Singular Manual: nashmult

  | #### D.6.2.1 nashmult Procedure from library `arcpoint.lib` (see arcpoint_lib). Usage: nashmult(f,bound); f polynomial, bound positive integer Create: allsteps:
               a list containing all relevant locally closed sets
               up to order <bound> and their sequences of
               Nash Multiplicities
  setstep:
               list of relevant locally closed sets
               obtained from sequences of length bound+1
Return: ring, original basering with additional variables t and coefficients up to t^<bound> Example:
    LIB "arcpoint.lib";
    ring r=0,(x,y,z),dp;
    poly f=z4+y3-x2;
    def R=nashmult(f,2);
    setring R;
    allsteps;
    ==> [1]:
    ==>    [1]:
    ==>       [1]:
    ==>          2,2
    ==>       [2]:
    ==>          _[1]=a(1)
    ==>          _[2]=b(1)
    ==>       [3]:
    ==>          _[1]=1
    ==> [2]:
    ==>    [1]:
    ==>       [1]:
    ==>          2,2,1
    ==>       [2]:
    ==>          _[1]=a(1)
    ==>          _[2]=b(1)
    ==>          _[3]=c(1)^4-a(2)^2
    ==>       [3]:
    ==>          _[1]=a(1)
    ==>          _[2]=b(1)
    ==>          _[3]=c(1)
    ==>          _[4]=a(2)
    ==>    [2]:
    ==>       [1]:
    ==>          2,2,2
    ==>       [2]:
    ==>          _[1]=a(1)
    ==>          _[2]=b(1)
    ==>          _[3]=c(1)
    ==>          _[4]=a(2)
    ==>       [3]:
    ==>          _[1]=1

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