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Algebraic geometry

Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry.

It can be seen as the study of solution sets of systems of polynomials.

When there is more than one variable, geometric considerations enter and are important to understand the phenomenon.

One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.

Note:   The above text is excerpted from the Wikipedia article "Algebraic geometry", which has been released under the GNU Free Documentation License.
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