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 primadec(plist,vlist)

 primedec(plist,vlist)

:: Computes decompositions of ideals.
 return

 plist

list of polynomials
 vlist

list of variables

Function
primadec() and primedec are defined in `primdec'.

primadec() , primedec() are the function for primary
ideal decomposition and prime decomposition of the radical over the
rationals respectively.

The arguments are a list of polynomials and a list of variables.
These functions accept ideals with rational function coefficients only.

primadec returns the list of pair lists consisting a primary component
and its associated prime.

primedec returns the list of prime components.

Each component is a Groebner basis and the corresponding term order
is indicated by the global variables
PRIMAORD , PRIMEORD
respectively.

primadec implements the primary decompostion algorithm
in [Shimoyama,Yokoyama] .

If one only wants to know the prime components of an ideal, then
use
primedec because primadec may need additional costs
if an input ideal is not radical.
[84] load("primdec")$
[102] primedec([p*q*xq^2*y^2+q^2*y,p^2*x^2+p^2*x+p*q*y,
(q^3*y^42*q^3*y^3+q^3*y^2)*xq^3*y^4+q^3*y^3,
q^3*y^4+2*q^3*y^3+(q^3+p*q^2)*y^2],[p,q,x,y]);
[[y,x],[y,p],[x,q],[q,p],[x1,q],[y1,p],[(y1)*xy,q*y^22*q*yp+q]]
[103] primadec([x,z*y,w*y^2,w^2*yz^3,y^3],[x,y,z,w]);
[[[x,z*y,y^2,w^2*yz^3],[z,y,x]],[[w,x,z*y,z^3,y^3],[w,z,y,x]]]
 References

section
fctr , sqfr ,
section Setting term orderings.
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