TheAlgorithms/Python · error · ValueError

solve_simultaneous() requires at least 1 full equation

Error message

solve_simultaneous() requires at least 1 full equation

What it means

Raised by solve_simultaneous() when every equation row contains at least one zero and therefore no 'full' row exists to reorder to the top. The elimination algorithm needs a pivot row with all non-zero coefficients to start; it pops the first zero-free row, and if none exists it gives up with this ValueError. Singular/underdetermined systems that merely need row swapping are handled, but all-zero-containing systems are not.

Source

Thrown at maths/simultaneous_linear_equation_solver.py:99

        raise IndexError("solve_simultaneous() requires n lists of length n+1")
    _length = len(equations) + 1
    if any(len(item) != _length for item in equations):
        raise IndexError("solve_simultaneous() requires n lists of length n+1")
    for row in equations:
        if any(not isinstance(column, (int, float)) for column in row):
            raise ValueError("solve_simultaneous() requires lists of integers")
    if len(equations) == 1:
        return [equations[0][-1] / equations[0][0]]
    data_set = equations.copy()
    if any(0 in row for row in data_set):
        temp_data = data_set.copy()
        full_row = []
        for row_index, row in enumerate(temp_data):
            if 0 not in row:
                full_row = data_set.pop(row_index)
                break
        if not full_row:
            raise ValueError("solve_simultaneous() requires at least 1 full equation")
        data_set.insert(0, full_row)
    useable_form = data_set.copy()
    simplified = simplify(useable_form)
    simplified = simplified[::-1]
    solutions: list = []
    for row in simplified:
        current_solution = row[-1]
        if not solutions:
            if row[-2] == 0:
                solutions.append(0)
                continue
            solutions.append(current_solution / row[-2])
            continue
        temp_row = row.copy()[: len(row) - 1 :]
        while temp_row[0] == 0:
            temp_row.pop(0)
        if len(temp_row) == 0:
            solutions.append(0)

View on GitHub (pinned to f5988cc097)

Solutions

1. Rearrange so at least one equation has all non-zero entries, if the system permits
2. Scale/rewrite zero constant terms as small non-zero values only if mathematically acceptable
3. Use a proper solver (sympy.solve, numpy.linalg) for systems with structural zeros — this implementation cannot pivot through them

Example fix

# before
solve_simultaneous([[0, 2, 3], [4, 0, 6]])  # -> ValueError

# after (structural zeros: use a general solver)
import numpy as np
a = np.array([[0.0, 2.0], [4.0, 0.0]])
b = np.array([3.0, 6.0])
print(np.linalg.solve(a, b))  # [1.5  0.75]

if all(0 in row for row in equations):
    # solver needs one row with no zeros at all (incl. constant)
    print('system not supported; use numpy/sympy')
else:
    solve_simultaneous(equations)

def has_full_row(eq: list) -> bool:
    return any(all(x != 0 for x in row) for row in eq)

try:
    solve_simultaneous(equations)
except ValueError as e:
    if 'at least 1 full equation' in str(e):
        solutions = np.linalg.solve(np.array(a, float), np.array(b, float))

When it happens

Trigger: Calling solve_simultaneous([[0, 2, 3], [4, 0, 6]]) — each row has a 0 coefficient, so no row is 'full'. Note the constant term also participates in the 0 check: [[1, 2, 0], [3, 4, 0]] has zero constants and also raises, even though the system is solvable as homogeneous.

Common situations: Diagonal-style systems (x appears only in one equation); systems with zero right-hand sides; sparse coefficient matrices from modeling. The zero-in-constants false positive is a known sharp edge — a system like x+y=0 is rejected even though it is tractable.

Related errors

• solve_simultaneous() requires lists of integers
• Input list must be a non empty list
• Input series is not valid, valid series - [1, 2/3, 2]
• Input list must be a non empty list
• Input series cannot have 0 as an element

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/ed4709fd7ee4837f. Report an issue: GitHub.