isPrime(Ideal) -- whether an ideal is prime

• Function: isPrime

• Usage:

  isPrime I

• Inputs:
  • I, an ideal, in a polynomial ring or quotient of one
• Optional inputs:
  • Strategy => a string, default value null, See minimalPrimes(...,Strategy=>...)
  • Verbosity => an integer, default value 0, See minimalPrimes(...,Verbosity=>...)
  • SquarefreeFactorSize
• Outputs:
  • a Boolean value, true if I is a prime ideal, or false otherwise

i1 : R = QQ[a..d];

i2 : I = monomialCurveIdeal(R, {1, 5, 8})

               2    2      3    2 2   3     3    5        3   5    4
o2 = ideal (a*c  - b d, b*c  - a d , b c - a d, c  - a*b*d , b  - a c)

o2 : Ideal of R

i3 : isPrime I

o3 = true