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Matrix Y_matrix has size 16 x 15 and the full rank 15. If you add parameter check=False to Y_matrix.solve_right(...) and then print the difference Y_matrix * coeffs - vector(alpha.list()), you will see that the obtained solution does nullify the first 15 components in this difference, but not the 16th one. Given that the rank of Y_matrix is 15, it means that vector(alpha.list()) does not belong to the span of Y_matrix, and Sage is correct by saying that there are no solutions.