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Mathematica HowTo
How to | Work with Pure Functions
The ability to define and use your own functions is part of what gives Mathematica such power. It is often inconvenient to have to explicitly name a function for every small operation that you wish to perform. Mathematica lets you declare functions inline (called pure functions) to get around this.
The most transparent way to define a pure function is with Function. The first argument is a list of arguments, and the second is a function. This function adds its two arguments together:
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You do not need to give the function a name to use it:
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A common shorthand notation uses an & to mark the end of the pure function, with argument positions specified by #1, #2, and so on:
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The advantage of a pure function is that it does not require a separate definition or a name:
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If the pure function only has one argument, you can use # instead of #1. This function squares its argument:
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Pure functions become quite powerful when used together with Map.
This makes a list of complex numbers into a list of ordered pairs:
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This turns the ordered pairs back into complex numbers:
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You can use /@ as a shorthand for Map. Use a pure function to create a list of clickable buttons:
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