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- A linear system of equations Ax = b can be reduced to
row echelon form, whence the solutions can just be read off.
- Univariate polynomials have GCD's (Greatest Common Divisors)
that can be computed by the Euclidean algorithm (though modular
algorithms are significantly more efficient, and are what is actually
implemented in most computer algebra systems).
- An ideal I is a subset of a ring which is closed under addition
and by multiplication from elements of the ring. We can think of the
GCD of a pair of univariate polynomials as a useful generator (or basis) for
the ideal generated by the original polynomials.
Tue Mar 12 21:09:19 EST 1996