108 lines
1.9 KiB
Python
108 lines
1.9 KiB
Python
from random import randint
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from tqdm import tqdm
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from sage.rings.polynomial.msolve import variety as msolve_variety
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F = GF(3301, names=("z", ))
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f_a = list(F)
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# m = 32
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# n = 80
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# m = 44
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# n = 112
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# m = 72
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# n = 184
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# m = 8
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# n = 20
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# m = 2
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# n = 5
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m = 44
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n = 112
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print("vars: ", n)
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print("eqns: ", m)
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print("actual vars: ", n - m)
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print("actual eqns: ", m + m)
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O = random_matrix(F, (n - m), m)
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output = ""
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poly_m = []
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z = zero_matrix(F, m, (n - m))
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for i in tqdm(range(m)):
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P1 = random_matrix(F, (n - m), (n - m))
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for j in range(0, len(P1.rows())):
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for k in range(0, j): P1[j, k] = 0
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P2 = random_matrix(F, (n - m), m)
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P3 = -O.T * P1 * O - O.T * P2
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for j in range(0, len(P3.rows())):
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for k in range(j+1, len(P3.rows())):
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P3[j, k] += P3[k, j]
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P3[k, j] = 0
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for i in P1:
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for j in i:
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output += hex(f_a.index(j))[2:]
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for i in P2:
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for j in i:
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output += hex(f_a.index(j))[2:]
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for i in P3:
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for j in i:
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output += hex(f_a.index(j))[2:]
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P = block_matrix([ [P1, P2], [z, P3]])
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poly_m.append(P)
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v = matrix(F, n, 1, [randint(0, 1) for i in range(n)])
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oil_basis = block_matrix(F, 2, 1, [O, identity_matrix(F, m)])
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var_list = ','.join([f'x{i}' for i in range(n - m)])
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R = PolynomialRing(F, var_list)
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value = zero_matrix(R, n, 1)
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hint = zero_matrix(R, n, 1)
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hint2 = zero_matrix(R, n, 1)
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for i in oil_basis.columns():
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value += F.random_element() * matrix(F, n, 1, list(i))
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hint += F.random_element() * matrix(F, n, 1, list(i))
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hint2 += F.random_element() * matrix(F, n, 1, list(i))
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print(value)
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print()
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print(n - m)
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print()
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for i in range(n - m):
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value[i] = R(f'x{i}')
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polys = []
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for i in poly_m:
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polys.append((value.T * i * value)[0][0])
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polys.append((value.T * (i + i.T) * hint)[0][0])
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polys.append((value.T * (i + i.T) * hint2)[0][0])
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I = R.ideal(*polys)
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print(msolve_variety(I, F, proof=False))
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