[sage-support] Re: How do I create a matrix whose elements are functions of the row & column indices?
On Dec 10, 2008, at 4:23 PM, Alasdair wrote: > Thanks - I didn't know (being a COMPLETE newbie) about the "range" > command. Where in the documentation would I find this? - I've had a > bit of a search and couldn't find it. Python both the language that much of Sage is written in, and the user interface to Sage, so I would recommend keeping a Python resource handy for basic stuff like this. For example, http:// docs.python.org/ and http://www.diveintopython.org/ are both pretty good. Note that Sage preparses things a bit to make it a nicer math language, so 2^3 becomes exponentiation (instead of xor) and 1/3 is the rational number 1/3, not 0 or 0.333 as it is in pure Python. - Robert --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Spreading Sage
Hi everyone, i am currently supporting a university class (mostly for future teachers) in germany in elementary number theory. I think the students really like using sage, but we had a rough start getting to install and start using sage on their windows boxes. I think you could greatly improve the number of people using sage, if the install-process on windows were easier. Maybe the VMware company is interested in developing a modified package of their VMwareplayer including sage as a killer app? I imagine after the install of this you just have to klick on a desktop-icon, some banner comes up telling you "powerd by vmware" (so vmware gets credit ;)) and the browser just starts with the sage-gui... Do the offical sage developer like this idea? Will they ask Vmware if thats in a way possible? bye, Benjamin --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Spreading Sage
On Dec 11, 12:30 pm, Benjamin Otto <[EMAIL PROTECTED]> wrote: > I think you could greatly improve the number of people using sage, if the > install-process on windows were easier. Hi, we are aware of that but it's not that easy ;) Instead of vmware, there is also the possiblity (just a test) to run it with andlinux.org: http://picasaweb.google.com/wstein/SageAndLinux Hopefully, some day there will be a .msi package for easy distribution across the network and everything works out of the box ;) h --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Is there a utility to compute the value of the error function of a complex number?
Thanks! On Dec 9, 5:17 pm, Jason Grout <[EMAIL PROTECTED]> wrote: > Doug Bradshaw wrote: > > Okay, here's the story: I wanted to plot a Fourier transform of a > > Gaussian that is truncated (mulitplied by unit stepfunction). Using > > "integral", I got an answer that looked nice, but contained anerror > >functionwith an imaginary argument. Because thaterrorfunction > > couldn't be evaluated, I couldn't plot. So, that brings up the > > question: is there a nice way to evaluate theerrorfunctionof an > > imaginary number (or more generally a complex number) in Sage? > > > sage: erf(1) > > erf(1) > > sage: erf(1).n() > > 0.842700792949715 > > sage: erf(I) > > erf(I) > > sage: erf(I).n() > > --- > > TypeError Traceback (most recent call > > last) > > I'm not sure about the Sage erf, but you could also use the scipy erf: > > sage: import scipy.special > sage: scipy.special.erf(complex(I)) > 1.6504257587975433j > > You could also do scipy.special. (press tab) to see the other > variants of erf that scipy has. > > Note that you need to do complex(I) or the equivalent, since scipy does > not understand Sage complex numbers. > > Seehttp://docs.scipy.org/doc/scipy/reference/special.html#error-function... > > Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] python 3.0 (py3k or python 3000 too)
What are our plans for py3k? I ask because there are some youth education efforts moving to 3.0 so that the kids don't get introduced to "legacy" concepts! Here's one: http://www.briggs.net.nz/log/writing/snake-wrangling-for-kids/ Thanks, -- Owen --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: python 3.0 (py3k or python 3000 too)
On Dec 11, 10:10 am, Owen <[EMAIL PROTECTED]> wrote: Hi Owen, > What are our plans for py3k? This has been discussed twice in the last couple weeks, so the answer is "wait and see". We will first upgrade to Python 2.6 once numpy supports it (roughly January 2009 unless something goes wrong) and then sooner or later go to 3.0. But to do that there need to be clear benefits and I would expect that to easily take us six months or more to switch. This will also likely depend on numpy working with python 3.0. > I ask because there are some youth education efforts moving to 3.0 so > that the kids don't get introduced to "legacy" concepts! Here's one: > http://www.briggs.net.nz/log/writing/snake-wrangling-for-kids/ > > Thanks, > -- Owen Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Adjoint of matrix over a ring?
Suppose I create a matrix over the ring of integers mod 10: M=random_matrix(IntegerModRing(10),3,3) Now the adjoint certainly exists, but M.adjoint() isn't as yet implemented over general rings - only over ZZ or QQ. How can I use, say, Maxima or Pari within Sage to compute the adjoint of M? Thanks, Alasdair --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Adjoint of matrix over a ring?
On Thu, Dec 11, 2008 at 2:52 PM, Alasdair wrote: > > Suppose I create a matrix over the ring of integers mod 10: > > M=random_matrix(IntegerModRing(10),3,3) > > Now the adjoint certainly exists, but M.adjoint() isn't as yet > implemented over general rings - only over ZZ or QQ. How can I use, > say, Maxima or Pari within Sage to compute the adjoint of M? You can do it as illustrated below. However, note that for a random input matrix it does not work in PARI (as you seem to think it should), as illustrated below: sage: M=random_matrix(IntegerModRing(10),3,3) sage: b = pari(M) sage: b.matadjoint() --- PariError Traceback (most recent call last) CODE: sage[2]=matadjoint(sage[1]); GP/PARI ERROR: *** matadjoint: impossible inverse modulo: Mod(8, 10). --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Adjoint of matrix over a ring?
