[sage-support] Re: Maximal eigenvalue of symmetric positive integer matrix
I asked What is fastest way in Sage to compute biggest eigenvalue of a symmetric matrix whose elements are positive integers? and got answer to use M=scipy.matrix(...) scipy.linalg.eigh(M, eigvals=..., eigvals_only=True) However, now I should compute smallest eigenvalues with bigger precision than IEEE-745 floats. About 1000 bit should be enought. Is there an easy way for that? -- Jori Mäntysalo -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] PDF docs unavailable on Sage site
The pdf files on http://www.sagemath.org/help.html#SageStandardDoc aren't accessible, due to wrong permissions. (Forbidden. You don't have permission to access ...) -- Peter Mueller -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Composition of morphisms of affine varieties
I am trying to compose 3 affine automorphisms of the Markoff surface. The following code produces an error: A.x,y,z = AffineSpace(QQ,3) M = A.subscheme([x^2+y^2+z^2-3*x*y*z]) H = Hom(M,M) f1 = H([3*y*z-x,y,z]) f2 = H([x,3*x*z-y,z]) f3 = H([x,y,3*x*y-z]) f3*f2*f1 What am I doing wrong? -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Composition of morphisms of affine varieties
On 18 November 2014 13:38, Soli vishkautsan wish...@gmail.com wrote: I am trying to compose 3 affine automorphisms of the Markoff surface. The following code produces an error: A.x,y,z = AffineSpace(QQ,3) M = A.subscheme([x^2+y^2+z^2-3*x*y*z]) H = Hom(M,M) f1 = H([3*y*z-x,y,z]) f2 = H([x,3*x*z-y,z]) f3 = H([x,y,3*x*y-z]) f3*f2*f1 What am I doing wrong? This could be a bug. Both f3*f2 and f2*f1 work ok, returning Composite maps. Also (f3*f2)*(f2*f1) works (not what you want of course. It looks to me as if the people who implemented Composite maps did not define the * operator to work with a combination of Composite and ordinary maps. Silly workaround: sage: id = H([x,y,z]) sage: (f3*f2)*(f1*id) Composite map: From: Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 To: Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 Defn: Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 John Cremona -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Composition of morphisms of affine varieties
Thanks, another workaround is to use (f2*f1).post_compose(f3) which also works. The same problem when composing the homogenization of these morphisms. I will add this to trac, unless someone else intervenes :) On Tuesday, November 18, 2014 2:47:33 PM UTC+1, John Cremona wrote: On 18 November 2014 13:38, Soli vishkautsan wis...@gmail.com javascript: wrote: I am trying to compose 3 affine automorphisms of the Markoff surface. The following code produces an error: A.x,y,z = AffineSpace(QQ,3) M = A.subscheme([x^2+y^2+z^2-3*x*y*z]) H = Hom(M,M) f1 = H([3*y*z-x,y,z]) f2 = H([x,3*x*z-y,z]) f3 = H([x,y,3*x*y-z]) f3*f2*f1 What am I doing wrong? This could be a bug. Both f3*f2 and f2*f1 work ok, returning Composite maps. Also (f3*f2)*(f2*f1) works (not what you want of course. It looks to me as if the people who implemented Composite maps did not define the * operator to work with a combination of Composite and ordinary maps. Silly workaround: sage: id = H([x,y,z]) sage: (f3*f2)*(f1*id) Composite map: From: Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 To: Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 Defn: Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 then Generic endomorphism of Closed subscheme of Affine Space of dimension 3 over Rational Field defined by: -3*x*y*z + x^2 + y^2 + z^2 John Cremona -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com javascript:. To post to this group, send email to sage-s...@googlegroups.com javascript:. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Coefficient of Boolean Polynomial
Thank you so much. On 18 November 2014 00:02, slelievre samuel.lelie...@gmail.com wrote: Santanu wrote: R.v1, v2, v3=BooleanPolynomialRing(3) f=v1*v2+v1*v3+v1 print f.coefficient(v1) I am getting Traceback (click to the left of this block for traceback) ... AttributeError: 'sage.rings.polynomial.pbori.BooleanPolynomial' object has no attribute 'coefficient' Answer should be v2+v3+1. I do not want to use R.v1, v2, v3=GF(2)[] as in this ring operations are much slower than R.v1, v2, v3=BooleanPolynomialRing(3). Here v1 divides f so you could do sage: sum(m/v1 for m in f.monomials()) Without that assumption you could do sage: sum(m/v1 for m in (f-f(v1=0)).monomials()) -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib
I tried installing sage 6.4 from several binaries but everytime I started a
new sage and type in some calculations, the above warning message appears.
