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1 Polynomial ideals - MIT OpenCourseWare

1 Polynomial ideals - MIT OpenCourseWare

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Figure 1: Two algebraic varieties. The one on the left is defined by the equation (x2 + y2 − 1)(3x + 6y − 4) = 0. The one on the 2right 4is a quartic surface, defined by 1 − x2 − y2 − 2z + z = 0. Algebraic varieties An (affine) algebraic variety is the zero set of a finite collection of polynomials (see formal definition below).

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