Singular Manual: displayMultsequence

  | #### D.6.15.9 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.

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