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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
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setstep:
| | list of relevant locally closed sets
obtained from sequences of length bound+1
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- 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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