| from mpmath import mp | |
| mp.dps = 110 | |
| def bloch_wigner(z): | |
| # D(z) = Im(Li_2(z)) + Arg(1-z)*log|z| | |
| # = Im(Li_2(z) + log(1-z)*log|z|) | |
| return mp.im(mp.polylog(2, z) + mp.log(1 - z) * mp.log(abs(z))) | |
| def compute(): | |
| with mp.extradps(30): | |
| # Find all roots of z^3 - z^2 + 1 = 0 | |
| roots = mp.polyroots([1, -1, 0, 1]) | |
| # Find the root in the upper half-plane (positive imaginary part) | |
| z = None | |
| for r in roots: | |
| if mp.im(r) > 0: | |
| z = r | |
| break | |
| if z is None: | |
| raise ValueError("No root found in upper half-plane") | |
| # Volume(5_2) = 3 * D(z) | |
| vol = 3 * bloch_wigner(z) | |
| return mp.re(vol) | |
| if __name__ == "__main__": | |
| print(str(compute())) |