A constructive proof of the density of algebraic Pfaff equations without algebraic solutions
The author presents a constructive proof of Jouanolou's theorem, which was proved by using projective varieties, that the set of algebraic Pfaff equation without algebraic solution over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree. The author also constructs an example of a Pfaff equation with coefficients in the field of Gaussian numbers, that does not have any algebraic solutions. The construction is explicit and can be implemented as an algorithm.
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