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Topics on Computational Algebra
Lecture Notes, Spring 2001

Shuhong Gao

Clemson University

Contents
Polynomial systems and the related problems
Nonlinear Systems
Nonlinear Systems (continued)
Euclidean algorithm and its applications
Euclidean Algorithm and its applications (continued)
Gröbner Bases
Gröbner Bases (continued)
Gröbner Bases (continued)
Gröbner Bases (continued)
Gröbner Bases (continued)
Computation in ${\mathbb F}[x_1, \dots, x_n]/{\mathbf I}$
Computation in ${\mathbb F}[x_1, \dots, x_n]/{\mathbf I}$ (continued)
Computation in ${\mathbb F}[x_1, \dots, x_n]/{\mathbf I}$ (continued)
Eigenvalues and Fourier Transform
Topics for Course Projects
Multidimensional Recurrence Relation
Affine Variety Codes
Decoding Reed-Solomon Codes
Decoding Reed-Solomon Codes (continued)
Hermitian Codes
Decoding Hermitian Codes
Decoding Hermitian Codes
About this document ...

Xuhong Gao
2001-05-10