1 | initial version |

The book Calcul mathÃ©matique avec Sage was translated into German as Rechnen mit Sage and into English as Computational mathematics with SageMath.

Section 5.3 of the English translation ends like this:

Algebraic Numbers.An algebraic number is defined as root of a polynomial. When the polynomial degree is 5 or more, in general it is not possible to explicitly write its roots in terms of the operations $+$, $âˆ’$, $\times$, $/$, $\sqrt{}$. However, many computations involving the roots can be performed successfully without any other information than the polynomial itself.`sage: k.<a> = NumberField(x^3 + x + 1); a^3; a^4+3*a -a - 1 -a^2 + 2*a`

This book does not describe in detail how to play with algebraic numbers in Sage, however several examples can be found in Chapters 7 and 9.

In general I would recommend this book as a very good introduction to computer algebra and numerical computation as well as to SageMath, with a lot of examples.

(Disclaimer: I know some of the authors.)

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