Symbolic computation includes computer algebra, exact numeric computation, and rule-based theorem proving. It lies at the heart of modern mathematics research, with the goal to do exact or validated mathematics by computer.
Symbolic computations work with computer representations of algebraic expressions or other mathematical objects. Common algorithms are computations of Gröbner basis, lattice basis reduction, polynomial factorisation, and p-adic methods. Example applications include: the study of varieties and their birational geometry in Algebraic Geometry; the development of databases of modular forms and L-functions in Number Theory; and the systematic analysis of convex bodies in Combinatorics.
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