I remark on solving for the radical roots of f(x) in Z[x]? We need all solution (g,h) to f divides g(h(x)) which I call the ideal decompositon problem. This - by Casperson, Ford, & McKay - is in:
Casperson, D., Ford, D., McKay, J., Ideal Decompositions and Subfields. J. Symbolic Computation, J.Symb.Comp., 21,133-137, (1996). where we use lattice reduction. Thanks, John McKay On Wed, 8 May 2013, Andreas Distler wrote: > Dear Daniel, > > I cannot reproduce your problem. Which version of PARI/GP are you using? > > Anyway, you can use the function SetPariStackSize from the Alnuth > package to increase the amount of memory PARI/GP will use. The function > takes a positive integer as argument specifying the amount of memory in > MB. The default value is 128 MB as you may have guessed. > > It's an oversight that SetPariStackSize is not documented. I will change > this in the next version of Alnuth. Thanks for pointing me to this > shortcoming. > > Best wishes, > > Andreas > > On 07/05/13 21:31, Daniel Blazewicz wrote: > > Hi, > > > > I use RootsOfPolynomialAsRadicals from RadiRoot package to compute roots of > > some simple polynomials of degree 5 and 6. In many cases mentioned method > > works excellent and produces very nice formulas. However for few specific > > polynomials it fails with stack overflow error. This is fully deterministic > > behavior on my environment, e.g. for f(x) = x^6+30*x+93 : > > > > > > ┌───────┐ GAP, Version 4.6.2 of 02-Feb-2013 (free software, GPL) > > │ GAP │ http://www.gap-system.org > > └───────┘ Architecture: i686-pc-linux-gnu-gcc-default32 > > Libs used: gmp, readline > > Loading the library and packages ... > > Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0 > > Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, Browse > > 1.8.2, CRISP 1.3.5, Cryst 4.1.11, CrystCat 1.1.6, CTblLib 1.2.1, > > FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO 4.2, IRREDSOL > > 1.2.1, LAGUNA 3.6.3, Polenta 1.3.1, Polycyclic 2.10.1, RadiRoot 2.6, > > ResClasses 3.3.0, Sophus 1.23, TomLib 1.2.2 > > Try '?help' for help. See also '?copyright' and '?authors' > > gap> x := Indeterminate( Rationals, "x" );; > > gap> f := UnivariatePolynomial( Rationals, [93,30,0,0,0,0,1]);; > > gap> RootsOfPolynomialAsRadicals(f, "latex", "x6_30x_93");; > > *** at top-level: ...n(),[2,4,3])>=0,fac=lift(nffactor(f,pol)),if( > > *** ^-------------------- > > *** nffactor: the PARI stack overflows ! > > current stack size: 128000000 (122.070 Mbytes) > > [hint] you can increase GP stack with allocatemem() > > > > *** at top-level: for(i=1,#fac[,1],for(j=1,fac[i,2 > > *** ^-------------------- > > *** _[,_]: not a matrix. > > Error, List Element: <list>[1] must have an assigned value in > > faktoren[1] := lcoeff * faktoren[1]; called from > > FactorsPolynomialPari( AlgExtEmbeddedPol( H, poly ) ) called from > > FactorsPolynomialAlgExt( erw.H, CyclotomicPolynomial( Rationals, i ) ) > > called from > > RR_RootOfUnity( erw, DegreeOverPrimeField( erw.K ) ) called from > > CallFuncList( RootsOfPolynomialAsRadicalsNC, arg ) called from > > <function "RootsOfPolynomialAsRadicals">( <arguments> ) > > called from read-eval loop at line 3 of *stdin* > > you can 'return;' after assigning a value > > brk> > > > > > > Other examples: > > f(x) = x^6+105*x+237 > > f(x) = x^6+243*x+513 > > > > I don't know how to work around this problem. Tried to increase workspace > > size but it did not solve the issue. I will be grateful for your help. > > > > With regards, > > Daniel > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
