The Functions tab

In both editions

A reference of every built-in function, plus the list of names you may not reuse.

Typed in, answered back

Every example here has been run and tested.

These are not merely illustrations; they are carefully verified examples drawn directly from the system's own reference. Every example is automatically tested, and the build will stop if even one result has changed unexpectedly. That gives us something important as teachers and scientists: a reliable connection between what we see in the manual and what the system actually does. When an example is included here, you can trust that it has been tested and works as described.

The functions a physics course runs into

InbesselY(0, 1)

Out0.0883

This is the Bessel function of the second kind, which is finite everywhere except at the origin, where it diverges.

A matrix in an exponent

InmatrixExponential([[2, 0], [0, -3]])

Out[[7.3891, 0], [0, 0.0498]]

For a diagonal matrix, each entry becomes e raised to that entry. This is a case you can check by hand before trusting the ones you cannot.

The last two examples are recent additions, and they arrived with many others. The special functions are included in full: both kinds of Bessel function, the Airy pair, the error function and its relatives, the Fresnel and Dawson integrals, the exponential integrals, the Riemann zeta and Debye functions, Lambert W, digamma, the Voigt profile, the spherical harmonics, and the hypergeometric functions on which many of the others rest. Beside them are the matrix functions: matrixExponential, which, given a vector as well, acts on the vector without forming the matrix exponential itself; matrixLogarithm, its inverse; and matrixSquareRoot. Finally, random is a class with several members, so random.uniform(), random.integer(1, 6), random.choice(...) and random.shuffle(...) read the way you would say them, and every distribution the program knows can be sampled.

The Functions tab open at the Fourier and Signals page, showing the FFT card with its usage line, its written-out definition, and worked examples in colored code beneath each one — The Functions tab, where these functions are documented. There is one card per function, with a usage line for every way it can be called and, where there is one, the exact definition written out, followed by examples that the build runs, colored the way the editor colors what you type. The tab can be searched by name or by any word in a description.

Previous: Chem All tabs Next: Manual