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Coding workflows · Integer characteristic polynomials
03
A concrete starting point
Return descending coefficients of det(xI−A) for a square integer matrix of order zero through six with entries bounded by 1000 in magnitude. Test the empty matrix and repeated eigenvalues, rejecting ragged or Boolean entries without approximating roots.
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Integer characteristic polynomials
A concrete starting point
def characteristic_polynomial(matrix):
if type(matrix) not in (list, tuple) or len(matrix) > 6:
raise ValueError("charpoly.size")
n = len(matrix)
if any(type(row) not in (list, tuple) or len(row) != n or any(type(v) is not int or abs(v) > 1000 for v in row) for row in matrix):
raise ValueError("charpoly.entry")
block = [[int(i == j) for j in range(n)] for i in range(n)]
coefficients = [1]
for degree in range(1, n+1):
product = [[sum(matrix[i][k]*block[k][j] for k in range(n)) for j in range(n)] for i in range(n)]
trace = sum(product[i][i] for i in range(n))
coefficient = -trace // degree
coefficients.append(coefficient)
block = [[product[i][j] + (coefficient if i == j else 0) for j in range(n)] for i in range(n)]
return coefficientsThe example is a starting point for a real project, not a claim that generated code is already tested. Adjust paths, dependencies and expected behavior to match your application.
