Re: Polresultant bug ?

[simon <simon@math.unicaen.fr>]

Hi,

This is not a problem of polresultant, but of precision in your 
computations.

Indeed, the coefficients of your annulator_for_c have about 80 digits.
In order to have a coherent result, you have to do your computations with 
a number of digits significatively larger than 80.
Try for example 2*80 = 160.

Denis SIMON.



On Wed, 18 Dec 2013, Ewan Delanoy wrote:

>   Hello all,
>
>   it seems I found an example where according to GP, the resultant of two
> expressions that evaluate
> to zero gives an expression that evaluate to a nonzero (and in fact, huge)
> value.
>   Below I paste both the source code and the output I got.
>   Thanks in advance for any help,
>
>   Ewan
>
>
> /****************************************************************************
> ********** */
> /*The source code */
> /****************************************************************************
> ********** */
>
> annulator_for_a=256*a^12 - 363776*a^10 + 193847136*a^8 - 46812817968*a^6 +
> 4719167653697*a^4 - 114005664356542*a^2 + 1412780238606961
> floating_a=polroots(annulator_for_a)[1]
> annulator_for_b=b^6 - 108*b^4 + 2684*b^2 - 59536
> floating_b=real(polroots(annulator_for_b)[2])
> floating_c=floating_a-floating_b
> term1=subst(annulator_for_a,a,b+c)
> should_be_zero1=subst(subst(term1,b,floating_b),c,floating_c)
> annulator_for_c=polresultant(term1,annulator_for_b,b)
> should_be_zero2=subst(annulator_for_c,c,floating_c)
>
> /****************************************************************************
> ********** */
> /*The output  */
> /****************************************************************************
> ********** */
>
> MacBook-Pro-de-Ewan:~ ewandelanoy$ gp
>                   GP/PARI CALCULATOR Version 2.5.3 (released)
>           i386 running darwin (x86-64/GMP-5.0.4 kernel) 64-bit version
> compiled: Jan 24 2013, gcc-4.2.1 (Based on Apple Inc. build 5658) (LLVM
> build 2336.11.00)
>                  (readline v6.2 enabled, extended help enabled)
>
>                      Copyright (C) 2000-2011 The PARI Group
>
> PARI/GP is free software, covered by the GNU General Public License, and
> comes
> WITHOUT ANY WARRANTY WHATSOEVER.
>
> Type ? for help, \q to quit.
> Type ?12 for how to get moral (and possibly technical) support.
>
> parisize = 8000000, primelimit = 500509
> ? annulator_for_a=256*a^12 - 363776*a^10 + 193847136*a^8 - 46812817968*a^6 +
> 4719167653697*a^4 - 114005664356542*a^2 + 1412780238606961
> %1 = 256*a^12 - 363776*a^10 + 193847136*a^8 - 46812817968*a^6 +
> 4719167653697*a^4 - 114005664356542*a^2 + 1412780238606961
> ? floating_a=polroots(annulator_for_a)[1]
> %2 = 16.507639886376369964102375152715808868 -
> 1.1732991791154715940767062706818971012*I
> ? annulator_for_b=b^6 - 108*b^4 + 2684*b^2 - 59536
> %3 = b^6 - 108*b^4 + 2684*b^2 - 59536
> ? floating_b=real(polroots(annulator_for_b)[2])
> %4 = 9.1973372100322392595456421736424968201
> ? floating_c=floating_a-floating_b
> %5 = 7.3103026763441307045567329790733120478 -
> 1.1732991791154715940767062706818971012*I
> ? term1=subst(annulator_for_a,a,b+c)
> %6 = 256*b^12 + 3072*c*b^11 + (16896*c^2 - 363776)*b^10 + (56320*c^3 -
> 3637760*c)*b^9 + (126720*c^4 - 16369920*c^2 + 193847136)*b^8 + (202752*c^5 -
> 43653120*c^3 + 1550777088*c)*b^7 + (236544*c^6 - 76392960*c^4 +
> 5427719808*c^2 - 46812817968)*b^6 + (202752*c^7 - 91671552*c^5 +
> 10855439616*c^3 - 280876907808*c)*b^5 + (126720*c^8 - 76392960*c^6 +
