solvers.tex

SymPy has equation solvers that can handle ordinary differential equations,
recurrence relationships, Diophantine equations\footnote{See
  section~\ref{S-suppsec:Dioph} of the supplementary material for an in depth
  discussion on the Diophantine submodule.}, and algebraic equations. There is
also rudimentary support for simple partial differential equations.

There are two functions for solving algebraic equations in SymPy:
\texttt{solve} and \texttt{solveset}.
\texttt{solveset} has several design changes with respect to the older
\texttt{solve} function. This distinction is present in order to resolve the
usability issues with the
previous \texttt{solve} function API while maintaining backward compatibility
with earlier versions of SymPy.
\texttt{solveset} only requires essential input information from the user.
The function signatures of \texttt{solve} and \texttt{solveset} are
\begin{verbatim}
solve(f, *symbols, **flags)
solveset(f, symbol, domain=S.Complexes)
\end{verbatim}
The \texttt{domain} parameter can be any set from the \texttt{sympy.sets}
module (see section~\ref{S-suppsec:Sets} of the supplementary material for
details on \texttt{sympy.sets}), but is typically either \texttt{S.Complexes}
(the default) or \texttt{S.Reals}; the latter causes \texttt{solveset} to only
return real solutions.

An important difference between the two functions is that the output API of \texttt{solve}
varies with input (sometimes returning a Python list and sometimes a Python dictionary) whereas
\texttt{solveset} always returns
a SymPy set object.

Both functions implicitly assume that expressions are equal to 0. For
instance, \texttt{solveset(x - 1, x)} solves $x - 1 = 0$ for $x$.

\texttt{solveset} is under active development as a planned replacement for
\texttt{solve}. There are certain features which are implemented in
\texttt{solve} that are not yet implemented in \texttt{solveset}, including
multivariate systems, and some transcendental equations.

Some examples for \texttt{solveset} and \texttt{solve} can be found in
section~\ref{S-suppsec:examples} of the supplementary material.