TFPT scientific source excerpt
Original repository path: verification/v983_simple_current_generator.py
Original file SHA-256: 769a9c5cb5e6518d8d2a445d347150f5ce0d1410c95db263ca2db72466e176c8
Inclusive original lines: 60-95
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000060 | OMEGA_S = [sp.Rational(1, 2)] * 5
000061 | OMEGA_F = [sp.Rational(3, 4), sp.Rational(-1, 4),
000062 |            sp.Rational(-1, 4), sp.Rational(-1, 4)]
000063 | LAM = OMEGA_S + OMEGA_F
000064 | 
000065 | 
000066 | def in_D5(x):
000067 |     return all(v.is_integer for v in x) and sum(x) % 2 == 0
000068 | 
000069 | 
000070 | def in_A3(y):
000071 |     return all(v.is_integer for v in y) and sum(y) == 0
000072 | 
000073 | 
000074 | def in_L0(z):
000075 |     return in_D5(z[:5]) and in_A3(z[5:])
000076 | 
000077 | 
000078 | def coset_roots(k):
000079 |     """number of norm-2 vectors in L0 + k*lambda (exact rational count),
000080 |     combining D5-part and A3-part norm multisets."""
000081 |     t = [k * v for v in LAM]
000082 |     d5 = {}
000083 |     for x in itertools.product(range(-5, 4), repeat=5):
000084 |         if sum(x) % 2 != 0:
000085 |             continue
000086 |         n = sum((x[i] + t[i]) ** 2 for i in range(5))
000087 |         if n <= 2:
000088 |             d5[n] = d5.get(n, 0) + 1
000089 |     a3 = {}
000090 |     for y in itertools.product(range(-6, 7), repeat=3):
000091 |         y4 = list(y) + [-sum(y)]
000092 |         n = sum((y4[i] + t[5 + i]) ** 2 for i in range(4))
000093 |         if n <= 2:
000094 |             a3[n] = a3.get(n, 0) + 1
000095 |     return sum(c * a3.get(2 - n, 0) for n, c in d5.items())