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  • Maple can't find linear recurrence

    From Peter Luschny@21:1/5 to All on Mon Oct 9 08:20:51 2017
    restart: with(gfun):

    L := [1,2,5,8,13,18,25,31,41,49,61,71,85,97,113,126, 145,160,181,198,221,240,265,285,313,335,365,389,421, 447,481,508,545,574,613,644,685,718]:
    rec := listtorec(L, u(n));

    # Maple fails immediately, although there is a linear recurrence:

    recS := {-a(n)+2*a(n+2)-a(n+4)+a(n+8)-2*a(n+10)+a(n+12),a(0)=1,a(1)=2,a(2)=5, a(3)=8,a(4)=13,a(5)=18,a(6)=25,a(7)=31,a(8)=41,a(9)=49,a(10)=61,a(11)=71};
    r := rectoproc(recS, a(n), remember):
    seq(r(n), n=0..150);

    # I found this recurrence of order 12 'by hand'. Mathematica's
    # FindLinearRecurrence found this recurrence of order 11 from
    # the same data:

    # LinearRecurrence[ {1,1,-1,0,0,0,0,1,-1,-1,1} ,
    # {1, 2, 5, 8, 13, 18, 25, 31, 41, 49, 61}, 150]

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  • From G. A. Edgar@21:1/5 to Peter Luschny on Thu Oct 12 04:33:55 2017
    In article <[email protected]>,
    Peter Luschny <[email protected]> wrote:

    L := [1,2,5,8,13,18,25,31,41,49,61,71,85,97,113,126, 145,160,181,198,221,240,265,285,313,335,365,389,421, 447,481,508,545,574,613,644,685,718]:
    rec := listtorec(L, u(n));

    Maple 2015.2

    L := [1,2,5,8,13,18,25,31,41,49,61,71,85,97,113,126, 145,160,181,198,221,240,265,285,313,335,365,389,421, 447,481,508,545,574,613,644,685,718]:
    rec := gfun[listtorec](L, u(n));

    rec := [{-u(n) + u(n + 1) + u(n + 2) - u(n + 3) + u(n + 8)

    - u(n + 9) - u(n + 10) + u(n + 11), u(0) = 1, u(1) = 2,

    u(2) = 5, u(3) = 8, u(4) = 13, u(5) = 18, u(6) = 25, u(7) = 31,

    u(8) = 41, u(9) = 49, u(10) = 61}, ogf]

    --
    G. A. Edgar http://www.math.ohio-state.edu/~edgar/

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  • From Thomas Richard@21:1/5 to All on Fri Oct 13 00:14:19 2017
    Am Donnerstag, 12. Oktober 2017 12:33:58 UTC+2 schrieb G. A. Edgar:

    Maple 2015.2

    L := [1,2,5,8,13,18,25,31,41,49,61,71,85,97,113,126, 145,160,181,198,221,240,265,285,313,335,365,389,421, 447,481,508,545,574,613,644,685,718]:
    rec := gfun[listtorec](L, u(n));

    rec := [{-u(n) + u(n + 1) + u(n + 2) - u(n + 3) + u(n + 8)

    - u(n + 9) - u(n + 10) + u(n + 11), u(0) = 1, u(1) = 2,

    u(2) = 5, u(3) = 8, u(4) = 13, u(5) = 18, u(6) = 25, u(7) = 31,

    u(8) = 41, u(9) = 49, u(10) = 61}, ogf]

    To reproduce the result, one needs to insert

    gfun:-Parameters('maxordereqn'=11): # or higher; default value is 3

    I suppose you have such a setting in your initialization file.

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  • From Peter Luschny@21:1/5 to All on Tue Oct 17 12:42:23 2017
    Am Freitag, 13. Oktober 2017 09:14:19 UTC+2 schrieb Thomas Richard:
    one needs to insert
    gfun:-Parameters('maxordereqn'=11): # or higher; default value is 3

    Thanks for the advice Thomas, works for me!

    The default value 3 is ridiculously low and should be increased.

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  • From G. A. Edgar@21:1/5 to Peter Luschny on Wed Oct 18 07:59:43 2017
    In article <[email protected]>,
    Peter Luschny <[email protected]> wrote:

    Am Freitag, 13. Oktober 2017 09:14:19 UTC+2 schrieb Thomas Richard:
    one needs to insert
    gfun:-Parameters('maxordereqn'=11): # or higher; default value is 3

    Thanks for the advice Thomas, works for me!

    The default value 3 is ridiculously low and should be increased.




    Using gfun:=Parameters to set the value is deprecated.
    Instead do gfun[Parameters]('maxordereqn'=11) .
    Why is the default value 3? Perhaps because in 1994, when gfun
    was implemented, computers were much slower and had much less RAM.

    When I run Maple, gfun[Parameters] reports that maxordereqn has value
    infinity. It seems this is because I have installed the package
    "algolib" from http://algo.inria.fr/libraries/ ... which includes
    enhanced versions of the gfun library.

    I looked there today to write this reply. It seems the Algo team at
    INRIA closed in 2007. But download of algolib is still possible.

    --
    G. A. Edgar http://www.math.ohio-state.edu/~edgar/

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  • From Peter Luschny@21:1/5 to All on Fri Oct 20 04:15:40 2017
    Am Mittwoch, 18. Oktober 2017 15:59:46 UTC+2 schrieb G. A. Edgar:
    Why is the default value 3? Perhaps because in 1994, when gfun
    was implemented, computers were much slower and had much less RAM.

    I do understand that 23 years ago software was subject to other
    restrictions than today.

    What I don't understand is that MapleSoft does not take this fact
    into account.

    It seems this is because I have installed the package
    "algolib" from http://algo.inria.fr/libraries/ ... which includes
    enhanced versions of the gfun library.
    I looked there today to write this reply. It seems the Algo team at
    INRIA closed in 2007. But download of algolib is still possible.

    In other words, I do not understand how carelessly and indifferently
    MapleSoft handles this valuable module. Seemingly they do not even use
    the latest version 10 years after the last update.

    Thanks for hinting to "algolib"!

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  • From Axel Vogt@21:1/5 to Peter Luschny on Fri Oct 20 21:13:43 2017
    On 20.10.2017 13:15, Peter Luschny wrote:
    Am Mittwoch, 18. Oktober 2017 15:59:46 UTC+2 schrieb G. A. Edgar:
    Why is the default value 3? Perhaps because in 1994, when gfun
    was implemented, computers were much slower and had much less RAM.

    I do understand that 23 years ago software was subject to other
    restrictions than today.

    What I don't understand is that MapleSoft does not take this fact
    into account.

    It seems this is because I have installed the package
    "algolib" from http://algo.inria.fr/libraries/ ... which includes
    enhanced versions of the gfun library.
    I looked there today to write this reply. It seems the Algo team at
    INRIA closed in 2007. But download of algolib is still possible.

    In other words, I do not understand how carelessly and indifferently MapleSoft handles this valuable module. Seemingly they do not even use
    the latest version 10 years after the last update.

    Thanks for hinting to "algolib"!


    http://perso.ens-lyon.fr/bruno.salvy/software/the-gfun-package/
    for the standalone version of gfun, 3.76, July 2015

    Concurrent Maple uses 3.20 (not sure why - copyright discussions?)

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