[sage-support] Re: sage-nauty-directed graphs isomorphism vs. magma -- smth is very wrong
I would not be surprised it it was the finite field arithmetic that is
causing the difference.
On Friday, February 28, 2014 4:18:44 PM UTC-5, Aleksandr Kodess wrote:
As far as I know both sage and magma utilize Brendan McKay's program nauty
in order to check whether two given graphs (directed or undirected) are
isomorphic. As is demonstrated by the following example, sage and magma
greatly differ in the efficiency in which this program is utilized.
# sage code
q = 19
n1 = 7
n2 = 13
F = FiniteField(q, 'xi')
V = [(x,y) for x in F for y in F]
G1 = DiGraph([V, lambda x,y: x[1] + y[1] == x[0]*(y[0]**n1)])
G2 = DiGraph([V, lambda x,y: x[1] + y[1] == x[0]*(y[0]**n2)])
G1.is_isomorphic(G2)
// magma code for the same operation
q := 19;
n1 := 7;
n2 := 13;
F := FiniteField(q);
V := {[x,y] : x,y in F};
G1 := Digraph V|{ [x,y] : x,y in V | x[2] + y[2] eq
((x[1])^1)*((y[1])^n1)};
G2 := Digraph V|{ [x,y] : x,y in V | x[2] + y[2] eq
((x[1])^1)*((y[1])^n2)};
IsIsomorphic(G1,G2);
It takes sage forever to test whether these two directed graphs of order
19^2 are isomorphic (they are in fact not), while it takes magma only a
second. The same problem occurs for other values of q, n1 and n2. The
version of sage I'm running is 5.12, and the version of magma I'm running
is 2.19.10.
Is this a known issue? Is this going to be fixed any time soon?
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[sage-support] Re: SIGABRT in Graph.clique_number() and assertion in cliquer
sage: k4=graphs.CompleteGraph(4) sage: k4.complement().line_graph().complement() complement(): Graph on 0 vertices clique_number() is crashing on the empty graph, On Saturday, December 1, 2012 9:30:27 AM UTC-5, Georgi Guninski wrote: for g in graphs(4): g.complement().line_graph().complement().clique_number() cliquer file graph.c: line 31: assertion failed: (n0) Unhandled SIGABRT: An abort() occurred in Sage. This probably occurred because a *compiled* component of Sage has a bug On sagenb.org don't get any output, don't know how to interpret this. -- You received this message because you are subscribed to the Google Groups sage-support group. 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. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] show3d does not show (on a mac)
I'm running OS 10.6.2 a Mac airbook. I had problems with the binary sage-4.3-osx10.6-intel-64bit-i386-Darwin.dmg, so I downloaded the source and compiled it. I've found that show3d() does not work. After the commands sage: P = graphs.PetersenGraph() sage: P.show3d() I get the sage prompt and no drawing window. -- 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 URL: http://www.sagemath.org
[sage-support] Re: show3d does not show (on a mac)
Under sage-4.2, the command P.show3d() works, giving a jmol drawing. From what a very quick look revealed, the result of P.=show3d? is the same under sage 4.2 and 4.3. I am reporting this chiefly as a data point. Thsnks Chris On Dec 28, 11:33 am, kcrisman kcris...@gmail.com wrote: It seems that this is poor documentation at work. sage: P.show3d(engine='tachyon') works fine, but it isn't obvious from sage: P.show3d? that one has to specify this. Apparently jmol isn't rendering this, at least not on Macs. Someone more knowledgeable about Jmol will hopefully reply with more details, but in the meantime the tachyon plotter should do at least some of what you want. - kcrisman On Dec 28, 10:53 am, Chris Godsil cgod...@uwaterloo.ca wrote: I'm running OS 10.6.2 a Mac airbook. I had problems with the binary sage-4.3-osx10.6-intel-64bit-i386-Darwin.dmg, so I downloaded the source and compiled it. I've found that show3d() does not work. After the commands sage: P = graphs.PetersenGraph() sage: P.show3d() I get the sage prompt and no drawing window. -- 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 URL: http://www.sagemath.org
[sage-support] eigenvalue difficulties
I'm running Mac OS X 10.6.1. The command matrix.eigenvalues() has stopped working, as follows: wombat:sgwork chris$ sage -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information.| -- sage: C = graphs.CycleGraph(5) sage: A = C.am() sage: A.eigenvalues() --- RuntimeError Traceback (most recent call last) /Users/chris/Code/sgwork/ipython console in module() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues (sage/matrix/ matrix2.c:19901)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.fcp (sage/matrix/matrix2.c: 8560)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense.charpoly (sage/ matrix/matrix_integer_dense.c:10599)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense._charpoly_linbox (sage/matrix/matrix_integer_dense.c:11242)() RuntimeError: -- Thanks for any help Chris Godsil --~--~-~--~~~---~--~~ 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: eigenvalue difficulties
