Compute coeffs using Rationals

[oxinabox]

Fixed #64

Turns out this can make a difference.

This not only gets result on julia 1.4 up to the standard of julia 1.2,
but actually does much more than that, significantly improving out accuracy

With this PR. in julia 1.2 or 1.4 (identical):

julia> using FiniteDifferences

julia> k3 = FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 5), y->exp(y), 1.0, adapt=4)
2.7182817496168528

julia> abs(k3-exp(1))  # Should be 0
7.884219233034173e-8

julia> f(x) = @. 4x^3 + 3x^2 + 2x + 1
f (generic function with 1 method)

julia> FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 3), f, 1.0, adapt=4) - 24
5.538680625249981e-12

Without this PR. 1.4

julia> using FiniteDifferences

julia> k3 = FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 5), y->exp(y), 1.0, adapt=4)
2.7182663156747684

julia> abs(k3-exp(1))  # Should be 0
1.5512784276694447e-5

julia> f(x) = @. 4x^3 + 3x^2 + 2x + 1
f (generic function with 1 method)

julia> FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 3), f, 1.0, adapt=4) - 24
6.48253006829691e-10

Without this PR on 1.2

julia> using FiniteDifferences

julia> k3 = FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 5), y->exp(y), 1.0, adapt=4)
2.7182815825355453

julia> abs(k3-exp(1))  # Should be 0
2.459234997864712e-7

julia> f(x) = @. 4x^3 + 3x^2 + 2x + 1
f (generic function with 1 method)

julia> FiniteDifferences.fdm(FiniteDifferences.central_fdm(9, 3), f, 1.0, adapt=4) - 24
1.071143174158351e-11

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I feel like this is going to increase our cost a fair bit.
So it would be really good to get #61 done, to avoid recomputing coeffs.

[willtebbutt]

This looks like a fantastic improvement in accuracy -- I'm definitely in favour of doing this. Would definitely be good to prevent reverting by tying this down with a couple of unit tests. The above snippets would probably suffice.

[oxinabox]

I think the improvements are only really big when using higher order and a high degree of adapt

[willtebbutt]

I think the improvements are only really big when using higher order and a high degree of adapt

Oh okay. Would be good to see some numbers on this then, both benchmarking and accuracy.

[oxinabox]

tests have been added

[willtebbutt]

LGTM modulo the typo! Thanks @oxinabox