Erlang (programming language)/Tutorials/Simplify

The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right.

Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template]

---

Simply Numerics

(auto-demotion of numerical types)

Lets simplify some numerical values recursively. Humans like to read numbers in simplest form. Rather than

    0 + 1i 

humans prefer

    i

Rather than

    4.000

the integer

    4 

looks nicer. In a matrix, we prefer the integers when possible, so we construct the following function: simplify, which is overloaded for many types of arguments, integer, float, imaginary, complex and matrix. We wish to remove extra zeros when possible, because they can be a distraction, and do not add any thing to calculations. This is an example of auto-demotion of numerical types. Many programming languages have auto-promotion of numerical types but almost never have auto-demotion.

-module(simple).
-compile(export_all). 

% Simplifies numbers by removing zeros 
 
start() -> 
	Inputs = [ 
 		3.3, 
 		3.0,
		{4,0,i},
		{3.0,i}, 
		{0,3,i}, 
		{0,3.3,i},
		[ [1.0,2.0], [3.0,4.0] ],
		[ [{0,1,i},{3.0,i}], [4,5.0] ],
		[ [1, 2, 3], [5.0, 4, 3] ]
		],
	Outputs = lists:map(fun simple:simplify/1, Inputs),
	Arrows = lists:duplicate(length(Outputs),"  ->  "),
	Inputs_and_Outputs = zipit(Inputs,Arrows,Outputs),
	Inputs_and_Outputs.

simplify(A) when trunc(A) == A ->          % 1.0 -> 1
	trunc(A);                           % make float integer
	
simplify({B,i}) ->                         % 1.0 i ->  1 i
	{simplify(B),i};                    % simplify imaginary

simplify({A,0,i}) ->                       % 2.2 + 0 i -> 2.2
       simplify(A);                        % make complex real
 	
simplify({0,B,i}) ->                       % 0 + B i -> B i 
       {simplify(B),i};                    % make complex imaginary
	
simplify({A,B,i}) ->                       % 1.0 + 2.0 i -> 1 + 2 i
       {simplify(A),simplify(B),i};        % simplify complex
 	
simplify([[A,B],[C,D]]) ->                 % [[ A.0, B.0 ]   ->  [[A,B]   
       [ [simplify(A), simplify(B)],       %  [ C.0, D.0 ]]       [C,D]] 
         [simplify(C), simplify(D)] ];     % simplify 2x2 matrix

simplify([]) -> [];                        %  [A.0, B.0, C.0 ...] -> [A,B,C...]
simplify([H|T]) ->                         % simplify vectors and matrixes   
       [simplify(H)] ++ simplify(T);       % of any size
	                                        
simplify(A) ->								 
       A.
	
zipit([],[],[]) -> [];                      % [1,2,3],[a,b,c],[do,re,me] ->	
zipit([H1|T1],[H2|T2],[H3|T3]) ->           %   [{1,a,do},{2,b,re},{3,b,me}]
       [{H1,H2,H3}] ++ zipit(T1,T2,T3).     % tripple zip

Outputs

Simplified numbers

1> c(simple).                       % compile
{ok,simple}
2> simple:start().                  % run
[{3.30000,"  ->  ",3.30000},
 {3.00000,"  ->  ",3},
 {{4,0,i},"  ->  ",4},
 {{3.00000,i},"  ->  ",{3,i}},
 {{0,3,i},"  ->  ",{3,i}},
 {{0,3.30000,i},"  ->  ",{3.30000,i}},
 {[[1.00000,2.00000],[3.00000,4.00000]],
  "  ->  ",
  [[1,2],[3,4]]},
 {[[{0,1,i},{3.00000,i}],[4,5.00000]],
  "  ->  ",
  [[{1,i},{3,i}],[4,5]]},
 {[[1,2,3],[5.00000,4,3]],"  ->  ",[[1,2,3],[5,4,3]]}]