heuristicSmoothness -- Check whether an affine curve is smooth

Synopsis

• Usage:

  b=heuristicSmoothness c

• Inputs:
  • c, an ideal, of an affine curve
• Optional inputs:
  • BaseField
  • Verbose => ..., default value false
• Outputs:
  • b, a Boolean value, true if the computation showes that c is smooth false otherwise

Description

i1 : kk=ZZ/2; S=kk[x_0..x_3]

o2 = S

o2 : PolynomialRing

i3 : setRandomSeed "some singular and some smooth curves";

i4 : elapsedTime tally apply(10,i-> (
             c=minors(2,random(S^2,S^{3:-2}));
             c=sub(c,x_0=>1);
             R=kk[support c];c=sub(c,R);
             heuristicSmoothness c))
 -- 1.96215s elapsed

o4 = Tally{false => 6}
           true => 4

o4 : Tally