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Old 2020-10-06, 13:18   #1
wildrabbitt
 
Jul 2014

3·149 Posts
Default 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?

Last fiddled with by wildrabbitt on 2020-10-06 at 13:24 Reason: latex wasn't coming out right
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Old 2020-10-10, 04:54   #2
wblipp
 
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"William"
May 2003
New Haven

3×787 Posts
Default

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

Start with the "obvious" 29 = 52 + 22
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Old 2020-10-10, 16:54   #3
wildrabbitt
 
Jul 2014

1101111112 Posts
Default

Thanks.
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