isARandomFiberSmooth -- Test whether a random fiber is smooth

Synopsis

• Usage:

  b=isARandomFiberSmooth(I,J1,family)

• Inputs:
  • I, an ideal, semigroup ideal
  • J1, an ideal, flatness relations among the parameters
  • family, a matrix, a flat family
• Optional inputs:
  • BaseField
  • Verbose => ..., default value false
• Outputs:
  • b, a Boolean value, true if a random fiber is smooth, false otherwise

Description

i1 : L={6,8,10,11}

o1 = {6, 8, 10, 11}

o1 : List

i2 : genus L

o2 = 9

i3 : (I,J1,family)=getFlatFamily(L,0.30,0);

i4 : isARandomFiberSmooth(I,J1,family)

o4 = true

i5 : SA=ring family

o5 = SA

o5 : PolynomialRing

i6 : transpose family

o6 = {-16} | x_2^2-x_0x_4+x_0a_{0, 1}-a_{1, 3}^2+x_2a_{0, 2}-a_{1, 3}a_{0, 2}
     {-18} | x_0^3-x_2x_4+x_0a_{1, 1}+x_2a_{1, 2}+x_4a_{1, 3}-a_{1, 2}a_{1, 3
     {-20} | x_0^2x_2-x_4^2+x_2a_{1, 1}+x_4a_{1, 2}+x_4a_{0, 1}-a_{1, 2}a_{0,
     {-22} | x_0^2x_4-x_5^2+a_{3, 0}+x_0a_{3, 1}+x_2a_{3, 2}+x_4a_{3, 3}+x_5a
     ------------------------------------------------------------------------
                                                                       |
     }                                                                 |
      1}+x_0^2a_{1, 3}+a_{1, 1}a_{1, 3}+x_0^2a_{0, 2}+a_{1, 1}a_{0, 2} |
     _{3, 4}+x_0^2a_{3, 5}+x_0x_2a_{3, 6}                              |

              4       1
o6 : Matrix SA  <-- SA

See also

• makeUnfolding -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• flatteningRelations -- Compute the flattening relations of an unfolding
• getFlatFamily -- Compute the flat family depending on a subset of parameters of the universal unfolding