primedec_mod

primedec_mod(plist,vlist,ord,mod,strategy)

:: Computes decompositions of ideals over small finite fields.

return

plist

list of polynomials

vlist

list of variables

ord

number, list or matrix

mod

positive integer

strategy

integer

• Function primedec_mod() is defined in `primdec_mod' and implements the prime decomposition algorithm in [Yokoyama].
• primedec_mod() is the function for prime ideal decomposition of the radical of a polynomial ideal over small finite field, and they return a list of prime ideals, which are associated primes of the input ideal.
• primedec_mod() gives the decomposition over GF(mod). The generators of each resulting component consists of integral polynomials.
• Each resulting component is a Groebner basis with respect to a term order specified by [vlist,ord].
• If strategy is non zero, then the early termination strategy is tried by computing the intersection of obtained components incrementally. In general, this strategy is useful when the krull dimension of the ideal is high, but it may add some overhead if the dimension is small.
• If you want to see internal information during the computation, execute dp_gr_print(2) in advance.

[0] load("primdec_mod")$
[246] PP444=[x^8+x^2+t,y^8+y^2+t,z^8+z^2+t]$
[247] primedec_mod(PP444,[x,y,z,t],0,2,1);
[[y+z,x+z,z^8+z^2+t],[x+y,y^2+y+z^2+z+1,z^8+z^2+t],
[y+z+1,x+z+1,z^8+z^2+t],[x+z,y^2+y+z^2+z+1,z^8+z^2+t],
[y+z,x^2+x+z^2+z+1,z^8+z^2+t],[y+z+1,x^2+x+z^2+z+1,z^8+z^2+t],
[x+z+1,y^2+y+z^2+z+1,z^8+z^2+t],[y+z+1,x+z,z^8+z^2+t],
[x+y+1,y^2+y+z^2+z+1,z^8+z^2+t],[y+z,x+z+1,z^8+z^2+t]]
[248] 

References

section modfctr, section dp_gr_main, dp_gr_mod_main, dp_gr_f_main, dp_weyl_gr_main, dp_weyl_gr_mod_main, dp_weyl_gr_f_main, section Setting term orderings, section dp_gr_flags, dp_gr_print.

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