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How to force numerical coefficients for non-polynomials?

asked 2020-09-18 22:42:15 -0600

dsejas gravatar image

updated 2020-09-18 22:42:42 -0600

Hello, Sage Community!

Suppose I have a function like

f(x) = 4/27*t^9*log(t)^2 - 32/243*t^9*log(t) + 59/2187*t^9 - 2/21*t^7*log(t)^2

I would like to force Sage to write the coefficients numerically, i.e.,

f(x) = 0.148148148148148*t^9*log(t)^2 - 0.131687242798354*t^9*log(t) + 0.0269775948788294*t^9 - 0.0952380952380952*t^7*log(t)^2

Thanks in advance! Is there a way to achieve this without having to create my own specialized function?

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answered 2020-09-19 03:45:23 -0600

rburing gravatar image

I'm pretty sure it can't be done with a built-in function, but I have written one (rather, a class) as an answer to a previous (slightly different) question: is it possible to round numbers in symbolic expression.

from sage.symbolic.expression_conversions import ExpressionTreeWalker

class SubstituteNumericalApprox(ExpressionTreeWalker):
    def __init__(self, **kwds):
        self.kwds = kwds

    def pyobject(self, ex, obj):
        if not isinstance(obj, Integer) and hasattr(obj, 'numerical_approx'):
            return obj.numerical_approx(**self.kwds)
        else:
            return obj

Here I added an exception for integers, so it works in your use case:

sage: var('t')
sage: f(t) = (4/27*t^9*log(t)^2 - 32/243*t^9*log(t) + 59/2187*t^9 - 2/21*t^7*log(t)^2)
sage: SubstituteNumericalApprox()(f(t))
0.148148148148148*t^9*log(t)^2 - 0.131687242798354*t^9*log(t) + 0.0269775948788294*t^9 - 0.0952380952380952*t^7*log(t)^2

Or in the definition of f:

sage: f(t) = SubstituteNumericalApprox()(4/27*t^9*log(t)^2 - 32/243*t^9*log(t) + 59/2187*t^9 - 2/21*t^7*log(t)^2)
sage: f
t |--> 0.148148148148148*t^9*log(t)^2 - 0.131687242798354*t^9*log(t) + 0.0269775948788294*t^9 - 0.0952380952380952*t^7*log(t)^2

It could be a nice idea to have such a class included in SageMath.

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Comments

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Thank you very much, @rburing! Your solution worked even better than what I thought originally. For example, your code works perfectly even if I have expressions inside nested inside parentheses or functions. Awesome!

dsejas gravatar imagedsejas ( 2020-09-21 23:28:33 -0600 )edit

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Asked: 2020-09-18 22:42:15 -0600

Seen: 63 times

Last updated: Sep 19