[sage-support] Re: numerically solving a polynomial system of equations
There is a matlab/octave interface to it. Look at the following reference on http://www.math.uic.edu/~jan/ I don't know more about this since I am also at the moment collecting information on how to solve a large system of polynomial equations. Yun Guan and Jan Verschelde: PHClab: A MATLAB/Octave interface to PHCpack. The abstract and paper . Take a look at the Poster. In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer- Verlag, 2008. Bhalchandra Thatte On Aug 24, 10:29 pm, mabshoff [EMAIL PROTECTED] dortmund.de wrote: On Aug 24, 2:22 pm, William Stein [EMAIL PROTECTED] wrote: On Sun, Aug 24, 2008 at 2:03 PM, Joshua Kantor [EMAIL PROTECTED] wrote: 1. I would recommend looking at phcpack, it is designed to exploit the special nature of large polynomial systems, however, supposedly I believe it is sometimes difficult to compile, I've never used it but ^ It is written in ADA. And building the GNU Ada compiler from sources is a giant pain unless you have the GNU Ada compiler to bootstrap. I did build some phcpack binaries for x86-64 Linux and it has a tendency to segfault when run on say Debian if the binary was build on a FC8 box and vice versa. I mainly wanted an Itanium binary, but cross compiling the ada toolchain was just plainly not worth it for it. So in conclusion: great code if you can use a binary that works, if you need to build from sources it plainly sucks. The lesson learned here is not to use exotic languages since the (alleged) benefit from using Ada is far outweight by the fact that the practicality of building the code :) SNIP William Stein Cheers, Michael 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: numerically solving a polynomial system of equations
On Aug 25, 1:21 am, iSAGE [EMAIL PROTECTED] wrote: There is a matlab/octave interface to it. Look at the following reference onhttp://www.math.uic.edu/~jan/ I don't know more about this since I am also at the moment collecting information on how to solve a large system of polynomial equations. Yun Guan and Jan Verschelde: PHClab: A MATLAB/Octave interface to PHCpack. The abstract and paper . Take a look at the Poster. In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer- Verlag, 2008. Bhalchandra Thatte There is also a quite sophisticated interface in Sage, but as long as the code is written in Ada there is a zero percent chance that that code will become standard in Sage. The optional package we have is a bunch of binaries since Ada support is usually not available. Note that at least until recently there was not even a 64 bit x86-64 ot Itanium binary on Verschelde's website. 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] Re: numerically solving a polynomial system of equations
On Aug 24, 12:16 pm, Michael [EMAIL PROTECTED] wrote: I have a polynomial system of 50 equations in 50 unknowns. I would like to numerically solve this system (I'm interested in complex zeros). Seems to me that if I use sage's solve, it will sttempt to solve these algebraically. Are there any funcitons in sage for solving a polynomial or non-linear system numerically. Other people have suggested phcpack, but not explained how to use it. The following may or may not work for you (it depends on your processor architecture and operating system); but if it does work, it's actually quite easy. First, install phc, by typing at the command line: sage -i phc-2.3.39.p0 Then, from within Sage, you can do things like this: sage: from sage.interfaces.phc import phc sage: R2.x,y = PolynomialRing(QQ,2) sage: start_sys = [x^6-y^2,y^5-1] sage: sol = phc.blackbox(start_sys, R2) sage: len(sol.solutions()) 30 sage: sol.solutions()[0] # display the first solution [0.309016994374947 + 0.951056516295154*I, 0.104528463267653 + 0.994521895368273*I] Carl --~--~-~--~~~---~--~~ 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: numerically solving a polynomial system of equations
On Mon, Aug 25, 2008 at 5:32 PM, Carl Witty [EMAIL PROTECTED] wrote: On Aug 24, 12:16 pm, Michael [EMAIL PROTECTED] wrote: I have a polynomial system of 50 equations in 50 unknowns. I would like to numerically solve this system (I'm interested in complex zeros). Seems to me that if I use sage's solve, it will sttempt to solve these algebraically. Are there any funcitons in sage for solving a polynomial or non-linear system numerically. Other people have suggested phcpack, but not explained how to use it. The following may or may not work for you (it depends on your processor architecture and operating system); but if it does work, it's actually quite easy. First, install phc, by typing at the command line: sage -i phc-2.3.39.p0 Then, from within Sage, you can do things like this: sage: from sage.interfaces.phc import phc sage: R2.x,y = PolynomialRing(QQ,2) sage: start_sys = [x^6-y^2,y^5-1] sage: sol = phc.blackbox(start_sys, R2) sage: len(sol.solutions()) 30 sage: sol.solutions()[0] # display the first solution [0.309016994374947 + 0.951056516295154*I, 0.104528463267653 + 0.994521895368273*I] I installed phc into the public sage notebook servers, so you can try the above at https://sage.math.washington.edu:8102 -- William --~--~-~--~~~---~--~~ 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: numerically solving a polynomial system of equations
