Chris Burke wrote:
> I don't think Mathematica had any influence on J, though perhaps APL had
> a minor influence on Mathematica.

Mathematica was directly inspired by APL in certain operations, notably
Map, Apply, Scan and Fold.  Early versions of the Mathematica
documentation contained a lot of references to APL: these have decreased
over time.

Much of the symbolic programming in Mathematica comes from Macsyma, in
particular the ideas of many different types for mathematical expressions
assembled in a directed acyclic graph; the functional programming idea of
remembering the result of every functional evaluation; and a knowledge
base of rules and heuristics for simplification of expressions.  These
types of operations have no equivalent in APL or J, and there has been
little cross-pollination.

Mathematica (like everyone else) relies on LAPACK and other Fortran
libraries for hard-core numerical calculations.

Best wishes,

John


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