Can someone please explain how to write functions in Wolfram Mathematica ?

[Physics_rocks]

I'm good in writing functions in Matlab , however since moving to Mathematica , I find it pretty hard to write them . For instance I need to write a function that returns a [1,0,-1] to integers, meaning x>0 , x==0 , x<0

with a single If , but I didn't find a way with one (only two)
sigNum[x_] := If[x < 0, -1, If[x > 0, 1, 0]]

and then using with PATTERNS . what are patterns and how do I use them ? tnx

 

[Dale]

There is a built in function for this called Sign.

Regarding patterns, you may want to start with the tutorial on patterns. In the search field of the help window type in: tutorial/PatternsOverview

Basically, you are already using patterns in the above definition, specifically, in sigNum[x_] the x_ is a pattern named x. You can refine your patterns to only apply in certain conditions by using the /; operator and the ? operator and you can also specify the head of the pattern. So x_Integer/;(x<0) would be a pattern that would match any negative integer.

 

[oswaler]

Sure, I'd be happy to explain how to write functions in Wolfram Mathematica. Functions in Mathematica are defined using the syntax "FunctionName[arguments]:= expression", where FunctionName is the name of the function, arguments are the variables that the function takes as input, and expression is the code that the function evaluates and returns as output.

In your specific case, if you want to write a function that returns -1 for x<0, 1 for x>0, and 0 for x=0, you can use the built-in function "Piecewise" which allows you to define functions with different behaviors for different input values. The syntax for using Piecewise is "Piecewise[{{value1, condition1}, {value2, condition2},...}]", where value1, value2, etc. are the values that the function returns for different conditions.

For your function, you can write it as "sigNum[x_] := Piecewise[{{-1, x < 0}, {1, x > 0}, {0, x == 0}}]". This will return -1 if x<0, 1 if x>0, and 0 if x=0. You can then use this function by simply calling "sigNum[x]" with your desired value for x.

Now, let's talk about patterns. Patterns in Mathematica are used to match specific types of input. For example, if you want your function to only accept integers as input, you can define it with the pattern "FunctionName[x_Integer]". This will ensure that the function only evaluates for integer values of x.

In your case, you can use patterns to make your function more robust and handle different types of input. For example, you can define your function as "sigNum[x_Integer] := Piecewise[{{-1, x < 0}, {1, x > 0}, {0, x == 0}}]". This will ensure that your function only evaluates for integer values of x, and returns an error message if a non-integer value is passed as input.

I hope this explanation helps you in writing functions in Mathematica. If you have any further questions, please feel free to ask.