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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