Logiweb(TM)

6.5.2 Definitions

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Recall the source of the combinations page:

     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	

Line 7 defines that the combinations construct looks thus in the source text: (( m , n )).

Line 47-50 define that the combinations construct looks thus in the rendering: (( m , n )).

Try to put you mouse over (( m , n )). In the present documentation you can see the source of rendered constructs as tooltips.

Line 47-50 define the 'show' aspect of the combinations construct. The show aspect is used for rendering. The 'tex' in Line 47 is a rudiment.

Line 33 to 34 define the 'value' aspect of combinations construct. A 'value definition' is what programmers may think of as the definition of the construct. Mathematicians may also think of the value definition as the definition or they may prefer the 'math' definitions treated later, or they may prefer to define and use their own aspects.

On the combinations page, the combinations construct has four definitions: a value, a show, a name, and a charge definition. The latter two are generated by the N and C escapes in Line 10.

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