Solving a system of equations over the field of rational functions in Q

Malte
45 ●1 ●3 ●8

I have a system of equations over the field of rational functions with coefficients in Q:

g == x^2 (r + b+1), r == x^3 (g + b+1), b == x (r + g+1),

where g, r and b are unknown rational functions with coefficients in Q. How do I solve this with Sage?

Thank you!

Comments

Am I right in supposing that you mean that b, r, g are rational functions of the sole x variable ?

Emmanuel Charpentier ( 2022-11-24 11:14:28 +0100 )edit

Yes, that's true.

Malte ( 2022-11-24 11:31:23 +0100 )edit

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Malte
45 ●1 ●3 ●8

I've figured it out now. Syntactically, we can treat r, g, b as if they were numbers. I had not anticipated that at first. So this is how it works:

var('r g b x')
solve([r == x^3 * (b + g + 1), g == x^2 * (b + r + 1), b == x * (r + g + 1)], [r, g, b])

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Asked: 2022-11-24 10:30:01 +0100

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Last updated: Nov 24 '22