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A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties to the real numbers.
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The following tables list the computational complexity of various algorithms for common mathematical operations.
Henri Cohen is a number theorist, and a professor at the University of Bordeaux. He is best known for leading the team that created the PARI/GP computer algebra system. He introduced the Rankin–Cohen bracket and has written several textbooks in computational and algebraic number theory.
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In mathematics, a fundamental discriminantD is an integer invariant in the theory of integral binary quadratic forms. If Q(x, y) = ax2 + bxy + cy2 is a quadratic form with integer coefficients, then D = b2 − 4ac is the discriminant of Q(x, y). Conversely, every integer D with D ≡ 0, 1 (mod 4) is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory.
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References
- 1 2 Carl Pomerance (2009), Timothy Gowers (ed.), "Computational Number Theory" (PDF), The Princeton Companion to Mathematics, Princeton University Press
- ↑ Eric Bach; Jeffrey Shallit (1996). Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. ISBN 0-262-02405-5.
- ↑ Henri Cohen (1993). A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics. Vol. 138. Springer-Verlag. doi:10.1007/978-3-662-02945-9. ISBN 0-387-55640-0.
