[sage-devel] Re: Exterior algebras.
Exterior algebras were included as part of http://trac.sagemath.org/ticket/15300 (which was merged into Sage 6.4). sage: E.x,y = ExteriorAlgebra(QQ) sage: a = x * y + x - 3*y / 2; a x^y + x - 3/2*y sage: a.interior_product(x) y + 1 sage: a.interior_product(y) -x - 3/2 Great. Any other Grassmann stuff beyond this? (E.g. regressive product.) Is this interface with similar functionality in Singular or elsewhere (and/or the differential forms/manifolds folks)? -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Exterior algebras.
Great. Any other Grassmann stuff beyond this? (E.g. regressive product.) Is this interface with similar functionality in Singular or elsewhere (and/or the differential forms/manifolds folks)? I didn't implement anything like that as I wanted to do the relationship with Lie algebras (the boundary/coboundary methods, which might deserve some alias...). There are likely many improvements and extensions that can be made to this implementation. Best, Travis -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Exterior algebras.
On Tue, Apr 7, 2015 at 9:12 AM, kcrisman kcris...@gmail.com wrote: Sorry for dredging this up from the depths... So I see that http://trac.sagemath.org/ticket/14418 has a more explicit interface. What gets me wondering about the current state in Sage is an article in the most recent Notices which contains a reference to https://sites.google.com/site/grassmannalgebra/thegrassmannalgebrabook which has a fairly fully-featured (apparently) computational set of Mma extensions for all sorts of Grassmann algebra types - including the internal product and regressive product. Just putting this out there in case anyone knows anything about it - or even the author, in the event that it were possible to just port things to Sage. Sympy (in Sage) as a lot of this stuff: http://docs.sympy.org/0.7.4/modules/galgebra/GA.html -- 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 http://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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Exterior algebras.
Sorry for dredging this up from the depths... So I see that http://trac.sagemath.org/ticket/14418 has a more explicit interface. What gets me wondering about the current state in Sage is an article in the most recent Notices which contains a reference to https://sites.google.com/site/grassmannalgebra/thegrassmannalgebrabook which has a fairly fully-featured (apparently) computational set of Mma extensions for all sorts of Grassmann algebra types - including the internal product and regressive product. Just putting this out there in case anyone knows anything about it - or even the author, in the event that it were possible to just port things to Sage. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Exterior algebras.
Exterior algebras were included as part of http://trac.sagemath.org/ticket/15300 (which was merged into Sage 6.4). sage: E.x,y = ExteriorAlgebra(QQ) sage: a = x * y + x - 3*y / 2; a x^y + x - 3/2*y sage: a.interior_product(x) y + 1 sage: a.interior_product(y) -x - 3/2 Best, Travis -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Exterior algebras.
Ok, i have seen how to define them in singular properly. Something like this: ring r=0,(x,y,z),lp; def a=nc_algebra(-1,0); setring a; ideal i=x2,y2z2; i=std(i); qring e=i; setring e; creates an exterior algebra. The command Exterior() from the package nctools.lib does essentially the same. I think the best way to implement this in sage would be to build a class that wraps this singular cosntruction in the same way that PolynomialRing wraps the singular rings. Any suggesttion in that sense? -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
Re: [sage-devel] Re: Exterior algebras.
Hi! For the simple case of exterior algebras there exists already ring creation code in the track ticket. It might be a little bit hacky, but it works for now. What is mainly needed, is cleaning the construction for Sage class hierarchies and coercions. Cheers, Michael Am 25.03.2010 um 10:10 schrieb mmarco: Ok, i have seen how to define them in singular properly. Something like this: ring r=0,(x,y,z),lp; def a=nc_algebra(-1,0); setring a; ideal i=x2,y2z2; i=std(i); qring e=i; setring e; creates an exterior algebra. The command Exterior() from the package nctools.lib does essentially the same. I think the best way to implement this in sage would be to build a class that wraps this singular cosntruction in the same way that PolynomialRing wraps the singular rings. Any suggesttion in that sense? -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
Singular includes all necessary stuff, see #4539. Cheers, Michael On 24 Mrz., 00:31, javier vengor...@gmail.com wrote: Somebody wrote [1] a Reduce (cf. [2]) interface some time ago. If it works properly one could try to load Bergmann [3] from it. That would give access to plenty of Groebner basis, Hilbert series, Hochschild cohomology and many other ring theoretical methods for big families of noncommutative algebras. Since Bergmann is written in Lisp, maybe it can also be loaded directly from ECL. I don't have any clue how complicated interfacing Bergmann could get, though, but if we don't have many noncommutative algebra stuff, it might be worth giving it a shot. Cheers J [1]http://groups.google.com/group/sage-devel/browse_thread/thread/87e888... [1]http://www.reduce-algebra.com/ [2]http://servus.math.su.se/bergman/ On Mar 23, 4:34 pm, mmarco mma...@unizar.es wrote: Thanks for the code. From what i see, it does not inherit ideals or groebner basis. I will try to take a look at that. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
