring, but without relying on product_on_basis, and use a Cython class for the elements. And please do use the category and coercion framework! You may want to read this thematic tutorial: http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html In a second moment I would like to be able to evaluate the element of this ring at point on the group; is there a way to make them callable? There is no default implementation for the __call__() method of ring elements. So, I guess you can just provide it. It's the usual cython way of making something callable. Best regards, Simon -- You received
Re: [sage-devel] Re: Implementing rings of coordinates
Hi Simon, thank you for the explanation. As you guessed I do not need ideals nor Gröbner basis. Forget for the moment the matter of infinitely many generators: what I would like to implement is a polynomial ring whose variables are certain functions. One possible way to do this would be to wrap around multivariate polynomials with a class that keeps a dictionary in between the actual dummy variables in the ring and the functions I would like as generators. I would then perform substitutions every time that's needed. My impression though is that this will get soon very messy. Going the CombinatorialFreeModule route sounds like a good option (speed is not a concern at the moment) but I am not sure if there is any facility already in place to build a monomial basis out of some generators. Thanks again Salvatore * Simon King [2018-11-21 12:03:24]: Dear S., On 2018-11-20, VulK wrote: I am trying to implement the ring of coordinates of a Lie group in the perspective of Peter-Weyl theorem. Concretely I would like to define a polynomial ring with infinitely many generators each depending on two points on a lattice. These generators satisfy many relations but, for the moment, I am happy to forget this fact. Is this possible in the current sage framework? Which are the classes I should inherit from? From a quick look at available classes it looks like InfinitePolynomialRing and InfinitePolynomial might be the one I am after but I do not see how to change the indexing sets as I need apart from brute force: I could keep a dictionary and hack _repr_ accordingly. Any better idea? I guess as the author of InfinitePolynomial*, I should chime in. Unfortunately I don't know the background of what you want to achieve. In particular, I don't know what indexing set you need. Of course, changing _repr_ in a sub-class is not a hack but common usage. Perhaps I should try to explain the purpose of InfinitePolynomial: You have a finite list of symbols and for each symbol you have a family of generators indexed by natural numbers. Together, they generate a free commutative K-algebra R (an "infinite polynomial ring"), where K is a field. Then, the symmetric group S of the natural numbers acts on each family of generators by permuting indices. Any ideal J in R that is (as a set) invariant under the S-action is finitely generated in the sense that there is a finite list of elements g1,...,gn of J such that the union of the S-orbits of g1,...,gn generates J as an R-ideal. Moreover, ideal containment can be effectively tested by some flavour of Gröbner basis theory ("symmetric Gröbner bases"). The purpose of my implementation is to compute symmetric Gröbner bases and test ideal containment. Is any of that useful for your application? Or do you just need an algebra with an indexed family of generators? Then, I suppose it is possible to implement it using the stuff in sage.sets.family, together with sage.combinat.free_module.CombinatorialFreeModule Inspite of its name, CombinatorialFreeModule can be used to implement an algebra. Beware, however, that it is all a very *general* implementation in *Python* (not Cython) and (I think) quite convoluted and indirect [e.g., apparently one is supposed to implement multiplication of elements not by providing _mul_ for the elements but by providing a method product_on_basis for the ring, which is then used in a multiplication method (again not of the elements but of the ring) that is provided by the category of AlgebrasWithBasis that is then finally used in a multiplication method for elements that (if I recall correctly) also is implemented in Python and is inherited from the category framework]. So, my impression has been that CombinatorialFreeModule is by design not to be competitive in terms of speed. But I am sure that other people will disagree with me on that point. I would recommend to find an appropriate Cython base class for your elements. You'd sub-class it (in Cython, if you care for speed), by providing _mul_ and _lmul_ for the elements. The parent (i.e., ring) can very well be implemented in Python, as typically speed matters less for the ring than for its elements. I could actually imagine to use CombinatorielFreeModule to implement the ring, but without relying on product_on_basis, and use a Cython class for the elements. And please do use the category and coercion framework! You may want to read this thematic tutorial: http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html In a second moment I would like to be able to evaluate the element of this ring at point on the group; is there a way to make them callable? There is no default implementation for the __call__() method of ring elements. So, I guess you can just provide it. It's the usual cython way of making something callable. Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from