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Technology Guide--The Technology Inside Matters
Symbolically Enhanced Numeric Computing

Entering this differential equation into a non-Mathematica, numeric-only system required its manual rewriting into two first-order equations. In contrast, Mathematica performs the transformation automatically.

Symbolically enhanced numeric computing is the ability of Mathematica to apply symbolic transformations automatically to an ostensibly numerical computation to optimize computation time and accuracy--or to make it directly computable at all.

Often a numerical algorithm requires a particular form of expression with which to operate. In non-Mathematica systems, that specific form must be input to enable computation; with symbolically enhanced numeric computing, Mathematica automatically transforms the provided expression to reach this required form. The benefit of this approach is crucial for ease of use: it enables a wide range of problems to be input without a user's (sometimes complex) pencil-and-paper transformation beforehand.

Additionally, this intelligent expression transformation cuts unnecessary computations by getting expressions into the easiest-to-evaluate form, sometimes even avoiding a failure of the computation where the untransformed expression would have exhibited numerical instability.

Mathematica is unique in being equipped to take this approach because of its mixed symbolic-numeric architecture and the range of its symbolic transformation capabilities.

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