Example at the top of page 162 of this book needs to be updated.

He gives some sage code, then claims "which yields a^2 + 1." as output. But the output is 0 (if you try it), and it's very obvious it should be 0 if you just think about what it's doing (so definitely not a bug). Then he claims "Careful: sage is not perfect, and if you change QQ above the ZZ, sage doesnâ€™t seem to be able to give the correct answer (as of the time these notes were written).". That also works fine.

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