Re: Is it possible to have several solutions in this way to this equation using Pari/ɢᴘ ?

[Laël Cellier <lael.cellier@laposte.net>]

Oui,

though it's true that time I used other more realistic parameters :
W=12438004062870150805985824702300829514410173439660932918536027933446793260856267466480836262233660219588987800746377618726093321822700238758702807937443158
c=4345239080824721190894169987815515575661330628540244556591209268566599842619559261226882765017761513946222422087647459870182058982895830694688719459939065090964555730674172809284571116420301134105356512590662065687450286780201121619907874241872348312178678962946180853503382813158994122023834030506210934146950730335961460530387633015593126701639832578742054622455262653444291835566869384321981019286323849631079678501184087982129951534843448939516611078558328816741047044014952080994413347989832544600053109756157191573630652293099275168552229771930167724964304634802834765358080780263538603018581479364959678360495569
V=25
f=1
b=672225628067123147116558149881995710798276995011447987050592328976012714865450985916447995662328919412047497279423045117446686729257128275949500746711043539189609725096112283848011986679159419553919508258509140939280500687680096737399531725624206572451821801127194059612210107252008495654751179194156314087179604128231565028033956354284599827623105506753176633926911713425185713779171315276262107447531504708473972729375105320057836498161030991644012650913993856801096153646999371792888290083986221329352989125748813940274976373895395812973914959320432965507828213792019827258803534256546308413647072827145489240887133613964672582561783150543532894610277494904922885667981168421365684201818690509788680019717332275925513478852164737660971344539051206444984192470274604219167707476386543960680385929829179479402230347862231026387872217799903692210388580045747193829740200677896152713759174914475170921132879055170900968153555891

which gives :
alpha=310950101571753770149645617557520737860254335991523322963400698336169831521406686662020906555841505489724695018659440468152333045567505968967570198436078950
if beta=0

and in which case I didn’t found a positive value of beta for which 
nfroots returns a non‑empty value. Only value of 0 to beta seems to 
leads to a nfroot

Though I’d like to find other nfroots values given such initial inputs…
Cordialement,
Le 23/01/2025 à 20:17, Bill Allombert a écrit :
> On Thu, Jan 23, 2025 at 02:06:53PM +0100, Laël Cellier wrote:
> > Bonjour,
> >
> > I might can set beta to any values, but then it seems nfroots returns
> > nothing for the second equation. Are you meaning then the second equation
> > should be solved by other means ?
> No. with the parameters V=25 c=60 W=3 b=85 f=-1, nfroots should not fail.
> Please give an example.
>
> In general, always provides an example when asking a question.
>
> Cheers,
> Bill