Thanks. I tried that but the problem remains. Chris On Sep 18, 11:07 pm, William Stein wst...@gmail.com wrote: On Fri, Sep 18, 2009 at 8:05 PM, Chris Godsil cgod...@uwaterloo.ca wrote: I'm running Mac OS X 10.6.1. The command matrix.eigenvalues() has stopped working, as follows: You have to force a rebuild of linbox. This will get fully resolved when Sage gets ported to OS X 10.6. sage -f linbox-1.1.6.p0 William wombat:sgwork chris$ sage -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information. | -- sage: C = graphs.CycleGraph(5) sage: A = C.am() sage: A.eigenvalues() --- RuntimeError Traceback (most recent call last) /Users/chris/Code/sgwork/ipython console in module() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues (sage/matrix/ matrix2.c:19901)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.fcp (sage/matrix/matrix2.c: 8560)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense.charpoly (sage/ matrix/matrix_integer_dense.c:10599)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense._charpoly_linbox (sage/matrix/matrix_integer_dense.c:11242)() RuntimeError: -- Thanks for any help Chris Godsil -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org --~--~-~--~~~---~--~~ 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: eigenvalue difficulties
Thanks again. Tried that too, no effect - same error. I have access to a Mac running 10.5, so it will not it be a serious problem if I have to wait for the nest release. And I should be writing reference letters anyway... Chris On Sep 18, 11:31 pm, William Stein wst...@gmail.com wrote: On Fri, Sep 18, 2009 at 8:25 PM, Chris Godsil cgod...@uwaterloo.ca wrote: Thanks. I tried that but the problem remains. One other thing to try would be to rebuild the sage--linbox extension (which is easy). Just do the following from the root of your Sage install: flat:sage wstein$ touch devel/sage/sage/libs/linbox/* flat:sage wstein$ ./sage -br William Chris On Sep 18, 11:07 pm, William Stein wst...@gmail.com wrote: On Fri, Sep 18, 2009 at 8:05 PM, Chris Godsil cgod...@uwaterloo.ca wrote: I'm running Mac OS X 10.6.1. The command matrix.eigenvalues() has stopped working, as follows: You have to force a rebuild of linbox. This will get fully resolved when Sage gets ported to OS X 10.6. sage -f linbox-1.1.6.p0 William wombat:sgwork chris$ sage -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information. | -- sage: C = graphs.CycleGraph(5) sage: A = C.am() sage: A.eigenvalues() --- RuntimeError Traceback (most recent call last) /Users/chris/Code/sgwork/ipython console in module() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues (sage/matrix/ matrix2.c:19901)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix2.so in sage.matrix.matrix2.Matrix.fcp (sage/matrix/matrix2.c: 8560)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense.charpoly (sage/ matrix/matrix_integer_dense.c:10599)() /Applications/sage/local/lib/python2.6/site-packages/sage/matrix/ matrix_integer_dense.so in sage.matrix.matrix_integer_dense.Matrix_integer_dense._charpoly_linbox (sage/matrix/matrix_integer_dense.c:11242)() RuntimeError: -- Thanks for any help Chris Godsil -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org --~--~-~--~~~---~--~~ 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] determinants of matrix polynomials
I want to compute determinants of matrix polynomials, for matrices up to 20 x 20, say. The attached transcript seems to indicate 9 or 10 might be my limit. (Or it's late and I am being stupd?) -- | Sage Version 3.4, Release Date: 2009-03-11 | | Type notebook() for the GUI, and license() for information.| -- # intel mac pro, binary distribution sage: P = graphs.PetersenGraph() sage: P.delete_edge([0,1]) sage: P.degree() [2, 2, 3, 3, 3, 3, 3, 3, 3, 3] sage: P Petersen graph: Graph on 10 vertices ## but P is not the Petersen graph now sage: A = P.am() sage: Id = identity_matrix(10) sage: R.t = QQ[] sage: (t+1)^5 t^5 + 5*t^4 + 10*t^3 + 10*t^2 + 5*t + 1 sage: M = t*Id - A; M [ t 0 0 0 -1 -1 0 0 0 0] [ 0 t -1 0 0 0 -1 0 0 0] [ 0 -1 t -1 0 0 0 -1 0 0] [ 0 0 -1 t -1 0 0 0 -1 0] [-1 0 0 -1 t 0 0 0 0 -1] [-1 0 0 0 0 t 0 -1 -1 0] [ 0 -1 0 0 0 0 t 0 -1 -1] [ 0 0 -1 0 0 -1 0 t 0 -1] [ 0 0 0 -1 0 -1 -1 0 t 0] [ 0 0 0 0 -1 0 -1 -1 0 t] sage: M.det() ## and sage hangs ## but the following worked sage: K =graphs.CompleteGraph(3) sage: B =K.am() sage: Id = identity_matrix(3) sage: (t*Id-B).det() t^3 - 3*t - 2 sage: C = graphs.CubeGraph(3) sage: C 3-Cube: Graph on 8 vertices sage: Id = identity_matrix(8) sage: (t*Id-C.am()).det() t^8 - 12*t^6 + 30*t^4 - 28*t^2 + 9 # and the cycle on 9 vertices hangs --~--~-~--~~~---~--~~ 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: determinants of matrix polynomials
