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quadraticForm -- part of a RandomNicePencil

Description

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 : setRandomSeed 0
 -- setting random seed to 0

o1 = 0
 
i2 : kk=ZZ/101;
 
i3 : g=1;
 
i4 : rNP=randNicePencil(kk,g);
 
i5 : S=rNP.qqRing;
 
i6 : qq=rNP.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 : S
 
i7 : q1=diff(S_(2*g+2), qq)

             2
o7 = x y  - z
      0 0    1

o7 : S
 
i8 : q2=diff(S_(2*g+3), qq)

         2                        2                                2
o8 = - 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

o8 : S
 
i9 : qq==S_(2*g+2)*q1+S_(2*g+3)*q2

o9 = true

See also

For the programmer

The object quadraticForm is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2448:0.