[sage-devel] trouble running n() on matrices
Hello all, I'm running into problems with coercing to complexes or reals in matrices: sage: d = matrix([[3, 0],[0,sqrt(2)]]) sage: b = matrix([[1, -1], [2, 2]]) sage: e = b * d * b.inverse(); e [1/sqrt(2) + 3/2 3/4 - 1/(2*sqrt(2))] [3 - sqrt(2) 1/sqrt(2) + 3/2] and when I try to run n() on the matrix e, I get: sage: e.n() # or n(e) [snip] type 'exceptions.TypeError': unable to coerce to a ComplexNumber but I can run n() on all the entries of e: sage: n(e[0,0]) 2.20710678118655 sage: n(e[1,0]) 1.58578643762690 sage: n(e[1,1]) 2.20710678118655 sage: n(e[0,1]) 0.396446609406726 Also, I can't run .n() on the matrix b, even though it's an integer matrix! sage: parent(b) Full MatrixSpace of 2 by 2 dense matrices over Integer Ring sage: b.n() [same as before] type 'exceptions.TypeError': unable to coerce to a ComplexNumber Yikes! It can't coerce integers into complexes! But in other situations, there's no trouble: sage: n(5) 5.00 sage: parent(sqrt(2)) Symbolic Ring sage: n(sqrt(2)) 1.41421356237310 It seems clear that when I have a matrix with expressions like 1/sqrt(2) + 3/2 and I run n() on it, I want the obvious floating point approximations. Am I going about this wrong? Is this not a correct use of matrices? Or is it a coercion bug? Any help is much appreciated. Dan -- --- Dan Drake [EMAIL PROTECTED] - KAIST Department of Mathematical Sciences --- http://math.kaist.ac.kr/~drake signature.asc Description: Digital signature
[sage-devel] Re: class variables in cython classes
Dear Jason, On Apr 7, 7:34 pm, Jason Grout [EMAIL PROTECTED] wrote: Thanks for the explanation. The issue came up when I wanted to just do M=self.transpose() or M=self, depending on if the user wanted right or left action computations (e.g., right vs. left kernels). However, then calls to M._nrows (which used to be calls to self._nrows) don't work. What about cdefining M? If self is of type FooType, then the following should work cdef FooType M M=self # or M=self.transpose() depending on what the user wants and if FooType has a cython attribute _nrows then M._nrows should work. However i am not sure if this is possible in your situation, because as much as i understand there are many matrix types. So, i don't know what FooType should be here. Cheers Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Google funds Sage
This is great news! My opinion of google was good before but this really improves it. Thanks very much for putting this together. It will be very useful for coding theory. On Tue, Apr 8, 2008 at 9:05 AM, William Stein [EMAIL PROTECTED] wrote: Hi, I posted the following on my blog, but am reposting this is an email to sage-devel, since it's important for Sage developers to know about. Today Chris DiBona (open source programs manager at Google) fully funded a proposal [1] that some students and I put together to carry out four Sage development projects this summer (2008): * Mike Hansen (UCSD): Implement combinatorial species in Sage. This will provide a backend to handle a wide range of new combinatorial objects with minimal effort. * Gary Furnish (Utah): Implement new optimized symbolic manipulation code in Cython. This will greatly speed up symbolic computation in Sage, and reduce Sage's dependence on Maxima. * Robert Miller (UW): Implement fast code for permutation groups and backtracking algorithms. This is needed for general applications to graph and code automorphism groups computations, and can be used to exhaustively generate isomorphism class representatives of a wide class of mathematical objects. * Yi Qiang (UW): Further document, improve the usability of, and provide numerous real world examples of distributed computing with Sage. This will greatly help in applications of Sage to research that involve parallel computation. This funding is not part of the Google Summer of Code (the projects above do not fit with any of the mentoring organizations), but is instead I hope part of more longterm support by Google for the Sage project. [1] http://wstein.org/grants/google08/google.pdf -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Google funds Sage
Hi, I posted the following on my blog, but am reposting this is an email to sage-devel, since it's important for Sage developers to know about. Today Chris DiBona (open source programs manager at Google) fully funded a proposal [1] that some students and I put together to carry out four Sage development projects this summer (2008): * Mike Hansen (UCSD): Implement combinatorial species in Sage. This will provide a backend to handle a wide range of new combinatorial objects with minimal effort. * Gary Furnish (Utah): Implement new optimized symbolic manipulation code in Cython. This will greatly speed up symbolic computation in Sage, and reduce Sage's dependence on Maxima. * Robert Miller (UW): Implement fast code for permutation groups and backtracking algorithms. This is needed for general applications to graph and code automorphism groups computations, and can be used to exhaustively generate isomorphism class representatives of a wide class of mathematical objects. * Yi Qiang (UW): Further document, improve the usability of, and provide numerous real world examples of distributed computing with Sage. This will greatly help in applications of Sage to research that involve parallel computation. This funding is not part of the Google Summer of Code (the projects above do not fit with any of the mentoring organizations), but is instead I hope part of more longterm support by Google for the Sage project. [1] http://wstein.org/grants/google08/google.pdf -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: multivariate factoring - use maxima ?