Thanks for your comments so far. Please note that I want to compute determinants of matrices whose entries are polynomials over QQ (so performance over ZZ is irrelevant). For the examples I offered, the determinants were characteristic polynomials but this would not be true for the cases I want to study. Also I would be computing tens of thousands of these determinants, ideally with matrices of orders of up to 30 x 30. Eventually I may want to look at cases where the entries are polynomials in two or three variables. So this leads to the following questions. What algorithm(s) does sage use to compute determinants over QQ[t] or QQ[t,u]? Does they work over the ring of definition, or over the field of fractions? Are they polynomial time? My limited experiments seem to suggest that the default algorithm sage uses for matrices over QQ[t] is not polynomial time. As the Reference Manual suggests, I entered M.determinant? to see what algorithm was being used, but did not get any useful information. Thanks Chris On Mar 19, 4:17 am, Chris Godsil cgod...@uwaterloo.ca wrote: I want to compute determinants of matrix polynomials, for matrices up to 20 x 20, say. The attached transcript seems to indicate 9 or 10 might be my limit. (Or it's late and I am being stupd?) -- | Sage Version 3.4, Release Date: 2009-03-11 | | Type notebook() for the GUI, and license() for information. | -- # intel mac pro, binary distribution sage: P = graphs.PetersenGraph() sage: P.delete_edge([0,1]) sage: P.degree() [2, 2, 3, 3, 3, 3, 3, 3, 3, 3] sage: P Petersen graph: Graph on 10 vertices ## but P is not the Petersen graph now sage: A = P.am() sage: Id = identity_matrix(10) sage: R.t = QQ[] sage: (t+1)^5 t^5 + 5*t^4 + 10*t^3 + 10*t^2 + 5*t + 1 sage: M = t*Id - A; M [ t 0 0 0 -1 -1 0 0 0 0] [ 0 t -1 0 0 0 -1 0 0 0] [ 0 -1 t -1 0 0 0 -1 0 0] [ 0 0 -1 t -1 0 0 0 -1 0] [-1 0 0 -1 t 0 0 0 0 -1] [-1 0 0 0 0 t 0 -1 -1 0] [ 0 -1 0 0 0 0 t 0 -1 -1] [ 0 0 -1 0 0 -1 0 t 0 -1] [ 0 0 0 -1 0 -1 -1 0 t 0] [ 0 0 0 0 -1 0 -1 -1 0 t] sage: M.det() ## and sage hangs ## but the following worked sage: K =graphs.CompleteGraph(3) sage: B =K.am() sage: Id = identity_matrix(3) sage: (t*Id-B).det() t^3 - 3*t - 2 sage: C = graphs.CubeGraph(3) sage: C 3-Cube: Graph on 8 vertices sage: Id = identity_matrix(8) sage: (t*Id-C.am()).det() t^8 - 12*t^6 + 30*t^4 - 28*t^2 + 9 # and the cycle on 9 vertices hangs --~--~-~--~~~---~--~~ 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] quaternions
I want to extract the real part of a quaternion, i.e., if L.i,j,k = QuaternionAlgebra(QQ,-1,-1); and a is in L, then I want the coefficient of 1 in the expansion of as a linear combination of 1, i, j and k. Is there a way to do this? A graceful way? (I have also discovered that using quaternions in combination with list comprehensions which have i as the dummy variable - [i for i in range(10)] - leads to quite unexpected results. But I suspect this reflects an underlying problem in python...) Thanks in advance for any help. Chris --~--~-~--~~~---~--~~ 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: quaternions
Just for reference, two comments on the documentation for quaternions: If x is an element of L as below, then neither x? nor x?? returns any information about methods that apply to x. Second, in the documentation on quaternions in the reference manual, there is no reference that I could find to the vector() method (and I went through this carefully a number of times). Also there is no indication in the reference manual that vector() applies to quaternions, although I did not spend much time on this search. But x.vector() does exactly what I need, and now I am an even-more happy customer. Chris On Mar 27, 6:19 pm, Justin Walker [EMAIL PROTECTED] wrote: On Mar 27, 2008, at 12:58 PM, Chris Godsil wrote: I want to extract the real part of a quaternion, i.e., if L.i,j,k = QuaternionAlgebra(QQ,-1,-1); and a is in L, then I want the coefficient of 1 in the expansion of as a linear combination of 1, i, j and k. Is there a way to do this? A graceful way? One way is: x.reduced_trace()/2 since you are working over QQ :-} Another is x.vector()[0]. Note that, if x is a Sage (or generally, python) object, x.TAB will get you a list of methods that might[*] apply to x. Then if 'foo' is one, x.foo? will get you documentation[+] on what 'foo' does. HTH Justin [*] Some methods are shown due to inheritance, and might actually not apply in a specific situation. [+] Documentation: the best documentation is had with ?? we might not find it in either case, if it's not in a .py file. -- Justin C. Walker, Curmudgeon at Large Director Institute for the Enhancement of the Director's Income --- Nobody knows the trouble I've been --- --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
