the keys are qqRing => S, quadraticForm => a pencil of quadrics qq=s*q1+t*q2, baseRing => R = kk[s,t], isotropicSpace => u, matFact1 => M1, matFact2 => M2, matFactu1 => Mu1, matFactu2 => Mu2,
The object RandomNicePencil is a type, with ancestor classes MutableHashTable < HashTable < Thing.