Just because an algorithm is probabilistic doesn't mean it necessarily gives wrong answers. By the way, see http://www-fourier.ujf-grenoble.fr/~parisse/publi/gcdheu.pdf which is I think a paper that proves correctness of the algorithm we're talking about. (I've not carefully read the above short paper, so I'm not vouching for it though.) More precisely it fills a little gap in the original proof of the correctness of the gcdheu algorithm for multivariate polynomials, and extends the coefficients from Z to Z[i]. Gcdheu is just one of about 4 main algorithms for GCD: ezgcd, modular (with a sparse variant), gcdheu, subresultant. Giac implements all of them, gcdheu being used for small problems. I have just created a benchmark page with Fermat tests: http://www-fourier.ujf-grenoble.fr/~parisse/giac.html follow the benchmark link. It seems giac is faster than maxima (around 5 to 10 times on these tests), I do not have access to magma which is most probably another factor of 10 * faster. Sage may of course decide to implement it's own algorithms, but as Roman Pearce said, it is a large piece of code to write and moreover test. Why not integrate giac and help me improve giac code instead? There are more interesting piece of codes to write, e.g. bivariate factorization (which would improve giac multivariate factorization), or absolute factorization over C. And once there is a link between sage and giac, sage could benefit from all the calculus code of giac (series, integration, etc.) which I believe is not the main interest of Sage developers. I would of course contribute to such a link, but I do not have time to do all the work myself. B. Parisse --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: multivariate factoring - use maxima ?
Just because an algorithm is probabilistic doesn't mean it necessarily gives wrong answers. By the way, see http://www-fourier.ujf-grenoble.fr/~parisse/publi/gcdheu.pdf which is I think a paper that proves correctness of the algorithm we're talking about. (I've not carefully read the above short paper, so I'm not vouching for it though.) More precisely it fills a little gap in the proof of correctness for multivariate polynomials and extends the coefficients from Z to Z[i]. Gcdheu is one of about 4 main algorithms (ezgcd, gcdheu, modular with sparse and dense variants, subresultant), all implemented in Giac. http://www-fourier.ujf-grenoble.fr/~parisse/giac.html I have added a benchmark link with Fermat gcd tests, giac seems 5 to 10 * faster than maxima. I don't have magma, it is most probably another factor of 10 * faster. Sage developers may of course decide to write their own gcd algorithms, but that's a large piece of code to write and test. Why not make a link to giac (which is a C++ library) instead? Sage and giac could then benefit from improvements and more interesting piece of code could be written, like bivariate factorization (which would improve giac multivariate factorization) or absolute factorization over C. Moreover, sage could benefit from the calculus code of giac (series, integration, etc.). I would be ready to contribute to write such a link, but I would need help on the sage side, I don't know python at all. B. Parisse --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Google funds Sage
Perhaps one day I will learn to spell congratulations. On Apr 8, 11:58 am, Chris Chiasson [EMAIL PROTECTED] wrote: That is really positive and impressive, on both the parts of Google Sage (and the people behind them). Congratualtions. On Apr 8, 8:05 am, William Stein [EMAIL PROTECTED] wrote: Hi, I posted the following on my blog, but am reposting this is an email to sage-devel, since it's important for Sage developers to know about. Today Chris DiBona (open source programs manager at Google) fully funded a proposal [1] that some students and I put together to carry out four Sage development projects this summer (2008): * Mike Hansen (UCSD): Implement combinatorial species in Sage. This will provide a backend to handle a wide range of