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Comment by tlb | Hacker News Reader

What’s the use case overlap between symbolic and huge? I might expect that with most huge expressions (they talk about disk space being the limit, not memory) you’d be satisfied with a numerical approximation. Does someone need to simplify a huge expression down to a small symbolic expression?

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One use case is in theoretical physics, where expressions that take up about a terabyte are generated when computing Feynman diagrams, but only in the intermediate stages. By the end of a two-month computation you get a result similar to equation 4.5 in this paper: https://arxiv.org/pdf/1707.01044

An exact answer is desired since the final result reveals some structure that can be studied, and because it is very hard to get a numerical result due to the occurrence of spurious poles. For example, evaluating

(1-x)/x - 1/x

numerically is challenging around x=0 even though symbolically it can be made regular.

What do you mean by "symbolically it can be made regular"?

(1-x)/x - 1/x =1/x - 1 - 1/x = -1

Evaluating the expression naively near zero you're going to get wild numerical errors, but if you do the symbolic manipulation you're going to notice that it's just equal to -1.

Edit: e.g. consider this interaction I just had with the python interpreter

    >>> x=1e-15
    >>> (1-x)/x - 1/x
    -1.0
    >>> x=1e-16
    >>> (1-x)/x - 1/x
    0.0

you get completely the wrong answer when x = 1e-16

The most obvious use case is to see that the expression does not simplify well and is inherently huge :-)

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