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Re: What does & mean?

  • To: mathgroup at
  • Subject: [mg107064] Re: [mg107050] What does & mean?
  • From: "David Park" <djmpark at>
  • Date: Tue, 2 Feb 2010 03:25:31 -0500 (EST)
  • References: <20738936.1265024588004.JavaMail.root@n11>

It's difficult to just use Mathematica off the shelf for advanced problems.
There is a somewhat steep learning curve. The example presupposes a fair
amount of Mathematica knowledge.

The Documentation Center itself can be intimidating. The places to start
might be:
1) First Steps with Mathematica (at the bottom of the main page).
2) Core Language: Language Overview, Expressions, Rules & Patterns, Lists,
Variables & Functions and Functional Programming.
3) Then what seems useful.

The '&' character is used to terminate a pure function. You can learn about
pure functions under Function in the Core/Functional Programming section.
(How would one know to look up Function? I don't know.) Pure functions are a
method for defining some action that might have only temporary use. (In your
example it sets up an equation between the two sides. MapThread is another
Functional programming construct. It is very worthwhile learning how to use
Functional programming. It is really great and Mathematica is generally more
efficient with functional programming than with procedural programming.)

Here is a little example of solving an equation 'by hand' using pure
functions. (Just copy and paste it into a notebook.) '#' stands for the
argument, in this case a side of the equation, and we Map ('/@' ) the pure
functions onto each side of the equations.

Print["Equation to Solve for y"]  
step1 = a (x + y) == b  
Print["Divide both sides by a"]  
step2 = #/a & /@ step1  
Print["Subtract x from both sides"]  
# - x & /@ step2  

The best way to learn may be to type the Doc Center examples into your own
notebook and evaluate, and to try a few modifications. Then once you are
familiar with the core constructs, try to 'fly solo' by working some SIMPLE
problems you know about from some NON-Mathematica book.

David Park
djmpark at  

From: Michael Knudsen [mailto:micknudsen at] 


I have recently bought Mathematica, and I have a really tough time
getting started. I'm reading the various documents found under
"Complete Documentation" at the Mathematica homepage, but it doesn't
feel like the right place to start.

For example, I'm now trying to solve some simple differential
equations, and the documentation provides the following example:

A = {{4, -6}, {1,-1}};

X[t_] = {x[t], y[t]};
system = MapThread[#1 == #2 &, {X'[t], A.X[t]}];

sol = DSolve[system, {x,y}, t]

However, there is no explanation of how & works here (and it isn't in
the MapThread documentation either). Where should one start reading in
order to understand basic constructs like this? This particular
example is really nasty, since & is generally ignored by search

Michael Knudsen

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