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D.6.9.6 invariants
Procedure from library hnoether.lib (see hnoether_lib).
- Usage:
- invariants(INPUT); INPUT list or poly
- Assume:
INPUT is the output of develop(f) , or of
extdevelop(develop(f),n) , or one entry of the list of HN data
computed by hnexpansion(f[,"ess"]) .
- Return:
- list
INV of the following format:
| INV[1]: intvec (characteristic exponents)
INV[2]: intvec (generators of the semigroup)
INV[3]: intvec (Puiseux pairs, 1st components)
INV[4]: intvec (Puiseux pairs, 2nd components)
INV[5]: int (degree of the conductor)
INV[6]: intvec (sequence of multiplicities)
| If INPUT contains no valid HN expansion, the empty list is
returned.
- Assume:
INPUT is a bivariate polynomial f, or the output of
hnexpansion(f) , or the list of HN data computed by
hnexpansion(f [,"ess"]) .
- Return:
- list
INV , such that INV[i] coincides with the output of
invariants(develop(f[i])) , where f[i] is the i-th branch of
f, and the last entry of INV contains further invariants of
f in the format:
| INV[last][1] : intmat (contact matrix of the branches)
INV[last][2] : intmat (intersection multiplicities of the branches)
INV[last][3] : int (delta invariant of f)
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- Note:
- In case the Hamburger-Noether expansion of the curve f is needed
for other purposes as well it is better to calculate this first
with the aid of
hnexpansion and use it as input instead of
the polynomial itself.
Example:
See also:
develop;
displayInvariants;
hnexpansion;
intersection;
multsequence.
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