Mathematica

Date: Aug 16, 2010

A gentle introduction to PSLQ

PSLQ is an algorithm to find integer relations between a set of real numbers. Last summer I had written an introduction to PSLQ, how it works, and how it can and has been used. This introduction, which can be downloaded below, should be easily understandable by an advanced undergraduate student.

The PSLQ algorithm is one of the basic tools of experimental mathematics. A very basic and naive implementation for Mathematica is attached to this post. The file pslq-usage.nb contains instructions and examples. read more »

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pslq.pdf
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pslq.m
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pslq-usage.nb
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Date: Mar 5, 2010

Computer proved monotonicity of some coefficients

Ming-Hua Lin from the University of Regina sent me the following problem:

Problem: Let p ≥ 2 be an integer, and define

$$ f (t) = \left( \frac{1}{1 - t \left( \frac{1}{p} + \frac{p - 1}{2 p^2} t<br /> \right)} \right)^p = \sum_{n \geqslant 0} c_n t^n . $$

Show that $ c_2 > c_3 > c_4 > \cdots $. read more »

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Date: Jun 12, 2009

Apollonian circle packings in Mathematica

Today, I have been playing a little bit with Apollonian circle packings. Here is the code I wrote in Mathematica to visualize such packings (see below for an example). read more »

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apolloniancirclepackings.nb
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Date: Jun 10, 2009

Fast q-binomials in Mathematica

Recently, I have been doing experiments involving q-binomial coefficients in Mathematica. Starting with version 7, Mathematica is prepared for some q-business; in particular, there exists a function named QBinomial giving the q-analog of Binomial. However, this implementation turned out to not be fast enough for my needs. Here is an alternative approach which is not only way faster but provides a full factorization. read more »

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