If I re-type the exact calculations again, such warnings disappear.
Further, it seems that these warnings are related to certain calculations,
but not all.
Example:
sage: 2+2
4
sage: x=var('x')
sage: diff(sin(x^2),x,4)
16*x^4*sin(x^2) - 48*x^2*cos(x^2) - 12*sin(x^2)
sage: integral(x*sin(x^2),x)
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
ld: warning: directory not found for option
'-L/Users/buildslave-sage/slave/sage_git/build/local/lib'
-1/2*cos(x^2)
sage: integral(x*sin(x^2),x)
-1/2*cos(x^2)
sage: t=var('t')
sage: integral(t*sin(t^2),t)
-1/2*cos(t^2)
-
I'm running on a OS X 10.9.5. I tried download binary files from different
locations, but the same warnings appear. I also tried to install via source
code, but unfortunately failed. Many thanks in advance.
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[sage-support] Re: ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib
I tried installing sage 6.4 from several binaries but everytime I started a new sage and type in some calculations, the above warning message appears. If I re-type the exact calculations again, such warnings disappear. Further, it seems that these warnings are related to certain calculations, but not all. Let me guess that they only happen when you do integration or symbolic summation? In which case somehow the Sage Maxima instance is looking for this. It doesn't appear to be affecting the calculation, at least. sage: integral(x*sin(x^2),x) ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' I'm running on a OS X 10.9.5. I tried download binary files from different locations, but the same warnings appear. I also tried to install via source code, but unfortunately failed. Many thanks in advance. Hopefully you won't need to, but did you manage to get the command line tools from Apple? That should suffice. (See the developer guide http://www.sagemath.org/doc/developer/index.html and installation guide http://www.sagemath.org/doc/installation/source.html#prerequisites .) -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: simple 'solve' error, possibly related to ecl and maxima installation
Problem solved. I did not install 'Command Line Tools for Xcode' previously on my Mac because I did not read instructions on installing Sage from source code. After installing Command Line Tools, it works now. Though the installation of Sage is still from a binary one. Yes, this would solve it. However, it should not be necessary! Volker, any ideas on what the buildbot was thinking? @Nils and @kcrisman, thanks again for all your help. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Why solve(5^( x -1) == (0.04)^(2*x), x) returns empty set?