new combinatorial objects with minimal effort. * Gary Furnish (Utah): Implement new optimized symbolic manipulation code in Cython. This will greatly speed up symbolic computation in Sage, and reduce Sage's dependence on Maxima. * Robert Miller (UW): Implement fast code for permutation groups and backtracking algorithms. This is needed for general applications to graph and code automorphism groups computations, and can be used to exhaustively generate isomorphism class representatives of a wide class of mathematical objects. * Yi Qiang (UW): Further document, improve the usability of, and provide numerous real world examples of distributed computing with Sage. This will greatly help in applications of Sage to research that involve parallel computation. This funding is not part of the Google Summer of Code (the projects above do not fit with any of the mentoring organizations), but is instead I hope part of more longterm support by Google for the Sage project. [1]http://wstein.org/grants/google08/google.pdf -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: trouble running n() on matrices
If you take a look at the source code for n(), you'll see that the first thing that it does is to try calling numerical_approx(prec) on the object, and then tries coercing to real or complex fields. So the solution is to write a method numerical_approx(prec) in the matrix base class that tries to numerically approximate the entries and make a new matrix out of them. This is now ticket 2857. David On Tue, Apr 8, 2008 at 2:32 AM, Dan Drake [EMAIL PROTECTED] wrote: Hello all, I'm running into problems with coercing to complexes or reals in matrices: sage: d = matrix([[3, 0],[0,sqrt(2)]]) sage: b = matrix([[1, -1], [2, 2]]) sage: e = b * d * b.inverse(); e [1/sqrt(2) + 3/2 3/4 - 1/(2*sqrt(2))] [3 - sqrt(2) 1/sqrt(2) + 3/2] and when I try to run n() on the matrix e, I get: sage: e.n() # or n(e) [snip] type 'exceptions.TypeError': unable to coerce to a ComplexNumber but I can run n() on all the entries of e: sage: n(e[0,0]) 2.20710678118655 sage: n(e[1,0]) 1.58578643762690 sage: n(e[1,1]) 2.20710678118655 sage: n(e[0,1]) 0.396446609406726 Also, I can't run .n() on the matrix b, even though it's an integer matrix! sage: parent(b) Full MatrixSpace of 2 by 2 dense matrices over Integer Ring sage: b.n() [same as before] type 'exceptions.TypeError': unable to coerce to a ComplexNumber Yikes! It can't coerce integers into complexes! But in other situations, there's no trouble: sage: n(5) 5.00 sage: parent(sqrt(2)) Symbolic Ring sage: n(sqrt(2)) 1.41421356237310 It seems clear that when I have a matrix with expressions like 1/sqrt(2) + 3/2 and I run n() on it, I want the obvious floating point approximations. Am I going about this wrong? Is this not a correct use of matrices? Or is it a coercion bug? Any help is much appreciated. Dan -- --- Dan Drake [EMAIL PROTECTED] - KAIST Department of Mathematical Sciences --- http://math.kaist.ac.kr/~drake -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.6 (GNU/Linux) iD8DBQFH+xGBr4V8SljC5LoRAmTfAJ9+otZSqPbrD3UjUYsnu6eB5I7rRQCeOnWl g/ob45B+hjZ6mNjKC0a1T9I= =tjOf -END PGP SIGNATURE- --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: trouble running n() on matrices
On 8-Apr-08, at 10:50 AM, David Roe wrote: If you take a look at the source code for n(), you'll see that the first thing that it does is to try calling numerical_approx(prec) on the object, and then tries coercing to real or complex fields. So the solution is to write a method numerical_approx(prec) in the matrix base class that tries to numerically approximate the entries and make a new matrix out of them. Could this be a bit more general? There are other things one wants to do that are similar, such as matrix.real() and matrix.imag(), or matrix.abs() for real, imaginary, and absolute values of the entries respectively. It sounds like we want a map operator for a lot of datatypes. Nick --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: multivariate factoring - use maxima ?
