Differences between revisions 11 and 12
 ⇤ ← Revision 11 as of 2007-11-05 20:44:13 → Size: 1817 Editor: RogerHui Comment: ← Revision 12 as of 2008-12-08 10:45:45 → ⇥ Size: 1818 Editor: anonymous Comment: converted to 1.6 markup Deletions are marked like this. Additions are marked like this. Line 9: Line 9: in conventional notation sum is [[latex($$\sum$$)]] and product is [[latex($$\prod$$)]]. in conventional notation sum is <> and product is <>. Line 21: Line 21: ||  (+%)/ y  || continued fraction; e.g. (+%)/n$1 approximates [[latex($$\phi$$)]] |||| {{{ +%/ y }}} || generalized continued fraction; e.g.{{{ +%/ 3,6,.~*:1+2*i.n }}}approximates [[latex($$\pi$$)]] || ||  (+%)/ y  || continued fraction; e.g. (+%)/n$1 approximates <> |||| {{{ +%/ y }}} || generalized continued fraction; e.g.{{{ +%/ 3,6,.~*:1+2*i.n }}}approximates <> || Line 24: Line 24: ||  y {~ /:@/:@,/ ((-i.)#y)#:x  || computation of x A. y ; see [:../Permutation_Index:Permutation Index] || ||  y {~ /:@/:@,/ ((-i.)#y)#:x  || computation of x A. y ; see [[../Permutation Index|Permutation Index]] || Line 34: Line 34: [[BR]] <
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is an adverb and u/y applies the dyad u between the items of y . For example, +/y computes the sum. This differs from conventional mathematical notation in making explicit that there is an adverb and that no special symbol is required for u/ for each function u . For example, in conventional notation sum is and product is .

The more general m/y inserts successive verbs from the gerund m between items of y , extending m cyclically as required.

Some examples of insert:

 +/ y sum */ y product; (!n) = */1+i.n -/ y alternating sum; e.g. -/ z (^%!@]) 1+2*i.n approximates sin z >./ y maximum <./ y minimum (+%)/ y continued fraction; e.g. (+%)/n\$1 approximates +%/ y generalized continued fraction; e.g. +%/ 3,6,.~*:1+2*i.n approximates +`*/ }:,x,.y computation of x p. y by Horner's rule y {~ /:@/:@,/ ((-i.)#y)#:x computation of x A. y ; see Permutation Index (<@i.@>:@I.~ C. ,)/ y an O(n2) sort of vector y *./ #&> C. p the size of the subgroup generated by permutation p *./ b Are all of b true? +./ b Is any of b true? ~:/ b 1 iff the number of 1s is odd =/ b 1 iff the number of 0s is even

Contributed by RogerHui.

Essays/Insert (last edited 2008-12-08 10:45:45 by anonymous)