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The usual way for certified numerics is to use inverval arihmetics and ball arithmetics.

You can have a look at this thematic tutorial about the various representations of real and complex numbers in Sage, which include the RealIntervalField and the RealBallField:

https://mathexp2018.metelu.net/worksheets/real_and_complex_numbers/real_and_complex_numbers.ipynb

In case the page disapears, you can finf a very close version on trac ticket 15944

(disclaimer : i am the author of the worksheet).

The usual way for certified numerics is to use inverval arihmetics and ball arithmetics.

You can have a look at this thematic tutorial about the various representations of real and complex numbers in Sage, which include the RealIntervalField and the RealBallField:

https://mathexp2018.metelu.net/worksheets/real_and_complex_numbers/real_and_complex_numbers.ipynb

In case the page disapears, you can finf a very close version on trac ticket 15944

(disclaimer : i am the author of the worksheet).

You can also have a look at the book Computational Mathematics with SageMath : http://sagebook.gforge.inria.fr/english.html