Rustify QED

[tgiani]

• implement aem1.rs
• add in anomalous_dimension::unpolarized::spacelike.rs missing QED ingredients
• hook rust kernels into python

[felixhekhorn]

I'm not sure we want to keep those - can we inline them?

[tgiani]

what do you mean? Could you please provide an example?

[felixhekhorn]

instead of

    let g3N = c.get(K::G3);
    let g3Np2 = c.get(K::G3p2);

we do

    let g3N = c.get(K::G3);
    let g3Np2 = g3N + f;

where $f = g_3(N+2)-g_3(N)$ is computed analytically beforehand

[tgiani]

I am afraid I don t understand. How do you compute f analytically beforehand? Do you mean to move g_functions::g3(self.n + 2., self.get(K::S1p2)) out of the cache?

[felixhekhorn]

out of the cache?

yes

How do you compute f analytically beforehand?

Mathematica 🙃 let's try to use a short cut: @giacomomagni can you compute quickly this $f$? (also feel free to give your opinion if we should keep that cache entry or not)

[felixhekhorn]

so I think
$$f = \frac{6 (n+1) (2 n+1) H_n+n \left(-\pi ^2 (n+1)^2-6 n\right)}{6 n^2 (n+1)^3}$$
which I computed half with pen and paper and half Mathematica and checked for $N=1$, $N=2$

to be more precise: for $g_3$ we could use the above equation and for the others we inline the expressions

[tgiani]

ok thank you! I ll first try to get things working as they are and then I will add this