randNicePencil -- sets up a random pencil of quadrics, and returns a hash table of the type RandomNicePencil.

i1 : kk=ZZ/101;

i2 : g=1;

i3 : L=randNicePencil(kk,g)

o3 = RandomNicePencil{...8...}

o3 : RandomNicePencil

i4 : keys L

o4 = {matFact1, matFact2, matFactu1, isotropicSpace, matFactu2,
     ------------------------------------------------------------------------
     quadraticForm, qqRing, baseRing}

o4 : List

i5 : L.qqRing

o5 = kk[x , y , z ..z , s, t]
         0   0   1   2

o5 : PolynomialRing

i6 : L.quadraticForm

              2      2                           2                       
o6 = x y s - z s - 5x t + 12x z t - 18y z t - 30z t - 12x z t + 10y z t +
      0 0     1      0       0 1       0 1       1       0 2       0 2   
     ------------------------------------------------------------------------
                 2
     6z z t - 48z t
       1 2       2

o6 : kk[x , y , z ..z , s, t]
         0   0   1   2

i7 : L.baseRing

o7 = kk[s, t]

o7 : PolynomialRing

i8 : (L.matFact1 * L.matFact2) - (L.quadraticForm)**id_(source L.matFact1)

o8 = 0

                                      8                               8
o8 : Matrix (kk[x , y , z ..z , s, t])  <-- (kk[x , y , z ..z , s, t])
                 0   0   1   2                   0   0   1   2

i9 : (L.matFact2 * L.matFact1) - (L.quadraticForm)**id_(source L.matFact1)

o9 = 0

                                      8                               8
o9 : Matrix (kk[x , y , z ..z , s, t])  <-- (kk[x , y , z ..z , s, t])
                 0   0   1   2                   0   0   1   2

i10 : L.isotropicSpace

o10 = | x_0 z_1 z_2 |

                                       1                               3
o10 : Matrix (kk[x , y , z ..z , s, t])  <-- (kk[x , y , z ..z , s, t])
                  0   0   1   2                   0   0   1   2

i11 : (L.matFactu1 * L.matFactu2) - (L.quadraticForm)**id_(source L.matFactu1)

o11 = 0

                                       4                               4
o11 : Matrix (kk[x , y , z ..z , s, t])  <-- (kk[x , y , z ..z , s, t])
                  0   0   1   2                   0   0   1   2

i12 : (L.matFactu2 * L.matFactu1) - (L.quadraticForm)**id_(source L.matFactu1)

o12 = 0

                                       4                               4
o12 : Matrix (kk[x , y , z ..z , s, t])  <-- (kk[x , y , z ..z , s, t])
                  0   0   1   2                   0   0   1   2