Re: How to roll up multiple Line calls into a loop
- To: mathgroup at smc.vnet.net
- Subject: [mg118341] Re: How to roll up multiple Line calls into a loop
- From: Dan <dflatin at rcn.com>
- Date: Sat, 23 Apr 2011 07:50:00 -0400 (EDT)
- References: <iorih5$o6t$1@smc.vnet.net>
On Apr 22, 5:41 am, Sol Lederman <sol.leder... at gmail.com> wrote:
> Hi,
>
> I'm new to Mathematica.
>
> I have the following bit of graphics:
>
> Graphics[{
> Line[{{0, 10}, {1, 0}}],
> Line[{{0, 9}, {2, 0}}],
> Line[{{0, 8}, {3, 0}}],
> Line[{{0, 7}, {4, 0}}],
> Line[{{0, 6}, {5, 0}}],
> Line[{{0, 5}, {6, 0}}],
> Line[{{0, 4}, {7, 0}}],
> Line[{{0, 3}, {8, 0}}],
> Line[{{0, 2}, {9, 0}}],
> Line[{{0, 1}, {10, 0}}],
> }]
>
> I want to simplify it to do some sort of iteration to compute the end points
> of the lines. I can do this easily in a variety of procedural languages but
> I haven't yet grokked how Mathematica would do this.
>
> Would someone please show me the short way, I imagine using Table somehow?
>
> Thanks.
>
> Sol
Graphics[(Line[{{0,11-#},{#,0}}]&)/@Range[10]]
But let's take this appart a little. This short Mathematica expression
has a number of parts and it is worth looking at each of them.
Beginning at the right hand side, look at Range[10]
In[10]:= Range[10]
Out[10]= {1,2,3,4,5,6,7,8,9,10}
See how it can generate a sequence of numbers. This function is very
general, having the flexibility for creating almost any sort of
uniformly spaced set of values.
The next key element is the operator /@. This is shorthand for Map
which takes a function and applies it to each element of a list.
The function applied is a pure function, also called an anonymous
function in some languages:
(Line[{{0,11-#},{#,0}}]&)
The key syntactical elements are the Slot symbol, #, and the function
terminator, &. The outer parentheses are not needed but it is a good
practice to delimit your inline functions so it is obvious when
reading your code what the function is.
Dan