Thanks for the code. From what i see, it does not inherit ideals or groebner basis. I will try to take a look at that. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
Somebody wrote [1] a Reduce (cf. [2]) interface some time ago. If it works properly one could try to load Bergmann [3] from it. That would give access to plenty of Groebner basis, Hilbert series, Hochschild cohomology and many other ring theoretical methods for big families of noncommutative algebras. Since Bergmann is written in Lisp, maybe it can also be loaded directly from ECL. I don't have any clue how complicated interfacing Bergmann could get, though, but if we don't have many noncommutative algebra stuff, it might be worth giving it a shot. Cheers J [1] http://groups.google.com/group/sage-devel/browse_thread/thread/87e88893228aed59/a71d7372949fbfe2?lnk=gstq=reduce#a71d7372949fbfe2 [1] http://www.reduce-algebra.com/ [2] http://servus.math.su.se/bergman/ On Mar 23, 4:34 pm, mmarco mma...@unizar.es wrote: Thanks for the code. From what i see, it does not inherit ideals or groebner basis. I will try to take a look at that. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
(suggestions, or better patches, to improve that example are welcome) Earlier I posted code to construct exterior algebras in Sage here: http://sporadic.stanford.edu/bump/exterior.sage This uses CombinatorialAlgebras. Currently the preferred method of constructing a ring is to implement it as a subclass of CombinatorialFreeModule using convenient hooks that are provided there. I reimplemented the exterior algebra that way and for comparison, here it is: http://sporadic.stanford.edu/bump/exterior1.sage Both methods are about the same number of lines of code, but the second method is cleaner and easier if you know how to do it. I think both rings have identical behavior. I would like to comment on the deprecation warnings in combinatorial_algebra.py. The method of constructing a ring in combinatorial_algebra.py is quick and convenient. I do agree that the preferred method is better. I think that any construation that is to be put into sage should not use CombinatorialAlgebras. However I think the deprecation warning (just deprecated - don't use!) in combinatorial_algebras.py is not helpful. After all, the old method does work and is convenient and quick. If I want a quick and dirty ring for some experiment I might use it. There is the deprecation warning but no pointer towards a better way. Dan -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
Re: [sage-devel] Re: Exterior algebras.
On Fri, Mar 19, 2010 at 01:00:38PM -0700, bump wrote: I hope other people respond, too. I would suggest looking at http://www.sagemath.org/doc/reference/coercion.html and the code in sage/algebras/quatalg (for quaternion algebras): use this as one model for how to implement a noncommutative algebra. Another place to look is algebras/iwahori_hecke_algebra.py, showing how to an algebra as a subclass of CombinatorialFreeModule. Yup. And the canonical example to look at shall be: sage: A = AlgebrasWithBasis(QQ).example() sage: A?? (suggestions, or better patches, to improve that example are welcome) Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
I hope other people respond, too. I would suggest looking at http://www.sagemath.org/doc/reference/coercion.html and the code in sage/algebras/quatalg (for quaternion algebras): use this as one model for how to implement a noncommutative algebra. Another place to look is algebras/iwahori_hecke_algebra.py, showing how to an algebra as a subclass of CombinatorialFreeModule. Dan -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
Re: [sage-devel] Re: Exterior algebras.
On Fri, Mar 19, 2010 at 1:00 PM, bump b...@match.stanford.edu wrote: I hope other people respond, too. I would suggest looking at http://www.sagemath.org/doc/reference/coercion.html and the code in sage/algebras/quatalg (for quaternion algebras): use this as one model for how to implement a noncommutative algebra. Another place to look is algebras/iwahori_hecke_algebra.py, showing how to an algebra as a subclass of CombinatorialFreeModule. There's also some code up at http://trac.sagemath.org/sage_trac/ticket/4539 which has some code for exterior algebras provided by Singular. --Mike -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
[sage-devel] Re: Exterior algebras.
On Mar 19, 10:46 am, mmarco wrote: I would need to deal with exterior algebras, and as far as i have seen, they are not defined in sage. I could try working on implementing them, but i have no idea how to build the corresponding class in sage. What should be the appropiate aproach? Is there some documentation about how to build new ring classes?. Here is an implementation of exterior algebras in sage: http://sporadic.stanford.edu/bump/exterior.sage This uses combinatorial_algebra.py. That has a deprecation warning (do not use). I think that means that you should not use it for code that is going into Sage itself, but it sure is handy to be able to implement a ring in just a few lines. The exterior algebra on [0, 1, 2, 3] After attaching the file, you can do this: sage: E = ExteriorAlgebra(4); E sage: [x0, x1, x2, x3] = E.generators() sage: x0*x1 x0*x1 sage: x1*x0 -x0*x1 sage: (x0+x1*x2+x3)*x0 -x0*x3 + x0*x1*x2 Daniel Bump -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-devel+unsubscribegooglegroups.com or reply to this email with the words REMOVE ME as the subject.
