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### `primadec`, `primedec`

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*x-q^2*y^2+q^2*y,-p^2*x^2+p^2*x+p*q*y,
(q^3*y^4-2*q^3*y^3+q^3*y^2)*x-q^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],[x-1,q],[y-1,p],[(y-1)*x-y,q*y^2-2*q*y-p+q]]
[103] primadec([x,z*y,w*y^2,w^2*y-z^3,y^3],[x,y,z,w]);
[[[x,z*y,y^2,w^2*y-z^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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