from fractions import Fraction as Q
import csv
import io
from komorebi_browser import show_plot, export_file

# Quantum and Circuits, quantum arithmetic QA13-QA14 and QA19-QA20.
c = (4, 0, 2, 0, -2, 0, -4, 0, -2, 0, 2, 0)
phase_real, phase_imag = Q(3, 5), Q(4, 5)
if phase_real**2 + phase_imag**2 != 1:
    raise ValueError("Choose a unit phase: real squared + imaginary squared = 1.")
projector = [[Q(c[(n-m) % 12], 12) for m in range(12)] for n in range(12)]
histogram = [Q(x*x, 48) for x in c]

def selected(real, imag):
    # Unnormalized v_+ + z v_-; divide squared norms by 48.
    vr = [Q(abs(x)) if x >= 0 else abs(x)*real for x in c]
    vi = [Q(0) if x >= 0 else abs(x)*imag for x in c]
    pr = [sum(row[m]*vr[m] for m in range(12)) for row in projector]
    pi = [sum(row[m]*vi[m] for m in range(12)) for row in projector]
    probability = sum(a*a+b*b for a, b in zip(pr, pi))/48
    assert probability == (1-real)/2
    return probability

dephased = sum(projector[n][n]*histogram[n] for n in range(12))
print("Common coordinate probabilities sum:", sum(histogram))
print("Selected probability, edited phase:", selected(phase_real, phase_imag))
print("Unsigned coherent:", selected(Q(1), Q(0)))
print("Signed coherent:", selected(Q(-1), Q(0)))
print("Complete coordinate dephasing:", dephased)
phases = [("1", Q(1), Q(0)), ("i", Q(0), Q(1)), ("-1", Q(-1), Q(0)),
          ("-i", Q(0), Q(-1)), ("edited phase", phase_real, phase_imag)]
rows = [(label, re, im, selected(re, im), dephased) for label, re, im in phases]
show_plot([
    {"type": "bar", "x": [r[0] for r in rows], "y": [float(r[3]) for r in rows], "name": "Coherent state"},
    {"type": "bar", "x": [r[0] for r in rows], "y": [float(r[4]) for r in rows], "name": "After coordinate dephasing"},
], {"title": {"text": "Same coordinate histogram, different arithmetic interference"},
    "barmode": "group", "yaxis": {"title": {"text": "Selected probability"}, "range": [0, 1]}},
    description="The modulus-12 projector selects four coprime Fourier labels. The unsigned coherent state has probability zero, the signed state one, and all fully coordinate-dephased states one third. Other phases interpolate without changing the original coordinate histogram. CSV fractions are exact; bar heights use floating-point conversion.")
stream = io.StringIO(newline="")
writer = csv.writer(stream, lineterminator="\n")
writer.writerow(["phase", "phase_real", "phase_imag", "coherent_selected_probability", "dephased_selected_probability"])
writer.writerows(rows)
export_file("arithmetic-phase.csv", stream.getvalue())
print("Exported 5 exact phase comparisons.")