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 dp_gr_main(plist,vlist,homo,modular,order)

 dp_gr_mod_main(plist,vlist,homo,modular,order)

:: Groebner basis computation (builtin functions)
 return

list
 plist, vlist

list
 order

number, list or matrix
 homo

flag
 modular

flag or prime

These functions are fundamental builtin functions for Groebner basis
computation and
gr()
,hgr()
and gr_mod()
are all interfaces to these functions.

If homo is not equal to 0, homogenization is applied before entering
Buchberger algorithm

For
dp_gr_mod_main()
, modular means a computation over
GF(modular).
For dp_gr_main()
, modular has the following mean.

If modular is 1 , trace lifting is used. Primes for trace lifting
are generated by
lprime()
, starting from lprime(0)
, until
the computation succeeds.

If modular is an integer greater than 1, the integer is regarded as a
prime and trace lifting is executed by using the prime. If the computation
fails then 0 is returned.

If modular is negative, the above rule is applied for modular
but the Groebner basis check and idealmembership check are omitted in
the last stage of trace lifting.

gr(P,V,O)
, hgr(P,V,O)
and gr_mod(P,V,O,M)
execute
dp_gr_main(P,V,0,1,O)
, dp_gr_main(P,V,1,1,O)
and dp_gr_mod_main(P,V,0,M,O)
respectively.

Actual computation is controlled by various parameters set by
dp_gr_flags()
, other then by homo and modular.
 References

section
dp_ord
,
section dp_gr_flags
, dp_gr_print
,
section gr
, hgr
, gr_mod
, dgr
,
section Controlling Groebner basis computations
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