Emmanuel Any way to make Sage act like it can't find the solution (emit question back to user) INSTEAD of emitting the empty set? I can't find the solution and There is no solution are NOT the same thing? cs -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib
Yes, I had Command Line Tools installed, and the Xcode version is 6.1. After I stop getting that error from my previous post (https://groups.google.com/forum/#!topic/sage-support/wj4ObDhv_xE), I get these new warnings. I know very little about Xcode or CLT so I'm quite confused. I can get correct answers now, with these haunting warnings. I think the problem still lies in Maxima, because when I enter $ sage -maxima these warnings appear in several places. For your reference, I paste the message below: $ sage -maxima ;;; Loading #P/Applications/sage/local/lib/ecl/cmp.fas ;;; OPTIMIZE levels: Safety=2, Space=0, Speed=3, Debug=0 ;;; ;;; End of Pass 1.ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ;;; OPTIMIZE levels: Safety=2, Space=0, Speed=3, Debug=0 ;;; ;;; End of Pass 1.ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ;;; OPTIMIZE levels: Safety=2, Space=0, Speed=3, Debug=0 ;;; ;;; End of Pass 1.ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ;;; OPTIMIZE levels: Safety=2, Space=0, Speed=3, Debug=0 ;;; ;;; End of Pass 1.ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' ;;; Loading #P/Applications/sage/local/lib/ecl/sb-bsd-sockets.fas ;;; Loading #P/Applications/sage/local/lib/ecl/sockets.fas ;;; Loading #P/Applications/sage/local/lib/ecl/defsystem.fas Maxima 5.34.1 http://maxima.sourceforge.net using Lisp ECL 13.5.1 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) On Tuesday, November 18, 2014 11:38:34 PM UTC+8, kcrisman wrote: I tried installing sage 6.4 from several binaries but everytime I started a new sage and type in some calculations, the above warning message appears. If I re-type the exact calculations again, such warnings disappear. Further, it seems that these warnings are related to certain calculations, but not all. Let me guess that they only happen when you do integration or symbolic summation? In which case somehow the Sage Maxima instance is looking for this. It doesn't appear to be affecting the calculation, at least. sage: integral(x*sin(x^2),x) ld: warning: directory not found for option '-L/Users/buildslave-sage/slave/sage_git/build/local/lib' I'm running on a OS X 10.9.5. I tried download binary files from different locations, but the same warnings appear. I also tried to install via source code, but unfortunately failed. Many thanks in advance. Hopefully you won't need to, but did you manage to get the command line tools from Apple? That should suffice. (See the developer guide http://www.sagemath.org/doc/developer/index.html and installation guide http://www.sagemath.org/doc/installation/source.html#prerequisites .) -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Version 6.4
I just downloaded version 6.4, specifically: sage-6.4-x86_64-Darwin-OSX_10.9_x86_64-app.dmg This package does not contain an app file like previous versions. Is this correct? john hanly Go Nats natsfan...@gmail.com -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Version 6.4
Hmm yes, the app and non-app dmg are identical for some reason On Tuesday, November 18, 2014 6:43:30 PM UTC, john wrote: I just downloaded version 6.4, specifically: sage-6.4-x86_64-Darwin-OSX_10.9_x86_64-app.dmg This package does not contain an app file like previous versions. Is this correct? john hanly Go Nats natsf...@gmail.com javascript: -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Version 6.4
Hmm yes, the app and non-app dmg are identical for some reason Possibly because SAGE_APP_BUNDLE=yes was not set? Or did it attempt but fail (but then the failure did not break the bdist process - which would be worrisome!)? Luckily this should be easier to fix than some other bugs! John, thanks for letting us know so quickly. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Version 6.4
No, the buildbot sets SAGE_APP_BUNDLE. Possibly a 10.10 SDK issue? On Tuesday, November 18, 2014 9:00:58 PM UTC, kcrisman wrote: Hmm yes, the app and non-app dmg are identical for some reason Possibly because SAGE_APP_BUNDLE=yes was not set? Or did it attempt but fail (but then the failure did not break the bdist process - which would be worrisome!)? Luckily this should be easier to fix than some other bugs! John, thanks for letting us know so quickly. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] basic probability simplification
Does anybody know how to do this sort of thing in Sage? Asked by me
today by a Stanford CS professor...
It would be nice if it knew how to simplify the tail probability of a
binomial distribution. Mathematica can do:
FullSimplify[ Sum[Binomial[total, k] x^k (1 - x)^(total - k), {k, 0, n}]]
- (1 - x)^total ((1/(1 - x))^
total - (1 - x)^(-1 - n) x^(1 + n)
Binomial[total, 1 + n] Hypergeometric2F1[1, 1 + n - total, 2 + n,
x/(-1 + x)])
With Sage it doesn't seem to have the hypergeometric functions (or
maybe it just doesn't know the simplification):
total, n, x, k = var('total', 'n', 'x', 'k')
simplify( sum( binomial(total,k) * x^k * (1-x)^(total - k), k, 0, n))
- sum(x^k*(-x + 1)^(-k + total)*binomial(total, k), k, 0, n)
I was finding it was really slow to evaluate this with big values...
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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