On Sun, Aug 24, 2008 at 12:16 PM, Michael [EMAIL PROTECTED] wrote: I have a polynomial system of 50 equations in 50 unknowns. I would like to numerically solve this system (I'm interested in complex zeros). Seems to me that if I use sage's solve, it will sttempt to solve these algebraically. Are there any funcitons in sage for solving a polynomial or non-linear system numerically. You're probably going to want to use scipy.optimize. It has a large range of sophisticated numerical optimization routines. Maybe they can be used for what you want. I've hardly used them, so I can't easily say more -- hopefully somebody who has can. sage: import scipy scisagimport scipy.optimize sage: scipy.optimize. scipy.optimize.NumpyTestscipy.optimize.broyden2 scipy.optimize.fmin_ncg scipy.optimize.moduleTNC scipy.optimize.anderson scipy.optimize.broyden3 scipy.optimize.fmin_powell scipy.optimize.newton scipy.optimize.anderson2scipy.optimize.broyden_generalized scipy.optimize.fmin_tnc scipy.optimize.nonlin scipy.optimize.anneal scipy.optimize.brute scipy.optimize.fminboundscipy.optimize.optimize scipy.optimize.approx_fprimescipy.optimize.check_grad scipy.optimize.fsolve scipy.optimize.ridder scipy.optimize.bisect scipy.optimize.cobyla scipy.optimize.golden scipy.optimize.rosen scipy.optimize.bisectionscipy.optimize.fixed_point scipy.optimize.lbfgsb scipy.optimize.rosen_der scipy.optimize.bracket scipy.optimize.fmin scipy.optimize.leastsq scipy.optimize.rosen_hess scipy.optimize.brentscipy.optimize.fmin_bfgs scipy.optimize.line_search scipy.optimize.rosen_hess_prod scipy.optimize.brenth scipy.optimize.fmin_cg scipy.optimize.linesearch scipy.optimize.test scipy.optimize.brentq scipy.optimize.fmin_cobyla scipy.optimize.minpack scipy.optimize.tnc scipy.optimize.broyden1 scipy.optimize.fmin_l_bfgs_b scipy.optimize.minpack2 scipy.optimize.zeros --~--~-~--~~~---~--~~ 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: numerically solving a polynomial system of equations
1. I would recommend looking at phcpack, it is designed to exploit the special nature of large polynomial systems, however, supposedly I believe it is sometimes difficult to compile, I've never used it but it might be better suited to your problem. http://www.math.uic.edu/~jan/download.html 2. The optimize.fsolve routine may be able to do what you want, though I'm not sure how it will deal with that large a system sage: import scipy sage: from scipy import optimize sage: def f(x): return [float(x[0]**2-x[0]*x[1]-1),float(x[1]**2+x[0]*x[1]-2)] : sage: optimize.fsolve(f,[0.1r,0.1r]) array([-0.46821319, 1.66756601]) Note the float and 0.1r. scipy is not happy with sage floats or ints, so you need to make sure everything is really python types and not sage types. The initial guess is very important if you give it a starting point of [0,0] it won't converge. Also, you can give it a jacobian which for that large a system is probably a good idea. do sage: optimize.fsolve? for the arguments. On Aug 24, 12:24 pm, William Stein [EMAIL PROTECTED] wrote: On Sun, Aug 24, 2008 at 12:16 PM, Michael [EMAIL PROTECTED] wrote: I have a polynomial system of 50 equations in 50 unknowns. I would like to numerically solve this system (I'm interested in complex zeros). Seems to me that if I use sage's solve, it will sttempt to solve these algebraically. Are there any funcitons in sage for solving a polynomial or non-linear system numerically. You're probably going to want to use scipy.optimize. It has a large range of sophisticated numerical optimization routines. Maybe they can be used for what you want. I've hardly used them, so I can't easily say more -- hopefully somebody who has can. sage: import scipy scisagimport scipy.optimize sage: scipy.optimize. scipy.optimize.NumpyTestscipy.optimize.broyden2 scipy.optimize.fmin_ncg scipy.optimize.moduleTNC scipy.optimize.anderson scipy.optimize.broyden3 scipy.optimize.fmin_powell scipy.optimize.newton scipy.optimize.anderson2scipy.optimize.broyden_generalized scipy.optimize.fmin_tnc scipy.optimize.nonlin scipy.optimize.anneal scipy.optimize.brute scipy.optimize.fminboundscipy.optimize.optimize scipy.optimize.approx_fprimescipy.optimize.check_grad scipy.optimize.fsolve scipy.optimize.ridder scipy.optimize.bisect scipy.optimize.cobyla scipy.optimize.golden scipy.optimize.rosen scipy.optimize.bisectionscipy.optimize.fixed_point scipy.optimize.lbfgsb scipy.optimize.rosen_der scipy.optimize.bracket scipy.optimize.fmin scipy.optimize.leastsq scipy.optimize.rosen_hess scipy.optimize.brentscipy.optimize.fmin_bfgs scipy.optimize.line_search scipy.optimize.rosen_hess_prod scipy.optimize.brenth scipy.optimize.fmin_cg scipy.optimize.linesearch scipy.optimize.test scipy.optimize.brentq scipy.optimize.fmin_cobyla scipy.optimize.minpack scipy.optimize.tnc scipy.optimize.broyden1 scipy.optimize.fmin_l_bfgs_b scipy.optimize.minpack2 scipy.optimize.zeros --~--~-~--~~~---~--~~ 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: numerically solving a polynomial system of equations
