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Hilbert`s Nullstellensatz and the Beginning of Algebraic Geometry
Hilbert`s Nullstellensatz and the Beginning of Algebraic Geometry

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R1. Rational Expressions: the Domain

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Sections 2.7/2.8 – Real Numbers/Properties of Real Number

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The Graph of Ax + By = C

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< 1 ... 130 131 132 133 134 135 136 137 138 ... 449 >

System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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