from typing import Any

from sympy.matrices.dense import MutableDenseMatrix
from sympy.polys.matrices.domainmatrix import DomainMatrix

class PolyNonlinearError(Exception): ...

class RawMatrix(MutableDenseMatrix):
    _sympify = ...
    def __init__(self, *args, **kwargs) -> None: ...

def eqs_to_matrix(eqs_coeffs, eqs_rhs, gens, domain) -> DomainMatrix: ...
def sympy_eqs_to_ring(eqs, symbols) -> tuple[Any, Any]: ...
def solve_lin_sys(eqs, ring, _raw=...) -> dict[Any, Any] | None: ...