lex_hensel_gsl, tolex_gsl, tolex_gsl_d

lex_hensel_gsl(plist,vlist1,order,vlist2,homo)

::Computation of an GSL form ideal basis

tolex_gsl(plist,vlist1,order,vlist2)

tolex_gsl_d(plist,vlist1,order,vlist2,procs)

:: Computation of an GSL form ideal basis stating from a Groebner basis

return

list

plist vlist1 vlist2 procs

list

order

number, list or matrix

homo

flag

• lex_hensel_gsl() and lex_hensel() are variants of tolex_gsl() and tolex() respectively. The results are Groebner basis or a kind of ideal basis, called GSL form. tolex_gsl_d() does basis computations in parallel on child processes specified in procs.
• If the input is zero-dimensional and a lex order Groebner basis has the form [f0,x1-f1,...,xn-fn] (f0,...,fn are univariate polynomials of x0; SL form), then this these functions return a list such as [[x1,g1,d1],...,[xn,gn,dn],[x0,f0,f0']] (GSL form). In this list gi is a univariate polynomial of x0 such that di*f0'*fi-gi divides f0 and the roots of the input ideal is [x1=g1/(d1*f0'),...,xn=gn/(dn*f0')] for x0 such that f0(x0)=0. If the lex order Groebner basis does not have the above form, these functions return a lex order Groebner basis computed by tolex().
• Though an ideal basis represented as GSL form is not a Groebner basis we can expect that the coefficients are much smaller than those in a Groebner basis and that the computation is efficient. The CPU time shown after an execution of tolex_gsl_d() indicates that of the master process, and it does not include the time in child processes.

[103] K=katsura(5)$
[104] V=[u5,u4,u3,u2,u1,u0]$
[105] G0=gr(K,V,0)$
[106] GSL=tolex_gsl(G0,V,0,V)$ 
[107] GSL[0];
[u1,8635837421130477667200000000*u0^31-...]
[108] GSL[1];
[u2,10352277157007342793600000000*u0^31-...]
[109] GSL[5];
[u0,11771021876193064124640000000*u0^32-...,
376672700038178051988480000000*u0^31-...]

References

section lex_hensel, lex_tl, tolex, tolex_d, tolex_tl, section Distributed computation

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