> 13569299520*c^4 - 702192269520*c^2 + 4719167653697)*b^4 + (56320*c^9 -
> 43653120*c^7 + 10855439616*c^5 - 936256359360*c^3 + 18876670614788*c)*b^3 +
> (16896*c^10 - 16369920*c^8 + 5427719808*c^6 - 702192269520*c^4 +
> 28315005922182*c^2 - 114005664356542)*b^2 + (3072*c^11 - 3637760*c^9 +
> 1550777088*c^7 - 280876907808*c^5 + 18876670614788*c^3 -
> 228011328713084*c)*b + (256*c^12 - 363776*c^10 + 193847136*c^8 -
> 46812817968*c^6 + 4719167653697*c^4 - 114005664356542*c^2 +
> 1412780238606961)
> ? should_be_zero1=subst(subst(term1,b,floating_b),c,floating_c)
> %7 = 9.556391613824554411 E-22 - 3.105697067803841053 E-22*I
> ? annulator_for_c=polresultant(term1,annulator_for_b,b)
> %8 = 281474976710656*c^72 - 2764647221252063232*c^70 +
> 12881090734407523762176*c^68 - 37900879189576872787705856*c^66 +
> 79099815954946491364482744320*c^64 - 124684759166630772970798278770688*c^62
> + 154348991980763936851992593913872384*c^60 -
> 154045742043145589406276188287109431296*c^58 +
> 126278018863764650417996510658035946881024*c^56 -
> 86188295361347830927179212093084919761207296*c^54 +
> 49478930044049671150743174794661019965550755840*c^52 -
> 24074514186962292770585768259851360789778778816512*c^50 +
> 9984746464975367599334473741516071684995601427070976*c^48 -
> 3544601773895860008395886389523866780061142280317173760*c^46 +
> 1080184220852605057051843703838564046424092897453830832128*c^44 -
> 283063744081987480169735131103108552441984386863102852857856*c^42 +
> 63829717334668411467356121108379367011430103612372083744374784*c^40 -
> 12380931236742739255452291376833192852560602832000266561304526848*c^38 +
> 2062669465587519366960798626747033680113649744703395573266979635200*c^36 -
> 294342896040799822278685004581163889813837967268955216247392575873024*c^34 +35822170668621222716189038834945741067330091385125921979038859956748800*c^3
> 2 -3694599094972804492903490053128068674286670925141467454235954938531409408*c
> ^30 +319960240851023753657282679654500912353276531225489928628714114061458570560
> *c^28 -229523124348646894674693749507943423678604971743540760886488234477385582240
> 32*c^26 +133540122622880453154192069395728174480573210717450941020933452226076490321
> 5361*c^24 -608091485575824049928810016694298694113579523852570953890936245732723388993
> 76068*c^22 +201756641433254568341552129401331699270034937209354126404620590151755348180
> 8626562*c^20 -396135443048892631637411626519338142317965576647394035113621469768341039106
> 76919316*c^18 -830734957146435644175388145522917471286550249793111950753257626172855716538
> 76743441*c^16 +332312675119643619106768952565308776883182037008020918543610524912665691806
> 88206374776*c^14 -990437872605966242896879211543870708900639163340555827418555490651344092124
> 153842082212*c^12 +932912335531598587420267492196329214620107896529499931168264848122095697606
> 4727122600216*c^10 +175291809114698568461616198975915940771681390157547657579559269812558585841
> 725448099842799*c^8 -551646020293422160604256097389154281421501271527752864787625977318114545794
> 3877549960013748*c^6 +418288683874030712474395958976663314737499086339637924696074115753271457709
> 62254753636273922*c^4 +839876356297955607038827371458654374227011532016895487424475243901159477944
> 48018764725358492*c^2 +503773428948680856170140977878135888394567173775246602443797048650457162370
> 78210026453561601
> ? should_be_zero2=subst(annulator_for_c,c,floating_c)
> %9 = 2.2768496195346216922 E60 - 5.226873626511962736 E59*I
>
>
>
>
>  
>