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D.5.5.8 invariants

Procedure from library hnoether.lib (see hnoether_lib).

Usage:
invariants(L); L list

Assume:
L is the output of develop(f), or of extdevelop(develop(f),n), or one entry of the output of reddevelop(f).

Return:
list, if L contains a valid HNE:
 
    invariants(L)[1]:  intvec    (characteristic exponents)
    invariants(L)[2]:  intvec    (generators of the semigroup)
    invariants(L)[3]:  intvec    (Puiseux pairs, 1st components)
    invariants(L)[4]:  intvec    (Puiseux pairs, 2nd components)
    invariants(L)[5]:  int          (degree of the conductor)
    invariants(L)[6]:  intvec    (sequence of multiplicities)
an empty list, if L contains no valid HNE.

Example:
 
LIB "hnoether.lib";
ring exring=0,(x,y),dp;
list hne=develop(y4+2x3y2+x6+x5y);
==> h(0) = 1
==> a(1,2) = -1
==> h(1) = 2
==> a(2,2) = -1
==> a(2,3) = -2
list erg=invariants(hne);
erg[1];                   // the characteristic exponents
==> 4,6,7
erg[2];                   // the generators of the semigroup of values
==> 4,6,13
erg[3],erg[4];            // the Puiseux pairs in packed form
==> 3,7 2,2
erg[5] / 2;               // the delta-invariant
==> 8
erg[6];                   // the sequence of multiplicities
==> 4,2,2,1
// To display the invariants more 'nicely':
displayInvariants(hne);
==>  characteristic exponents  : 4,6,7
==>  generators of semigroup   : 4,6,13
==>  Puiseux pairs             : (3,2)(7,2)
==>  degree of the conductor   : 16
==>  delta invariant           : 8
==>  sequence of multiplicities: 4,2,2,1
See also: develop; displayInvariants; intersection; multsequence.


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