On Sun, Aug 24, 2008 at 2:03 PM, Joshua Kantor [EMAIL PROTECTED] wrote: 1. I would recommend looking at phcpack, it is designed to exploit the special nature of large polynomial systems, however, supposedly I believe it is sometimes difficult to compile, I've never used it but ^ It is written in ADA. it might be better suited to your problem. http://www.math.uic.edu/~jan/download.html It is good when the zero locus is maybe not 0-dimensional, i.e., when there are infinitely many solutions and you want to understand them. 2. The optimize.fsolve routine may be able to do what you want, though I'm not sure how it will deal with that large a system sage: import scipy sage: from scipy import optimize sage: def f(x): return [float(x[0]**2-x[0]*x[1]-1),float(x[1]**2+x[0]*x[1]-2)] : sage: optimize.fsolve(f,[0.1r,0.1r]) array([-0.46821319, 1.66756601]) Note the float and 0.1r. scipy is not happy with sage floats or ints, so you need to make sure everything is really python types and not sage types. It's best to just do RealNumber = float; Integer = int first. Thanks Josh! The initial guess is very important if you give it a starting point of [0,0] it won't converge. Also, you can give it a jacobian which for that large a system is probably a good idea. do sage: optimize.fsolve? for the arguments. On Aug 24, 12:24 pm, William Stein [EMAIL PROTECTED] wrote: On Sun, Aug 24, 2008 at 12:16 PM, Michael [EMAIL PROTECTED] wrote: I have a polynomial system of 50 equations in 50 unknowns. I would like to numerically solve this system (I'm interested in complex zeros). Seems to me that if I use sage's solve, it will sttempt to solve these algebraically. Are there any funcitons in sage for solving a polynomial or non-linear system numerically. You're probably going to want to use scipy.optimize. It has a large range of sophisticated numerical optimization routines. Maybe they can be used for what you want. I've hardly used them, so I can't easily say more -- hopefully somebody who has can. sage: import scipy scisagimport scipy.optimize sage: scipy.optimize. scipy.optimize.NumpyTestscipy.optimize.broyden2 scipy.optimize.fmin_ncg scipy.optimize.moduleTNC scipy.optimize.anderson scipy.optimize.broyden3 scipy.optimize.fmin_powell scipy.optimize.newton scipy.optimize.anderson2scipy.optimize.broyden_generalized scipy.optimize.fmin_tnc scipy.optimize.nonlin scipy.optimize.anneal scipy.optimize.brute scipy.optimize.fminboundscipy.optimize.optimize scipy.optimize.approx_fprimescipy.optimize.check_grad scipy.optimize.fsolve scipy.optimize.ridder scipy.optimize.bisect scipy.optimize.cobyla scipy.optimize.golden scipy.optimize.rosen scipy.optimize.bisectionscipy.optimize.fixed_point scipy.optimize.lbfgsb scipy.optimize.rosen_der scipy.optimize.bracket scipy.optimize.fmin scipy.optimize.leastsq scipy.optimize.rosen_hess scipy.optimize.brentscipy.optimize.fmin_bfgs scipy.optimize.line_search scipy.optimize.rosen_hess_prod scipy.optimize.brenth scipy.optimize.fmin_cg scipy.optimize.linesearch scipy.optimize.test scipy.optimize.brentq scipy.optimize.fmin_cobyla scipy.optimize.minpack scipy.optimize.tnc scipy.optimize.broyden1 scipy.optimize.fmin_l_bfgs_b scipy.optimize.minpack2 scipy.optimize.zeros -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ 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: numerically solving a polynomial system of equations
On Aug 24, 2:22 pm, William Stein [EMAIL PROTECTED] wrote: On Sun, Aug 24, 2008 at 2:03 PM, Joshua Kantor [EMAIL PROTECTED] wrote: 1. I would recommend looking at phcpack, it is designed to exploit the special nature of large polynomial systems, however, supposedly I believe it is sometimes difficult to compile, I've never used it but ^ It is written in ADA. And building the GNU Ada compiler from sources is a giant pain unless you have the GNU Ada compiler to bootstrap. I did build some phcpack binaries for x86-64 Linux and it has a tendency to segfault when run on say Debian if the binary was build on a FC8 box and vice versa. I mainly wanted an Itanium binary, but cross compiling the ada toolchain was just plainly not worth it for it. So in conclusion: great code if you can use a binary that works, if you need to build from sources it plainly sucks. The lesson learned here is not to use exotic languages since the (alleged) benefit from using Ada is far outweight by the fact that the practicality of building the code :) SNIP William Stein Cheers, Michael 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
