- #1
My Name Is D
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Homework Statement
Hi. I've got the matrix from the Quadratic Sieve down to Gaussian Form and I'm wondering how to find the factor base which leads to a square number now.
Homework Equations
The Factor Base:
$${29,782,22678}$$
The original Matrix:
\begin{pmatrix}
0 & 0 & 0 & 1\\
1 & 1 & 1 & 0\\
1 & 1 & 1 & 1\\
\end{pmatrix}
The Attempt at a Solution
The Matrix after being transposed and Gaussian Elimination:
\begin{pmatrix}
1 & 0 & 1\\
0 & 1 & 1\\
0 & 0 & 0\\
0 & 0 & 0
\end{pmatrix}
I know I have to relate this back to the factor base somehow? I can see that $$29*782*22678 = 514291684 = 22678^2$$ But how does that relate to the matrix? I'm trying to implement it in Java and am using the Matrix package JAMA for computations. Any help would be much appreciated!