I have added a benchmark link with Fermat gcd tests, giac seems 5 to 10 * faster than maxima. I don't have magma, it is most probably another factor of 10 * faster. I think that comparison with Magma is a little optimistic, especially in the modular case. http://www-fourier.ujf-grenoble.fr/~parisse/giac/benchmarks/gcd_timings http://magma.maths.usyd.edu.au/users/allan/gcdcomp.html --Mike --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] fractional ideals
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Hi folks, On Sunday we had an interesting discussion on #sage-devel about the current implementation of fractional ideals in Sage. This was spurred mainly by #821, but went beyond the issues in that ticket. I am going to try to summarize the main points of the discussion, first so that we have a record of it, and also so it can continue and we can see what we can/should do about it. 1. At the moment, NumberFieldFractionalIdeal inherits from Ideal_generic, which David Harvey pointed out is *very bad*, since fractional ideals are *not ideals*. Yes, the terminology is confusing, but we don't have the luxury of convincing Kummer or whoever came up with it that it should be changed. 2. Another sketchy thing is that for a number field K, the method ideal() overrides the ring ideal method and returns 0 or a fractional ideal. Even if the objection from point 1 did not exist, this behavior is bad, because if I want to write a function that deals with ideals in rings, I would have to do something special if my ring is a number field (since ideal() does not have a consistent behavior). Here is, as far as I remember, what the irc discussion identified as preferred behavior: (a) For any ring R, R.ideal([list of elements of R]) should return the ideal of R which is generated by the elements in the list. This should in particular happen for a number field, i.e. if K is a number field then K.ideal([list of elements of K]) should return either the Principal ideal generated by 0 or the Principal ideal generated by 1. (b) mathematically speaking, a fractional ideal is a rank one projective module over a Dedekind domain R; equivalently, it is a nonzero finitely-generated R-submodule of the fraction field K=Frac(R). This latter description might be more amenable to computation. I don't think we have Dedekind domains in Sage, so maybe we can just have this work in the main area of application (algebraic number theory), by having fractional ideals in number fields. So if O is an order in a number field K, we would like O.fractional_ideal([list of elements of K]) to return the fractional ideal of O generated by the elements in the list. ~ For convenience, we might also want K.fractional_ideal([list of elements of K]) to be an alias for OK.fractional_ideal([list of elements of K]), where OK is the ring of integers of K. Just getting all of this straightened out for rings of integers would already be a serious but very worthwhile endeavor. Whoever was around #sage-devel when this was going on, please correct anything that I might have misrepresented. Everybody else, please comment! Best, Alex - -- Alexandru Ghitza Assistant Professor Department of Mathematics Colby College Waterville, ME 04901 http://bayes.colby.edu/~ghitza/ -BEGIN PGP SIGNATURE- Version: GnuPG v2.0.7 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFH+9U1dZTaNFFPILgRAhUfAJ0X846IOwIezS9TyJcunyWgQJ6shwCgmgCW KOsZVf/0ojPDm61RsYalwko= =611u -END PGP SIGNATURE- --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: fractional ideals
