D.5.5.10 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), or of extdevelop(develop(f),n), or of of hnexpansion(f[,"ess"]), or (one entry in) the list hne of the ring created by hnexpansion(f[,"ess "]).

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[,"ess"]) 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 transformed of all branches, (...) indicating branches meeting in an infinitely near point.

Note:

The same restrictions for INPUT as in multsequence apply.
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";
// ------ the example starts here -------
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.