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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