Re: galoisinit for large nilpotent groups

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Jul 12, 2019 at 04:38:45PM +0200, Bill Allombert wrote:
> Dear PARI developers,
> 
> I have pushed to master my new algorithm for galoisinit for nilpotent
> groups. The function should detect automatically the group is nilpotent
> automatically.
> 
> For nilpotent group of order larger than 100, this should be much faster
> than the previous algorithm.

For example for this degree-1024 polynomial, galoisinit() only takes
18h, 40min.

Q = a^1024 + 58643972510162897024*a^960 + 953121177124315103077053936794421927424*a^896 + 4068207433921716019631245118243640589730947826069445173248*a^832 + 2821563613469046330999077180980175589758180254847173626467399569715032604672*a^768 + 154757891589186883540207537884471023732973488442209092734240890205972340065777942556907667456*a^704 + 302953632898279131367289499068092017653991383206934773810458457636069990692578017787120132221402569435512832*a^640 + 8976371593211837458216294012752140319375836171379010641513515819939888218519186426503470237284012950203166105574846758912*a^576 + 1530624623504532981320269635094610824386103374469988633276352927111217371881063301861520982590669394912660074593400883383502033125376*a^512 + 483725772279351160315757602217050346484593988064428657479656818183143304621365252020822713464388359870699904732690988334234614239475192037376*a^448 + 71304204506023564005377553106051506321585679812407266583665043058495720306663436297745999605953853000254897556122203484682716363628790009787580416*a^384 + 845723088553198380443236815896426627565126162317637725387115273053128720641592510604678159762906867707672185479309987533215714717191790069226143744*a^320 + 75451547378494384076507501123216249601020148791297234942167344834686504065718562350535216776448827188188008075316656095253535088897619285508096*a^256 + 1598988510865112282966739950805218283886934224606035449804767242692300488128129730205398082322829947881584296758029764392703682936832*a^192 + 28011051684777650753200589844915108319476466407761241639572326207807735498849258158203985652295821969274171293696*a^128 + 4694396094797648169202831171947332990536556022341054431616572945204963553837056*a^64 + 281474976710656;

Cheers,
Bill.