A specialized alternative involves the generation of optimized code for quantities defined mathematically within a Computer algebra system (CAS).
MATHLAB ("mathematical laboratory") should not be confused with MATLAB ("matrix laboratory") which is a system for numerical computation built 15 years later at the University of New Mexico, accidentally named rather similarly.
Computer algebra systems, which can manipulate mathematical expressions, including evaluating simple calculations.
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The case of purely algebraic functions was solved and implemented in Reduce by James H. Davenport.
It was first implemented in Reduce in the case of purely transcendental functions; the case of purely algebraic functions was solved and implemented in Reduce by James H. Davenport; the general case was solved and implemented in Axiom by Manuel Bronstein.
Bill Gosper discovered this algorithm in the 1970s while working on the Macsyma computer algebra system at SAIL and MIT.
The HAM is an analytic approximation method designed for the computer era with the goal of "computing with functions instead of numbers." In conjunction with a computer algebra system such as Mathematica or Maple, one can gain analytic approximations of a highly nonlinear problem to arbitrarily high order by means of the HAM in only a few seconds.
Scientific WorkPlace includes a built-in computer algebra system (Maple in earlier versions and/or MuPAD in later versions) with which one can perform computations and generate plots from inside the editor.