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Technology Guide--The Technology Inside Matters
Interpolating Objects

Mathematica is unique in returning the results of numerical superfunctions (e.g. NDSolve) as symbolic functions representing the interpolation through ordinates taken--the interpolating object. This is in contrast to purely numerical systems, which return an unprocessed list of numbers.

Interpolating objects make results easily and immediately usable: for example, plotting, differentiating, or finding a specific value (whether or not it was picked for evaluation during the computation) can all be performed with a result as if it were any built-in mathematical function.

Solutions to complex differential equations are easy to plot accurately because interpolating functions are used to represent them.

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