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Hello, @john-bao! You could change the polynomial ring of the Taylor Polynomial. For example,

f(x) = sin(x)
T(x) = taylor(f, x, 1.0, 2)
R = PolynomialRing(RealIntervalField(10), 'x')
R(T)

This will give you something like

 -0.421?*x^2 + 1.39?*x - 0.120?

The ? sign indicates you have a loss of precision. I am working with 10 bits, because 3 gives you very poor precision. If you don't like the ?s, you can change the RealIntervalField(10) with Reals(10), for example.

I hope this helps!

Hello, @john-bao! You could change the polynomial ring of the Taylor Polynomial. For example,

f(x) = sin(x)
T(x) = taylor(f, x, 1.0, 2)
R = PolynomialRing(RealIntervalField(10), 'x')
R(T)

This will give you something like

 -0.421?*x^2 + 1.39?*x - 0.120?

example. If you want to know how many bits you need in order to have 4 digits, for example, you can use the digits_to_bits function:

from sage.arith.numerical_approx import digits_to_bits
R = PolynomialRing(RealIntervalField(digits_to_bits(4)), 'x')
R(T)

Here is an alternative approach (although a little slower). This allows you to fix the number of bits or the number of digits (I'll use digits). Define the function:

def poly_prec(p, digits=4):
    pol = 0
    for op in p.operands():
        if not op.is_constant():
            ex = op.operands()
            pol += ex[0] * N(ex[1], digits)
        else:
            pol += N(op, digits)
    return pol

I hope this helps!