[sage-support] Re: Solving recursion formula?
Hi Marc,
On 2018-12-08, Marc Mezzarobba wrote:
> In Sage itself, CFiniteSequence.closed_form() should be able to solve
> linear recurrence with constant coefficients.
Thank you!
Indeed, after changing my search keyword from resursive to reccurrence,
CFiniteSequence seemed to be the most helpful answer in Sage. What about
a more complicated recurrence, such as the one given by
x_(n+1) = 1 + x_n*2/n
Any chances to solve those and similar recurrences automatically?
My original hope was that some capability to solve a symbolic recurrence
is standard in Sage; after all, symbolic sums *can* to some extent be
computed in Sage:
sage: var('k', domain='integer')
k
sage: sum(x^k*(k+1)/(k+2), k,0,Infinity)
(x*(log(-x + 1) - 1) - log(-x + 1))/(x^3 - x^2)
Best regards,
Simon
--
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 https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Solving recursion formula?
Simon King wrote: > That's not what I am looking for. No data are given. Given is some > recursion formula; what we want to know is a corresponding closed > formula. Example: The recursion x_0=1 and x_(n+1) := f(x_n) = 2*x_n > should result in the closed formula x_n = 2^n. ore_algebra also has some limited support for solving linear recurrences with polynomial coefficients. Specifically, it can find polynomial and rational closed forms or prove that none exists. A related and perhaps more interesting feature is the ability to compute a basis of asymptotic expansions of solutions as n → ∞. On your example: sage: from ore_algebra import OreAlgebra sage: Pols. = QQ[] sage: RecOps. = OreAlgebra(Pols) sage: (Sn - 2).generalized_series_solutions() [2^n*(1 + O(n^(-5)))] A slightly more complicated one: sage: (Sn^2 + Sn - 2*(n^2+1)).generalized_series_solutions(2) [(n/e)^n*(1.414213562373095?)^n*n^(-1.353553390593274?) *(1 + 0.010110028629970214?*n^(-1) + O(n^(-2))), (n/e)^n*(-1.414213562373095?)^n*n^(-0.6464466094067262?) *(1 - 0.3434433619633035?*n^(-1) + O(n^(-2)))] In Sage itself, CFiniteSequence.closed_form() should be able to solve linear recurrence with constant coefficients. -- Marc -- 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 https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] make: did it fail? (Sage 8.3)
first of all, inspect what you have in your PATH, using "echo" from shell. E.g. I have $ echo $PATH /usr/lib/llvm/6/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/bin Now one can set it to what you need by using "export", e.g. $ export PATH=/usr/sbin:/usr/bin:/sbin:/bin Now in this shell session you have what you've set it to. To make it persistent, modify ~/.bashrc or/and similar file, such as ~/.profile, this is in every sensible tutorial on basic Unix shell usage... On Sat, Dec 8, 2018 at 9:51 AM Rohit Midha wrote: > > Hi, > I got the same error and I'm really new to all this, and this is probably a > stupid question but what exactly do you mean by ' sanitize your PATH' ? > > On Sunday, October 14, 2018 at 11:22:45 PM UTC+5:30, Dima Pasechnik wrote: >> >> oops, sorry. You got a conflict with Anaconda install: >> To fix this you probably need to sanitize your PATH >> >> indeed, your log says: >> >> >> checking for curl-config... /Users/cbgroves2001/anaconda3/bin/curl-config >> checking libcurl version ... 7.61.0 >> checking curl/curl.h usability... yes >> checking curl/curl.h presence... yes >> checking for curl/curl.h... yes >> checking if libcurl is version 7 and >= 7.22.0... no >> configure: error: libcurl >= 7.22.0 library and headers are required >> On Sun, Oct 14, 2018 at 5:43 PM Charles Groves wrote: >> > >> > i updated command line tools just prior to running make >> > >> > On Sun, Oct 14, 2018 at 7:36 AM Dima Pasechnik wrote: >> >> >> >> It looks as if your build got stuck waiting for something, and then got >> >> unstuck. Even on such an old machine it should not take more than 8-10 >> >> hours... >> >> >> >> I guess things related to R won't work in your install. It looks as if >> >> your libcurl is broken. Do you by any chance need to update Command Line >> >> Tools? >> >> >> >> >> >> >> >> On Sun, 14 Oct 2018, 11:59 , wrote: >> >>> >> >>> Make was still running fine after 24 hours. Then I forgot what I was >> >>> about and closed laptop's lid. Immediately re-opened laptop and found >> >>> the lines below. >> >>> >> >>> Sage runs and no longer crashes on "plot( x^2 )" like the .dmg version >> >>> did. >> >>> >> >>> So, did it fail? If so, what do I do? (Besides not closing my laptop :( ) >> >>> >> >>> Thankyouthankyou. >> >>> >> >>> >> >>> Last lines of output from make: >> >>> >> >>> *** >> >>> Error building Sage. >> >>> >> >>> The following package(s) may have failed to build (not necessarily >> >>> during this run of 'make all-start'): >> >>> >> >>> * package: r-3.4.4.p0 >> >>> log file: /Users/cbgroves2001/sage-8.3/logs/pkgs/r-3.4.4.p0.log >> >>> build directory: >> >>> /Users/cbgroves2001/sage-8.3/local/var/tmp/sage/build/r-3.4.4.p0 >> >>> >> >>> The build directory may contain