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D.4.15.4 HomJJ

Procedure from library normal.lib (see normal_lib).

Usage:
HomJJ (Li); Li = list: ideal SBid, ideal id, ideal J, poly p

Assume:
R = P/id, P = basering, a polynomial ring, id an ideal of P,
SBid = standard basis of id,
J = ideal of P containing the polynomial p,
p = nonzero divisor of R

Compute:
Endomorphism ring End_R(J)=Hom_R(J,J) with its ring structure as affine ring, together with the map R --> Hom_R(J,J) of affine rings, where R is the quotient ring of P modulo the standard basis SBid.

Return:
a list l of three objects
 
         l[1] : a polynomial ring, containing two ideals, 'endid' and 'endphi'
               such that l[1]/endid = Hom_R(J,J) and
               endphi describes the canonical map R -> Hom_R(J,J)
         l[2] : an integer which is 1 if phi is an isomorphism, 0 if not
         l[3] : an integer, = dim_K(Hom_R(J,J)/R) (the contribution to delta)
                if the dimension is finite, -1 otherwise

Note:
printlevel >=1: display comments (default: printlevel=0)

Example:
 


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