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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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