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D.6.11.9 displayMultsequence

Procedure from library hnoether.lib (see hnoether_lib).

Usage:
displayMultsequence(INPUT); INPUT list or poly

Assume:
INPUT is a bivariate polynomial, or the output of develop(f), resp. of extdevelop(develop(f),n), or (one entry of) the list of HN data computed by hnexpansion(f[,"ess"]), or the output of hnexpansion(f).

Return:
nothing

Display:
the sequence of multiplicities:
 
 - if INPUT=develop(f) or INPUT=extdevelop(develop(f),n) or INPUT=hne[i]:
                      a , b , c , ....... , 1
 - if INPUT=f or INPUT=hnexpansion(f) or INPUT=hne:
                      [(a_1, .... , b_1 , .... , c_1)],
                      [(a_2, ... ), ... , (... , c_2)],
                       ........................................ ,
                      [(a_n),(b_n), ....., (c_n)]
     with:
       a_1 , ... , a_n the sequence of multiplicities of the 1st branch,
       [...] the multiplicities of the j-th transform of all branches,
       (...) indicating branches meeting in an infinitely near point.

Note:
The Same restrictions as in multsequence apply for the input.
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:
 
LIB "hnoether.lib";
ring r=0,(x,y),dp;
// Example 1: Input = output of develop
displayMultsequence(develop(x3-y5));
==> The sequence of multiplicities is   3,2,1,1
// Example 2: Input = bivariate polynomial
displayMultsequence((x6-y10)*(x+y2-y3)*(x+y2+y3));
==> [(3,3,1,1)],
==> [(2,2,1,1)],
==> [(1,1),(1,1)],
==> [(1,1),(1),(1)],
==> [(1),(1),(1),(1)]
See also: develop; hnexpansion; multsequence; separateHNE.