The Euclidean Algorithm and other Algebra Demos
- Eucldiean algorithm for integers: The demo runs the extended Euclidean algorithm on a pair of integers computing their greatest common divisor.
- Eucldiean algorithm for polynomials: This demo runs the extended Euclidean algorithm on a pair of polynomials in $\mathbb{Q}[x]$ (rational coefficients) or $\mathbb{Z}_n[x]$ (coefficients modulo $n$).
- Descartes' rule of signs: This demo uses Descartes' method to give an upper bound on the number of positive and negative real roots of a polynomial by merely looking at the sign pattern of the polynomial's coefficients.
- Budan-Fourier method: This demo uses the Budan-Fourier theorem to give an upper bound on the number of real roots lying in a speicified interval.
- Sturm's method: This demo uses Sturm's method to give an exact count of the number of distinct real roots lying in a specified interval.
- (Advanced) Stum's method: This demo iterates Sturm's method to give the exact number of real roots in a specified interval counting multiplicities. The demo also allows the user to produce a table of sign patterns for the usual Sturm's method.
- Horner's method - synthetic division: This demo performs polynomial division with remainder by computing a minimal table of values.
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