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The values Q, P and R are often taken to be real numbers or complex numbers, but in fact, a quadric may be defined over any ring. In general, the locus of zeros of a set of polynomials is known as an algebraic variety, and is studied in the branch of algebraic geometry. — “Quadric - Wikipedia, the free encyclopedia”, en.wikipedia.org
In projective geometry a quadric is the set of points of a projective space where a certain quadratic form on the homogeneous coordinates becomes zero. It may also be defined as the set of all points that lie on their dual hyperplanes, under some projective duality of the space. Contents. — “Quadric (projective geometry) - Wikipedia, the free encyclopedia”, en.wikipedia.org
The 3-space, S, can be reconstructed again from the quadric, Q: the planes contained in Q fall into two equivalence classes, where planes in the same class meet in a point, and planes in different classes meet in a line or in the empty set. Let these classes be C and C'. — “Klein quadric - Wikipedia, the free encyclopedia”, en.wikipedia.org