#3867 Zeilberger summation bug

[dan hayes]

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build_info(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")build_info(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")

(kill(k,n,p,F),declare([k,n,p],integer),assume(k>-1,n>-1,p>-1),assume(p<n-k+1),load ("zeilberger")
,F(n,k):=binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k),t:Zeilberger(F(n,k),k,n),ln:length(part(t,1,2))
,disp(["F(n,k)"=binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k)]
,["part(t,1)",part(t,1),"part(t,1,1)",part(t,1,1),"part(t,1,2)",part(t,1,2),"length(part(t,1,2))",ln])
, dltkg:subst([k=ks+1,n=ns],part(t,1,1))*F(ns,ks+1)-subst([k=ks,n=ns],part(t,1,1))*F(ns,ks)
,tk:sum(subst([n=ns+i,k=ks],part(t,1,2)[i+1])*F(ns+i,ks),i,0,ln-1)
,fl:true,disp(["dltkg",(dltkg),"tk",tk]),for n thru 3 do for ps thru 3 do for k:-floor((2*ps+1)/2)-1 
thru n-ps do if ps-n+k-1#0 and 2*ps-2*n+2*k-1#0 and ps-n +k#0 and 2*ps-2*n+2*k+1#0 then(
t:subst([ns=n,p=ps,ks=k],dltkg-tk),if t#0 then(fl:false,disp(["n",n,"ps",ps,"k",k,"t",t]))),fl )
********************
comes back false not true for all param's examples
obviously dltkg should be equal tk by definition text A=B and maxima

[dan hayes]

don't know why it printed this one as it said it was not. If there is any wayto withdraw this i would and keep the #3868 which is same but more clear
On Friday, October 1, 2021, 04:39:53 AM CDT, dan hayes via Maxima-bugs maxima-bugs@lists.sourceforge.net wrote:

[bugs:#3867] maxima gives WRONG ans. for Zeilberger for simple example

Status: open
Group: None
Created: Fri Oct 01, 2021 09:39 AM UTC by dan hayes
Last Updated: Fri Oct 01, 2021 09:39 AM UTC
Owner: nobody

build_info(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")build_info(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")(version="branch_5_44_base_231_g5c411f69f",timestamp="2021-01-12 23:51:42",host="x86_64-w64-mingw32",lisp_name="SBCL",lisp_version="2.0.0",maxima_userdir="C:/Users/zmth1/maxima",maxima_tempdir="C:/Users/zmth1/AppData/Local/Temp",maxima_objdir="C:/Users/zmth1/maxima/binary/branch_5_44_base_231_g5c411f69f/sbcl/2_0_0",maxima_frontend="wxMaxima",maxima_frontend_version="20.12.2-DevelopmentSnapshot_MSW_OpenMP201511+Locks")
(kill(k,n,p,F),declare([k,n,p],integer),assume(k>-1,n>-1,p>-1),assume(p<n-k+1),load ("zeilberger")
,F(n,k):=binomial(2n+1,2p+2k+1)binomial(p+k,k),t:Zeilberger(F(n,k),k,n),ln:length(part(t,1,2))
,disp(["F(n,k)"=binomial(2n+1,2p+2k+1)binomial(p+k,k)]
,["part(t,1)",part(t,1),"part(t,1,1)",part(t,1,1),"part(t,1,2)",part(t,1,2),"length(part(t,1,2))",ln])
, dltkg:subst([k=ks+1,n=ns],part(t,1,1))F(ns,ks+1)-subst([k=ks,n=ns],part(t,1,1))F(ns,ks)
,tk:sum(subst([n=ns+i,k=ks],part(t,1,2)[i+1])F(ns+i,ks),i,0,ln-1)
,fl:true,disp(["dltkg",(dltkg),"tk",tk]),for n thru 3 do for ps thru 3 do for k:-floor((2ps+1)/2)-1
thru n-ps do if ps-n+k-1#0 and 2ps-2n+2k-1#0 and ps-n +k#0 and 2ps-2n+2k+1#0 then(
t:subst([ns=n,p=ps,ks=k],dltkg-tk),if t#0 then(fl:false,disp(["n",n,"ps",ps,"k",k,"t",t]))),fl )

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comes back false not true for all param's examples
obviously dltkg should be equal tk by definition text A=B and maxima

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[Robert Dodier]

Duplicate of #3868.