Logiweb(TM)

11.8 combinations: a small program and a testsuite

Prev Up Next Page 385 of 800 Search internet


The combinations page defines a function (the 'combinations' function, also known as the binomial coefficient) and a test case. It also defines the rendering of the function such the function looks the same as it does in math books. A numbered version of the combinations.lgs source text is included below. Also see the original, unnumbered lgs file, the main pdf, and the document root.

     1	"";;0143BAB3BC67212340C9406BDB560819F3DCD4E859FC96F7B1C2B2BB0806
     2	""P combinations
     3	
     4	""R base
     5	
     6	""D 0
     7	(( " , " ))
     8	
     9	""B
    10	page ( ""N , ""C )
    11	title "Combinations"
    12	bib "
    13	@techreport{appendix,
    14	  author    = {A. U. Thor},
    15	  year      = {2006},
    16	  title     = {Combinations - appendix},
    17	  institution={Logiweb},
    18	  note      =
    19	{\href{\lgwBlockRelay \lgwBlockThis /page/appendix.pdf}{%
    20	\lgwBreakRelay \lgwBreakThis /page/appendix.pdf}}}
    21	"
    22	main text "
    23	\title{Combinations}
    24	\author{A. U. Thor}
    25	\maketitle
    26	\tableofcontents
    27	\section{Combinations}
    28	The number of combinations of size "[[ k ]]" from a set
    29	of size "[[ n ]]" is given by the binomial coefficient
    30	"[[ (( n , k )) = n factorial div k factorial
    31	div ( n - k ) factorial ]]". A recursive definition
    32	of "[[ (( n , k )) ]]" may be stated thus:
    33	"[[[ value define (( n , k )) as if k = 0 then 1
    34	else (( n - 1 , k - 1 )) * n div k end define ]]]"
    35	As an example, we have "[[ ttst (( 4 , 2 )) = 6 end test ]]".
    36	For details on how the binomial coefficient is rendered, see
    37	\cite{appendix}.
    38	\bibliography{./page}
    39	"
    40	appendix "
    41	\title{Combinations - appendix}
    42	\author{A. U. Thor}
    43	\maketitle
    44	\tableofcontents
    45	\section{\TeX\ definitions}
    46	\begin{statements}
    47	\item "[[ tex show define (( n , k )) as "
    48	\left( \begin{array}{l} "[ n ]"
    49	\\ "[ k ]"
    50	\end{array}\right)" end define ]]"
    51	\end{statements}
    52	"
    53	end page
    54	
    55	
    56	
    57	

Prev Up Next Page 385 of 800 Search logiweb.eu

Copyright © 2010 Klaus Grue, GRD-2010-01-05