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SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.
Simplifying a piecewise linear curve with the Douglas–Peucker algorithm. The starting curve is an ordered set of points or lines and the distance dimension ε > 0. The algorithm recursively divides the line. Initially it is given all the points between the first and last point. It automatically marks the first and last point to be kept.
The number 1 (expressed as a fraction 1/1) is placed at the root of the tree, and the location of any other number a/b can be found by computing gcd(a,b) using the original form of the Euclidean algorithm, in which each step replaces the larger of the two given numbers by its difference with the smaller number (not its remainder), stopping when ...
For, if one applies Euclid's algorithm to the following polynomials [2] + + + and + +, the successive remainders of Euclid's algorithm are +, +,,. One sees that, despite the small degree and the small size of the coefficients of the input polynomials, one has to manipulate and simplify integer fractions of rather large size.
a simplifier, which is a rewrite system for simplifying mathematics formulas, a memory manager, including a garbage collector, needed by the huge size of the intermediate data, which may appear during a computation, an arbitrary-precision arithmetic, needed by the huge size of the integers that may occur,
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...