QI online calculation server help

Quadric 1/Quadric 2

Equations of the quadrics to intersect, either in affine form or
in homogeneous form, with integer coefficients. Example:

Affine form:x^2-2*y*z-9*y+8
Homogeneous form:x^2-2*x*z-9*y*w+8*w^2

These two fields can also be filled automatically (see Auto-fill).

Auto-fill by selecting the type of intersection

By selecting a type of intersection, the fields "Quadrics 1 and 2" are
automatically filled with two quadrics whose intersection is of the selected type.
The quadrics can then be modified by applying some random transformation (see Perturbation).


Applies some ``random'' transformation to the input quadrics without changing the type of the intersection. After transformation, the quadrics have coefficients of average size the specified perturbation value (for sufficiently large values).

Projective quadrics

In the output, recall the input quadrics in homogeneous/projective form, rather than in affine form.

Projective parameter

Ouput the parameterization using a real projective parameter (u, v) rather than a real parameter u.

Theoretical background

Please refer to the publications