[sage-support] Re: 2nd try: Integer solutions for systems of linear equations
Helloo !!! To consider the problem as linear program and use MixedIntegerLinearProgram() with integer constrains works, but it is very very slow for larger systems. Well, your problem is *precisely* what Integer Linear Program solvers are written for, so I guess that using them is the good way to go unless you plan on using some properties of the matrices you generate (and that the LP solvers would not notice) to solve your equation. They are indeed slow in some cases, but we have to work with the tools available, or rather those we know about. ILP's what I would try to do myself -- if you find some other way to solve these equations please let me know, for I use them very often and I would be delighted to solve my graph problems faster too :-) By the way, in Sage MixedIntegerLinearProgram uses GLPK by default to solve these problems, but you can also ask it to solve them with Gurobi or CPLEX, which are usually *MUCH* faster. Good luck ! :-) Nathann -- 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] Re: Is google groups buggy? Test posting
On Thursday, September 13, 2012 9:44:52 AM UTC+2, moritz wrote: Two days ago I tried to post on this list, using the UI of google groups. The message did not appear on sage-support .. I reported this in detail, that's all I can do :-( H (group admin) -- 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] Re: 2nd try: Integer solutions for systems of linear equations
Since the OP's problem has no inequalities (such as requiring that all integers in question are non-negative), it is solved by using Hermite normal form. If A is an m by n integer matrix, the Hermite normal form of A is an upper triangular integer matrix H (also m by n), along with an m by m integer matrix of determinant 1 (i.e. it's invertible) so that H = U A. So the original equation A x = b becomes (after multiplying by U): H x = U b, for which it's easy to get the general solution (just back solve. If you ever get a non-integer by dividing there are no solutions). Since U is invertible, multiplying the equation by U doesn't introduce spurious solutions. Victor On Friday, September 14, 2012 5:46:01 AM UTC-4, Nathann Cohen wrote: Helloo !!! To consider the problem as linear program and use MixedIntegerLinearProgram() with integer constrains works, but it is very very slow for larger systems. Well, your problem is *precisely* what Integer Linear Program solvers are written for, so I guess that using them is the good way to go unless you plan on using some properties of the matrices you generate (and that the LP solvers would not notice) to solve your equation. They are indeed slow in some cases, but we have to work with the tools available, or rather those we know about. ILP's what I would try to do myself -- if you find some other way to solve these equations please let me know, for I use them very often and I would be delighted to solve my graph problems faster too :-) By the way, in Sage MixedIntegerLinearProgram uses GLPK by default to solve these problems, but you can also ask it to solve them with Gurobi or CPLEX, which are usually *MUCH* faster. Good luck ! :-) Nathann -- 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] Re: Splitting a notebook
On 9/14/12 10:20 AM, Victor Miller wrote: There are times when I've added a bunch of cells to a notebook, and then I realize that I'd like to make those cells into a separate notebook. Is there a straightforward way of doing this? I know that I can cut and paste individual cells, but that gets rather tedious. I would go to the Edit view of the worksheet (upper right of worksheet) and then copy whatever cells I want. Open up a new worksheet, click Edit in the new worksheet, paste, and save. Thanks, Jason -- 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.
Re: [sage-support] Re: 2nd try: Integer solutions for systems of linear equations
Since the OP's problem has no inequalities (such as requiring that all integers in question are non-negative), it is solved by using Hermite normal form. If A is an m by n integer matrix, the Hermite normal form of A is an upper triangular integer matrix H (also m by n), along with an m by m integer matrix of determinant 1 (i.e. it's invertible) so that H = U A. So the original equation A x = b becomes (after multiplying by U): H x = U b, for which it's easy to get the general solution (just back solve. If you ever get a non-integer by dividing there are no solutions). Since U is invertible, multiplying the equation by U doesn't introduce spurious solutions. **Applause** Well... Thank you for teaching me that :-) Nathann -- 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] Re: 2nd try: Integer solutions for systems of linear equations
On 9/14/12 10:18 AM, Victor Miller wrote: Since the OP's problem has no inequalities (such as requiring that all integers in question are non-negative), it is solved by using Hermite normal form. If A is an m by n integer matrix, the Hermite normal form of A is an upper triangular integer matrix H (also m by n), along with an m by m integer matrix of determinant 1 (i.e. it's invertible) so that H = U A. So the original equation A x = b becomes (after multiplying by U): H x = U b, for which it's easy to get the general solution (just back solve. If you ever get a non-integer by dividing there are no solutions). Since U is invertible, multiplying the equation by U doesn't introduce spurious solutions. And for completeness, you can get hermite form by using the .hermite_form method: sage: a=random_matrix(ZZ,5) sage: a.hermite_form() [ 1 0 0 0 35] [ 0 1 0 0 73] [ 0 0 1 0 40] [ 0 0 0 1 51] [ 0 0 0 0 103] sage: a.hermite_form(transformation=True) ( [ 1 0 0 0 35] [ -37 -108 28 -10 97] [ 0 1 0 0 73] [ -77 -224 58 -21 201] [ 0 0 1 0 40] [ -44 -128 33 -12 115] [ 0 0 0 1 51] [ -59 -172 44 -16 154] [ 0 0 0 0 103], [-110 -321 83 -30 288] ) Thanks, Jason -- 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.
Re: [sage-support] Re: Splitting a notebook
On 2012-09-14 17:25, Jason Grout wrote: On 9/14/12 10:20 AM, Victor Miller wrote: There are times when I've added a bunch of cells to a notebook, and then I realize that I'd like to make those cells into a separate notebook. Is there a straightforward way of doing this? I know that I can cut and paste individual cells, but that gets rather tedious. I would go to the Edit view of the worksheet (upper right of worksheet) and then copy whatever cells I want. Open up a new worksheet, click Edit in the new worksheet, paste, and save. Alternatively, you can copy the worksheet (there is a menu option for that) and then from both worksheets delete the parts that you don't want. -- 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] Sagenb.org
Haven't been able to access sagenb.org or .com for over a day. Is this a long term outage? Thank you, -d -- 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] Strange sum() result and can't be evaluated numerically
The command sum( ((-1)^k*(x^(2*k+1))/factorial(2*k+1)),k,0,oo) should give sin(x) - it does in Mathematica. But in Sage it gives 1/2*sqrt(pi)*sqrt(2)*sqrt(x)*bessel_j(1/2, x) which can't be evaluated numerically: _(x=3).N() Traceback (most recent call last): File stdin, line 1, in module File _sage_input_4.py, line 10, in module exec compile(u'open(___code___.py,w).write(# -*- coding: utf-8 -*-\\n + _support_.preparse_worksheet_cell(base64.b64decode(Xyh4PTMpLk4oKQ==),globals())+\\n); execfile(os.path.abspath(___code___.py)) File , line 1, in module File /tmp/tmpMc56sG/___code___.py, line 3, in module exec compile(u'_(x=_sage_const_3 ).N() File , line 1, in module File expression.pyx, line 4319, in sage.symbolic.expression.Expression._numerical_approx (sage/symbolic/expression.cpp:20837) TypeError: cannot evaluate symbolic expression numerically What am I missing here? I am using Sage 5.3. Thanks! -- Renan Birck Pinheiro - Grupo de Microeletrônica Engenharia Elétrica - UFSM - Santa Maria, Brasil http://renanbirck.blogspot.com - +55 55 91162798 -- 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.
