# Monthly Archives: July, 2013

## Descent method with gaussian reduction.

Sorry for a very late blog post, I had a really busy week and finally I managed to find sometime to write about the progress I made in the last week. I implemented an improved version of the descent method which uses gaussian reduction. I found this algorithm in [1]. Here is a sketch of …

## Solving Ternary Quadratic forms by descent method

Now SymPy can solve Ternary Quadratic forms !!!! I thought of adopting a new style for giving more details on this amazing news, So Let’s try a Q&A approach and see how it goes. Q1. What is a “Ternary Quadratic form”? A ternary quadratic form is an equation of the form, (Yes, It’s a little …

## From Euclid To Gauss via Pell

While the fourth week of GSoC is coming to an end, I managed to finish two of the five deliverables of my project proposal. So the fourth week is more of a transition week for me as I had to correct few bugs associated with current implementation of QDEs (Quadratic Diophantine Equation) and LDEs (Linear …

## Solving the generalized Pell equation

Continuing the work from last week, I was aiming to solve quadratic Diophantine equations with delta = B**2 – 4*A*C > 0. I found two better references on this case which can be found in [1] and [2]. These two papers describe all the necessary algorithms for solving the generalized Pell equation, to which the …