Mathematica's task-oriented superfunctions (TOSF) each subsume the
functionality of a large number of algorithm-based functions
in non-Mathematica systems.
Unlike all other computation systems, Mathematica's functions
are "task-oriented"--named by which task they perform, not which
algorithm(s) they use to perform them.
This distinction particularly affects high-level, multistage,
multialgorithm tasks, handled by "superfunctions"
in Mathematica. Take numerical differential equation solving as
an example. In Mathematica, NDSolve
is all you need to use. Applying this TOSF analyzes your equation and
decides (unless you set an override) which of its dozens of algorithms and
controller methods to deploy to get you an accurate answer
quickly--sometimes switching mid-calculation for further optimization.
By contrast, non-Mathematica computation systems make you analyze
your equation manually to determine which function to apply--e.g.,
where in Mathematica you use NDSolve, in Matlab you
must choose among ode45, ode23, ode113, ode15s, bvp4c, pdepe, and so
on. Get the selection wrong and your computation could run
inefficiently, fail altogether, or, worse still, produce an inaccurate
answer. And there's no switching mid-calculation.
Another crucial benefit of the TOSF approach is future-proofing: algorithmic
innovations enable TOSF to perform better without the form of the input or
output being affected. Compatibility is therefore maintained while having
the latest computational technology under the skin.
This shows how task-oriented superfunctions can
each replace a large number of functions in non-Mathematica