This all sounds very sensible to me. It is a convention in number theory to talk of an ideal of the number field K when one actually means nonzero ideal of the rings of integers of K. I gained several grey hairs messing with this back in January, being forced to do so for the patches for #1946 (which started out just fixing some bugs and adding doctests for elliptic curves over number fields). It was a major achievement (for me, then) to get it into a state which is mainly consistent and also correct. I could like with ideal being changed to fractional ideal for number fields, thus releasing ideal for use in the literal mathematical sense. Even though I doubt if anyone would actually ever want to create either of the two ideals in a field! And the documentation would have to make it very clear that Sage was not following the near-universal abuse of language. Good luck... John On 08/04/2008, Alex Ghitza [EMAIL PROTECTED] wrote: -BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Hi folks, On Sunday we had an interesting discussion on #sage-devel about the current implementation of fractional ideals in Sage. This was spurred mainly by #821, but went beyond the issues in that ticket. I am going to try to summarize the main points of the discussion, first so that we have a record of it, and also so it can continue and we can see what we can/should do about it. 1. At the moment, NumberFieldFractionalIdeal inherits from Ideal_generic, which David Harvey pointed out is *very bad*, since fractional ideals are *not ideals*. Yes, the terminology is confusing, but we don't have the luxury of convincing Kummer or whoever came up with it that it should be changed. 2. Another sketchy thing is that for a number field K, the method ideal() overrides the ring ideal method and returns 0 or a fractional ideal. Even if the objection from point 1 did not exist, this behavior is bad, because if I want to write a function that deals with ideals in rings, I would have to do something special if my ring is a number field (since ideal() does not have a consistent behavior). Here is, as far as I remember, what the irc discussion identified as preferred behavior: (a) For any ring R, R.ideal([list of elements of R]) should return the ideal of R which is generated by the elements in the list. This should in particular happen for a number field, i.e. if K is a number field then K.ideal([list of elements of K]) should return either the Principal ideal generated by 0 or the Principal ideal generated by 1. (b) mathematically speaking, a fractional ideal is a rank one projective module over a Dedekind domain R; equivalently, it is a nonzero finitely-generated R-submodule of the fraction field K=Frac(R). This latter description might be more amenable to computation. I don't think we have Dedekind domains in Sage, so maybe we can just have this work in the main area of application (algebraic number theory), by having fractional ideals in number fields. So if O is an order in a number field K, we would like O.fractional_ideal([list of elements of K]) to return the fractional ideal of O generated by the elements in the list. ~ For convenience, we might also want K.fractional_ideal([list of elements of K]) to be an alias for OK.fractional_ideal([list of elements of K]), where OK is the ring of integers of K. Just getting all of this straightened out for rings of integers would already be a serious but very worthwhile endeavor. Whoever was around #sage-devel when this was going on, please correct anything that I might have misrepresented. Everybody else, please comment! Best, Alex - -- Alexandru Ghitza Assistant Professor Department of Mathematics Colby College Waterville, ME 04901 http://bayes.colby.edu/~ghitza/ -BEGIN PGP SIGNATURE- Version: GnuPG v2.0.7 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFH+9U1dZTaNFFPILgRAhUfAJ0X846IOwIezS9TyJcunyWgQJ6shwCgmgCW KOsZVf/0ojPDm61RsYalwko= =611u -END PGP SIGNATURE- --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: multivariate factoring - use maxima ?
