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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)

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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