Function candidate_integer_rotations

cpp_core/src/symmetry.cpp:71–93

Generate all 3x3 integer matrices with entries in {-1,0,1} and |det|=1. Returns column-major Mat3i (exactly 386 candidates). CONVENTION: We enumerate a_{row,col} values (matching Python's row-major iteration order). Then store in column-major: M[col][row] = a_{row,col}.

// CONVENTION: We enumerate a_{row,col} values (matching Python's row-major
// iteration order). Then store in column-major: M[col][row] = a_{row,col}.
std::vector<Mat3i> candidate_integer_rotations() {
    std::vector<Mat3i> out;
    out.reserve(386);

    const int vals[] = {-1, 0, 1};
    for (int a00 : vals) for (int a01 : vals) for (int a02 : vals)
    for (int a10 : vals) for (int a11 : vals) for (int a12 : vals)
    for (int a20 : vals) for (int a21 : vals) for (int a22 : vals) {
        // Determinant in row-major convention:
        int det = a00*(a11*a22 - a12*a21)
                - a01*(a10*a22 - a12*a20)
                + a02*(a10*a21 - a11*a20);
        if (det != 1 && det != -1) continue;

        // Store column-major: M[col][row] = a_{row,col}
        Mat3i m{};
        m[0][0] = a00; m[0][1] = a10; m[0][2] = a20;
        m[1][0] = a01; m[1][1] = a11; m[1][2] = a21;
        m[2][0] = a02; m[2][1] = a12; m[2][2] = a22;
        out.push_back(m);
    }
    return out;
}

// Try to find translation + permutation for a given rotation.
bool find_atomic_permutation(