Theo Bendit's profile - activity

I'm trying to use Sage to implement a slightly modified bisection algorithm on a certain function, and at each step, displaying the interval endpoints as well as the function at these endpoints. I don't need much precision for the latter numbers; I just want an indication of the size and sign of these numbers. However, the numerical_approx() function is giving me weird responses when I specify the number of digits. For example, the following calculation (which is the function value at the greater endpoint, in the final step of the algorithm)

numerical_approx(1/2427673471984599040*(1530627*sqrt(4630419677705) - 4630419677705)*(sqrt(4630419677705) - 482051) + 482051/524288)

evaluates to

1.64597827478907e-7

which appears to be "reasonable", though I don't know for certain. However, when I write,

numerical_approx(1/2427673471984599040*(1530627*sqrt(4630419677705) - 4630419677705)*(sqrt(4630419677705) - 482051) + 482051/524288,digits=3)

it evaluates to

-0.0000160

which is clearly unreasonable: it's the wrong sign and it's too large. Further more, these endpoints come back to this same number a lot, despite how the input changes. At one point, in the middle of this string of -0.0000160s, Sage estimates 0.000, just once, and goes back to -0.0000160.

Changing the precision to 4 and 5 does seem to improve the situation (correct sign, more reasonable magnitude), but the significant digits are all different!

So, my questions are:

1. What is going wrong here?
2. Can I fix it?
3. What methods could I use to be certain that these approximations have 3 correct significant figures?

Actually, I think I just answered my own question.

Thank you for the answer! The RIF command strikes me as particularly handy. There is something unsettling about this tho

Incorrect rounding at low precision I'm trying to use Sage to implement a slightly modified bisection algorithm on a cer