On Tuesday 08 April 2008 03:25:40 pm Mike Hansen wrote: Today 03:25:40 pm I have added a benchmark link with Fermat gcd tests, giac seems 5 to 10 * faster than maxima. I don't have magma, it is most probably another factor of 10 * faster. I think that comparison with Magma is a little optimistic, especially in the modular case. http://www-fourier.ujf-grenoble.fr/~parisse/giac/benchmarks/gcd_timings http://magma.maths.usyd.edu.au/users/allan/gcdcomp.html Now, it's true that we don't want to re-invent the wheel. However, it seems to me that there aren't any opensource packages that manage the range of base rings that we'd want sage to handle for multivariate polynomial rings. Singular is probably the closest, but ZZ is only experimental. So, while I may be reinventing the wheel for mpoly factoring over ZZ (although it appears somewhat feasible that the wheel will be re-invented better), it has already had a number of positive changes in the generic multivariate polydict polynomial implementation in sage. I think the generic-ness of the code is something worth pushing forward and seeing how fast we could be with a generic base ring. I (and Martin, too) am interested in this generic approach. Indeed, even the factoring algorithm has a large prefix (square-free decomposition and the like) which is largely independent of the base-ring. So, my bottom line is this, there might be special purpose implementations for specific base-rings, but I don't think that is reason to abandon pushing our own implementation because I think our implementation can handle base rings that nobody else can. Of course, it is likely that this generic-ness will cost us some speed. But, it is not obvious to me that that cost is necessarily prohibitive. -- Joel --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: fractional ideals
On Apr 8, 2008, at 4:27 PM, Alex Ghitza wrote: Hi folks, On Sunday we had an interesting discussion on #sage-devel about the current implementation of fractional ideals in Sage. This was spurred mainly by #821, but went beyond the issues in that ticket. I am going to try to summarize the main points of the discussion, first so that we have a record of it, and also so it can continue and we can see what we can/should do about it. 1. At the moment, NumberFieldFractionalIdeal inherits from Ideal_generic, which David Harvey pointed out is *very bad*, since fractional ideals are *not ideals*. Yes, the terminology is confusing, but we don't have the luxury of convincing Kummer or whoever came up with it that it should be changed. 2. Another sketchy thing is that for a number field K, the method ideal() overrides the ring ideal method and returns 0 or a fractional ideal. Even if the objection from point 1 did not exist, this behavior is bad, because if I want to write a function that deals with ideals in rings, I would have to do something special if my ring is a number field (since ideal() does not have a consistent behavior). Here is, as far as I remember, what the irc discussion identified as preferred behavior: (a) For any ring R, R.ideal([list of elements of R]) should return the ideal of R which is generated by the elements in the list. This should in particular happen for a number field, i.e. if K is a number field then K.ideal([list of elements of K]) should return either the Principal ideal generated by 0 or the Principal ideal generated by 1. (b) mathematically speaking, a fractional ideal is a rank one projective module over a Dedekind domain R; equivalently, it is a nonzero finitely-generated R-submodule of the fraction field K=Frac(R). This latter description might be more amenable to computation. I don't think we have Dedekind domains in Sage, so maybe we can just have this work in the main area of application (algebraic number theory), by having fractional ideals in number fields. So if O is an order in a number field K, we would like O.fractional_ideal([list of elements of K]) to return the fractional ideal of O generated by the elements in the list. ~ For convenience, we might also want K.fractional_ideal([list of elements of K]) to be an alias for OK.fractional_ideal([list of elements of K]), where OK is the ring of integers of K. Just getting all of this straightened out for rings of integers would already be a serious but very worthwhile endeavor. Whoever was around #sage-devel when this was going on, please correct anything that I might have misrepresented. Everybody else, please comment! Alex, Strongly support everything you've said here, and thanks for taking the time to write this summary. (I'm slightly concerned about what should happen for non-maximal orders, but I can't quite remember how this is supposed to work mathematically) david --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: fractional ideals