configuration files and other potentially >> >>> helpful information. WARNING: if you now run 'make' again, the build >> >>> directory will, by default, be deleted. Set the environment variable >> >>> SAGE_KEEP_BUILT_SPKGS to 'yes' to prevent this. >> >>> >> >>> make[1]: *** [all-start] Error 1 >> >>> make: *** [all] Error 2 >> >>> >> >>> >> >>> macOS High Sierra >> >>> Version 10.13.6 >> >>> >> >>> Hardware Overview: >> >>> >> >>> Model Name:MacBook Pro >> >>> Model Identifier:MacBookPro8,1 >> >>> Processor Name:Intel Core i5 >> >>> Processor Speed:2.3 GHz >> >>> Number of Processors:1 >> >>> Total Number of Cores:2 >> >>> L2 Cache (per Core):256 KB >> >>> L3 Cache:3 MB >> >>> Memory:4 GB >> >>> Boot ROM Version:MBP81.0050.B00 >> >>> SMC Version (system):1.68f99 >> >>> Serial Number (system):C02FJ0KKDH2L >> >>> Hardware UUID:5D364BA2-FD44-538D-90A1-79C43365442E >> >>> Sudden Motion Sensor: >> >>> State:Enabled >> >>> >> >>> >> >>> >> >>> -- >> >>> 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. >> >>> To post to this group, send email to sage-s...@googlegroups.com. >> >>> Visit this group at https://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...@googlegroups.com. >> >> To post to this group, send email to sage-s...@googlegroups.com. >> >> Visit this group at https://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
Re: [sage-support] make: did it fail? (Sage 8.3)
Hi, I got the same error and I'm really new to all this, and this is probably a stupid question but what exactly do you mean by ' sanitize your PATH' ? On Sunday, October 14, 2018 at 11:22:45 PM UTC+5:30, Dima Pasechnik wrote: > > oops, sorry. You got a conflict with Anaconda install: > To fix this you probably need to sanitize your PATH > > indeed, your log says: > > > checking for curl-config... /Users/cbgroves2001/anaconda3/bin/curl-config > checking libcurl version ... 7.61.0 > checking curl/curl.h usability... yes > checking curl/curl.h presence... yes > checking for curl/curl.h... yes > checking if libcurl is version 7 and >= 7.22.0... no > configure: error: libcurl >= 7.22.0 library and headers are required > On Sun, Oct 14, 2018 at 5:43 PM Charles Groves > wrote: > > > > i updated command line tools just prior to running make > > > > On Sun, Oct 14, 2018 at 7:36 AM Dima Pasechnik > wrote: > >> > >> It looks as if your build got stuck waiting for something, and then got > unstuck. Even on such an old machine it should not take more than 8-10 > hours... > >> > >> I guess things related to R won't work in your install. It looks as if > your libcurl is broken. Do you by any chance need to update Command Line > Tools? > >> > >> > >> > >> On Sun, 14 Oct 2018, 11:59 , > > wrote: > >>> > >>> Make was still running fine after 24 hours. Then I forgot what I was > about and closed laptop's lid. Immediately re-opened laptop and found the > lines below. > >>> > >>> Sage runs and no longer crashes on "plot( x^2 )" like the .dmg version > did. > >>> > >>> So, did it fail? If so, what do I do? (Besides not closing my laptop > :( ) > >>> > >>> Thankyouthankyou. > >>> > >>> > >>> Last lines of output from make: > >>> > >>> *** > >>> Error building Sage. > >>> > >>> The following package(s) may have failed to build (not necessarily > >>> during this run of 'make all-start'): > >>> > >>> * package: r-3.4.4.p0 > >>> log file: /Users/cbgroves2001/sage-8.3/logs/pkgs/r-3.4.4.p0.log > >>> build directory: > /Users/cbgroves2001/sage-8.3/local/var/tmp/sage/build/r-3.4.4.p0 > >>> > >>> The build directory may contain configuration files and other > potentially > >>> helpful information. WARNING: if you now run 'make' again, the build > >>> directory will, by default, be deleted. Set the environment variable > >>> SAGE_KEEP_BUILT_SPKGS to 'yes' to prevent this. > >>> > >>> make[1]: *** [all-start] Error 1 > >>> make: *** [all] Error 2 > >>> > >>> > >>> macOS High Sierra > >>> Version 10.13.6 > >>> > >>> Hardware Overview: > >>> > >>> Model Name:MacBook Pro > >>> Model Identifier:MacBookPro8,1 > >>> Processor Name:Intel Core i5 > >>> Processor Speed:2.3 GHz > >>> Number of Processors:1 > >>> Total Number of Cores:2 > >>> L2 Cache (per Core):256 KB > >>> L3 Cache:3 MB > >>> Memory:4 GB > >>> Boot ROM Version:MBP81.0050.B00 > >>> SMC Version (system):1.68f99 > >>> Serial Number (system):C02FJ0KKDH2L > >>> Hardware UUID:5D364BA2-FD44-538D-90A1-79C43365442E > >>> Sudden Motion Sensor: > >>> State:Enabled > >>> > >>> > >>> > >>> -- > >>> 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 . > >>> To post to this group, send email to sage-s...@googlegroups.com > . > >>> Visit this group at https://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...@googlegroups.com . > >> To post to this group, send email to sage-s...@googlegroups.com > . > >> Visit this group at https://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...@googlegroups.com . > > To post to this group, send email to sage-s...@googlegroups.com > . > > Visit this group at https://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 https://grou
