mò M©Fc@sŸdZdklZeddddddƒZededjpt‚[dd d Zd d dd ejod d dd jnpt‚dS(sAssorted mathematical tools and toys. Polynomials: Legendre -- spherical hamonics and Legendre polynomials multiangle -- expressing sin and cos, of multiples of an angle, as polynomials in those of the angle multinomial -- polynomials in several free variables polynomial -- polynomials in one free variable Combinatorics: Fibonacci -- computing the eponymous sequence Pascal -- factorials and the eponymous triangle (see also permute) stirling -- deploying Stirling's formula Permutations: permute -- interpreting lists of integers as permutations queens -- solving the 'eight queens' problem by iterating over permutations Distributions and probabilities: gamma -- the Gamma distribution (see also stirling) gauss -- the Gaussian (bell-shaped) distribution variate -- generating chaotic samples from assorted distributions Solving equations: cardan -- finds roots of polynomials of degree at most three root -- searching for zeros of a ({reals}::{reals}) function search -- similar, but in two dimensions (represented by complex) Miscellaneous: graph -- the find/unite algorithm and description of a graph integrate -- perform adequate approximations to integrating a function natural -- the natural numbers, and tools to work with types kindred to them primes -- factorisation and a disk-cached lazy list of all primes pythagorean -- integer-sided right-angle triangles ratio -- representing exact fractions and approximating numbers with them $Id: __init__.py,v 1.2 2007/03/24 22:42:21 eddy Exp $ (sQuantityif5.0f0.5itdocsThe golden ratio. This is the positive solution to the quadratic equation x*x = x+1; divide -1 by it to get the negative solution. One can re-write the equation as (2*x-1)**2 = 4*x*x -4*x +1 = 4*(x*x-x) + 1 = 5, whence the solutions are (1 +/- 5**.5)/2. ii ii ii i N(t__doc__tstudy.value.quantitytQuantityt goldenratiotAssertionErrort Ramanujan(RRR((t*/home/eddy/.sys/py/study/maths/__init__.pyt?&s