Integer characteristic polynomials
SpectrumGorse supports AI-assisted review of exact matrix algebra. Discuss characteristic coefficients with a compatible model and check the proposed routine using determinant identities. Keep coefficient computation separate from numerical root finding.
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 coefficients- Project
- Test the empty matrix and repeated eigenvalues, rejecting ragged or Boolean entries without approximating roots.
- Review before applying
- Compare actual behavior with the expected result. If a check fails, investigate it before applying more changes.
- Connection
- Base URL, credentials and a reachable server.
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 coefficientsGive mathematical code an application-level review
Mathematical notation can make an implementation look settled before its software contract has been examined. SpectrumGorse is a Windows AI coding workspace for reviewing both. Open the project and ask the connected model to identify accepted inputs, expected output representation and error handling before suggesting changes to the calculation.
A concrete task might review a characteristic-polynomial routine for small integer matrices. Supply the caller and independently known coefficient fixtures, then ask the assistant to explain any proposed edit in those terms. Keep coefficient calculation separate from other operations the application may perform later, so the review does not silently expand into a numerical solver replacement.
Verify representation as carefully as arithmetic. Run project tests for an empty matrix if supported, simple diagonal cases and rejected nonsquare inputs. Check coefficient order and sign conventions at the consumer, and inspect any introduced numeric conversion. An answer with plausible coefficients is insufficient if the caller interprets their order differently or requires exact integer results.
SpectrumGorse supports OpenAI-compatible and Anthropic endpoints for model connections. Select an uncensored AI model where your service offers one, with restrictions and tools governed by that setup. The conversation helps explain proposed code; your independent fixtures and application checks determine whether it fits.
Evaluating an exact calculation patch
What should I provide besides a matrix example?
Include the expected coefficient order, sign convention and the caller that consumes the result. Show valid dimensions and entry types. These details let the assistant assess software compatibility rather than only whether a mathematical expression appears familiar.
Can coefficients be checked with the same implementation?
That would provide weak independent evidence. Use simple matrices with known results or another justified check in your project. Explain how expected values were obtained so the review can distinguish a shared mistake from genuine agreement.
Should a polynomial routine also find its roots?
Only if that is a separate requirement. Exact coefficient computation and numerical root finding have different contracts. Keep the current patch focused unless the application explicitly needs both and you have defined how their outputs are used.
Why inspect numeric conversions in the diff?
A conversion can change exact arithmetic into an approximation even when ordinary fixtures still pass. State the representation the application requires and check that both intermediate operations and returned values preserve it within the supported input range.
SpectrumGorse · Updated 2026-10-25
