the polynomial that represents a pencil of quadrics qq=s*q1+t*q2 with a fixed isotropic subspace and a fixed corank one quadric in normal form q1.
i1 : kk=ZZ/101; |
i2 : g=1; |
i3 : rNP=randNicePencil(kk,g); |
i4 : S=rNP.qqRing; |
i5 : qq=rNP.quadraticForm 2 2 2 2 o5 = x y s - z s - 5x t + 12x z t - 18y z t - 30z t - 12x z t + 10y z t + 6z z t - 48z t 0 0 1 0 0 1 0 1 1 0 2 0 2 1 2 2 o5 : S |
i6 : q1=diff(S_(2*g+2), qq) 2 o6 = x y - z 0 0 1 o6 : S |
i7 : q2=diff(S_(2*g+3), qq) 2 2 2 o7 = - 5x + 12x z - 18y z - 30z - 12x z + 10y z + 6z z - 48z 0 0 1 0 1 1 0 2 0 2 1 2 2 o7 : S |
i8 : qq==S_(2*g+2)*q1+S_(2*g+3)*q2 o8 = true |
The object quadraticForm is a symbol.