> M=random_matrix(IntegerModRing(10),3,3) > > Now the adjoint certainly exists, but M.adjoint() isn't as yet > implemented over general rings - only over ZZ or QQ. How can I use, > say, Maxima or Pari within Sage to compute the adjoint of M? > It's pretty friendly to use Pari to do this ... in general, given any sage object a, you can try pari(a) to convert it to Pari. In this example, it works fine (though the pari output isn't the most pleasant to read): sage: M = random_matrix(IntegerModRing(10),3,3) sage: Mp = pari(M) sage: M [4 2 0] [5 4 8] [9 6 2] sage: Mp [Mod(4, 10), Mod(2, 10), Mod(0, 10); Mod(5, 10), Mod(4, 10), Mod(8, 10); Mod(9, 10), Mod(6, 10), Mod(2, 10)] Then you can call Mp.matadjoint() to get the adjoint. However, in this case, Pari fails to find the adjoint: sage: Mp.matadjoint() --- PariError Traceback (most recent call last) /Users/craigcitro/.sage/temp/sharma.local/8072/_Users_craigcitro__sage_init_sage_0.py in () > 1 2 3 4 5 /sage/local/lib/python2.5/site-packages/sage/libs/pari/gen.so in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:38577)() 8048 8049 -> 8050 8051 8052 PariError: impossible inverse modulo: (36) This is actually Pari behaving badly, not sage -- doing the same thing in a GP session gets the same error. Apparently Pari can't find the determinant of non-invertible square matrices of size at least 3x3 (???). I'll try to look at this and submit a bug report soon -- or you could beat me to it. :) In any event, say it worked (so I'll use 2x2 as an example). You *should* be able to just call M.parent()(Mp.matadjoint()), but that currently hits an error. However, the pari object Mp.matadjoint() has a _sage_ method that knows how to convert back to sage. So this works: sage: m = random_matrix(Integers(10),2,2) ; m [0 9] [3 5] sage: mp = pari(m) sage: mp.matadjoint() [Mod(5, 10), Mod(1, 10); Mod(7, 10), Mod(0, 10)] sage: mp.matadjoint()._sage_() [5 1] [7 0] sage: pari(m).matadjoint()._sage_() [5 1] [7 0] As you point out at the beginning, though, we really should have our own native adjoint function. Here's a one-liner: sage: M = random_matrix(Integers(10),3,3) ; M [9 7 5] [2 9 5] [7 8 8] sage: M.parent()([ (-1)^(i+j)*M.matrix_from_rows_and_columns([x for x in range(M.nrows()) if x != i], [y for y in range(M.ncols()) if y != j]).det() for i in range(M.nrows()) for j in range(M.nrows()) ]).transpose() [2 4 0] [9 7 5] [3 7 7] That function is terrible in a lot of ways -- but if you need something right now, it works. :) -cc --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Adjoint of matrix over a ring?
Actually, this seems to work (using Maxima): M=random_matrix(IntegerModRing(10),3,3) MM=maxima(M) MA=matrix(IntegerModRing(10),MM.adjoint()) However, MA refuses to be typeset properly in the notebook - I consistently get LaTeX code, rather than a nicely typeset matrix. It would be nice to have a built in adjoint... Thanks, Alasdair --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Modularity of sage?
I'd like to install Sage on a laptop with not much disk space left on it. Now, I already have Maxima, Axiom, Pari/GP, and Python; is it possible to just install some sort of "core" Sage from source code, and still have the interfaces to the other CAS's? Thanks, Alasdair --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Modularity of sage?
Hi Alasdair: I don't know the answer but I think it would be helpful to describe (a) how much disk space you have, (b) if there is a reason why you cannot delete maxima and python (you will get them with Sage and you can run them using "sage -python" and "sage -maxima"). - David On Thu, Dec 11, 2008 at 8:52 PM, Alasdair wrote: > > I'd like to install Sage on a laptop with not much disk space left on > it. Now, I already have Maxima, Axiom, Pari/GP, and Python; is it > possible to just install some sort of "core" Sage from source code, > and still have the interfaces to the other CAS's? > > Thanks, > Alasdair > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Modularity of sage?
On Thu, Dec 11, 2008 at 5:52 PM, Alasdair wrote: > > I'd like to install Sage on a laptop with not much disk space left on > it. Now, I already have Maxima, Axiom, Pari/GP, and Python; is it > possible to just install some sort of "core" Sage from source code, > and still have the interfaces to the other CAS's? No, unfortunately that isn't possible. William --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Modularity of sage?
In my case, I use some python packages that are not included in Sage. It is very to solve the problem to enhance the python computing over Sage: just create link from system to sage directory, This is possible to reduce disk space a little. And it is possible to upgrade additional packages and Sage partly. I also use such method to extend Maxima since some function needed in my system. Hope this can help. cch --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Modularity of sage?
On Dec 11, 7:41 pm, chu-ching huang wrote: > In my case, I use some python packages that are not included in Sage. > It is very to solve the problem to enhance the python computing over > Sage: just create link from system to sage directory, This is possible > to reduce disk space a little. And it is possible to upgrade > additional packages and Sage partly. I also use such method to extend > Maxima since some function needed in my system. Hope this can help. > > cch Using Sage in a more modular fashion is possible, but you really have to know what you are doing. Many of the components in Sage contain bug fixes from upstream, so using system components will expose you to subtle bugs. The only way to be reasonably sure that things more or less work as expected is to see if your Sage passes "make check", but even that is no guarantee that Sage will "just work". Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
