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Approximate real numbers by rationals

asked 2013-08-21 13:52:33 +0100

LMN gravatar image

Does sage have routines to approximate real numbers by fractions:

For example, suppose 13.000000000000000000001 is an approximation of a complicated expression involving $pi, e$ and other transcendental constants. Then it "is probably" a rational number. Can sage tell me what rational number it "probably" is.

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answered 2013-08-23 22:02:07 +0100

vdelecroix gravatar image

You can use the method nearby_rational which works for real numbers. If you do have a symbolic expression, you first have to take a numerical approximation as in

sage: pi.n().nearby_rational()

The term pi may be replaced by any symbolic expression.

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answered 2013-08-21 14:09:46 +0100

kcrisman gravatar image

See Trac 237 for the closest to this that has been proposed. I'm not sure if there would be anything for just rationals or not.

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Asked: 2013-08-21 13:52:33 +0100

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Last updated: Aug 23 '13