For non-maximal orders, not every ideal is invertible. People would normnally only want to use invertible ideals, I expect. I don't remember all the details either. John On 08/04/2008, David Harvey [EMAIL PROTECTED] wrote: On Apr 8, 2008, at 4:27 PM, Alex Ghitza wrote: Hi folks, On Sunday we had an interesting discussion on #sage-devel about the current implementation of fractional ideals in Sage. This was spurred mainly by #821, but went beyond the issues in that ticket. I am going to try to summarize the main points of the discussion, first so that we have a record of it, and also so it can continue and we can see what we can/should do about it. 1. At the moment, NumberFieldFractionalIdeal inherits from Ideal_generic, which David Harvey pointed out is *very bad*, since fractional ideals are *not ideals*. Yes, the terminology is confusing, but we don't have the luxury of convincing Kummer or whoever came up with it that it should be changed. 2. Another sketchy thing is that for a number field K, the method ideal() overrides the ring ideal method and returns 0 or a fractional ideal. Even if the objection from point 1 did not exist, this behavior is bad, because if I want to write a function that deals with ideals in rings, I would have to do something special if my ring is a number field (since ideal() does not have a consistent behavior). Here is, as far as I remember, what the irc discussion identified as preferred behavior: (a) For any ring R, R.ideal([list of elements of R]) should return the ideal of R which is generated by the elements in the list. This should in particular happen for a number field, i.e. if K is a number field then K.ideal([list of elements of K]) should return either the Principal ideal generated by 0 or the Principal ideal generated by 1. (b) mathematically speaking, a fractional ideal is a rank one projective module over a Dedekind domain R; equivalently, it is a nonzero finitely-generated R-submodule of the fraction field K=Frac(R). This latter description might be more amenable to computation. I don't think we have Dedekind domains in Sage, so maybe we can just have this work in the main area of application (algebraic number theory), by having fractional ideals in number fields. So if O is an order in a number field K, we would like O.fractional_ideal([list of elements of K]) to return the fractional ideal of O generated by the elements in the list. ~ For convenience, we might also want K.fractional_ideal([list of elements of K]) to be an alias for OK.fractional_ideal([list of elements of K]), where OK is the ring of integers of K. Just getting all of this straightened out for rings of integers would already be a serious but very worthwhile endeavor. Whoever was around #sage-devel when this was going on, please correct anything that I might have misrepresented. Everybody else, please comment! Alex, Strongly support everything you've said here, and thanks for taking the time to write this summary. (I'm slightly concerned about what should happen for non-maximal orders, but I can't quite remember how this is supposed to work mathematically) david --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] latest version of doc-main
Hi group, Does anyone know where I can download the latest version of the doc-main tree? I'm referring to the doc-main that is bundled with every release of Sage, including both the stable and alpha releases. AFAIK with each stable release, e.g. sage-2.11, doc-main is usually located at http://www.sagemath.org/doc-main.tar.bz2 And with each alpha release in the sage-3.0 release cycle, I think doc-main comes bundled with that alpha release and can be downloaded from http://sage.math.washington.edu/home/mabshoff/release-cycles-3.0/ However, I only want to get the doc-main tree associated with a particular alpha release, without having to download the whole alpha release tarball itself. The main reason is that the tarball is too big in terms of MB. I've browsed through a number of documentation TeX files at http://www.sagemath.org/hg/doc-main/file but I suspect that those TeX files aren't the latest version in the current release cycle. Regards Minh Van Nguyen --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: latest version of doc-main
On Apr 9, 7:17 am, Minh Nguyen [EMAIL PROTECTED] wrote: Hi group, Hi Minh, Does anyone know where I can download the latest version of the doc-main tree? I'm referring to the doc-main that is bundled with every release of Sage, including both the stable and alpha releases. AFAIK with each stable release, e.g. sage-2.11, doc-main is usually located at http://www.sagemath.org/doc-main.tar.bz2 I generally do not build the documentation in a release cycle until were are getting close to the final release. This is mostly due to sage.math not having all the needed bits in the LaTeX toolchain installed. And with each alpha release in the sage-3.0 release cycle, I think doc-main comes bundled with that alpha release and can be downloaded from http://sage.math.washington.edu/home/mabshoff/release-cycles-3.0/ However, I only want to get the doc-main tree associated with a particular alpha release, without having to download the whole alpha release tarball itself. The main reason is that the tarball is too big in terms of MB. I put releases together in /scratch/mabshoff/release-cycle, but that directory is not exported to the web. The reason not to do builds in $HOME is that all of those files end up being sync to the backup and I see little benefit of all those files getting moved. I've browsed through a number of documentation TeX files at http://www.sagemath.org/hg/doc-main/file but I suspect that those TeX files aren't the latest version in the current release cycle. I can provide you the individual doc-main.tar.bz2 once the LaTeX situation on sage.math has been fixed. Your corrections to the Sage documentation are very much appreciated. Regards Minh Van Nguyen Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
