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-   -   finding unimodular substitutions (https://www.mersenneforum.org/showthread.php?t=26049)

wildrabbitt 2020-10-06 13:18

finding unimodular substitutions
 
Hi,


does anyone know a method for finding a unimodular substitution from one
binary quadratic form ( \( ax^2 + bxy + cy^2 \) ) to another given that they are equivalent?


I'd like a find a unimodal substitution



\(x\prime = \alpha x + \beta y \)


\(y\prime = \gamma x + \delta y \)




with integer coefficients which transforms



\(29x^2 + 256xy + 565y^2\) into \(x^2 + y^2 \)


Can anyone help?

wblipp 2020-10-10 04:54

x' = 5 x + 22 y
y' = 2 x + 9 y

Start with the "obvious" 29 = 5[sup]2[/sup] + 2[sup]2[/sup]

wildrabbitt 2020-10-10 16:54

Thanks.


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