[Jprogramming] Interweave

[Martin Kreuzer]

To keep students organized in dealing with fractions I sometimes (on 
a good day) have them work out intermediate results of continued 
fractions like phi = [1; 1, 1, 1, ...] or sqrt(2) = [1; 2, 2, 2, ...].

This example I found at
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html

45/16 = [2; 1, 4, 3]

I then went on clumsily, further down using the "strategy" (as Linda 
Alford put it):

    ln=. 2 1 4 3  NB. list notation (shorthand)
    ] ip=. {. ln  NB. get integer part
2
    ] fp=. }. ln  NB. get fractional part
1 4 3
    ] nn=. (# fp) $ 1  NB. produce additional numerators (all 1)
1 1 1
    ] fpn=. ,nn ,.fp  NB. "interweave" fractional part with added 
numerators to yield
1 1 1 4 1 3
    ] lne=. ip ,fpn  NB. "list notation (expanded)" value for the 
Cont. Fraction function
2 1 1 1 4 1 3
    cf=. +`% /
    cf lne
2.8125
    ^.^ 45r16
2.8125

-M

At 2016-03-11 08:54, you wrote:
>Maybe...  The new list interweaves the two original lists. The 
>"strategy" also applies to lists of numbers. Linda -----Original 
>Message----- From: Programming 
>[mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Henry 
>Rich Sent: Thursday, March 10, 2016 6:58 PM To: 
>programming at jsoftware.com Subject: Re: [Jprogramming] Interweave 
>You're right... Now, how would you describe the order?  Would 'index 
>order" be enough?  The Dictionary says "normal order" and then goes 
>on to define it.  I have looked for years for the right words.  It 
>has to be short and intuitive - not a mathematical definition. How 
>about "in the order in which they appear in y"? Henry Rich On 
>3/10/2016 6:30 PM, Nicholas Spies wrote: > This is perhaps a 
>quibble, but... > > Looking at the NuVoc definition of , y Ravel > > 
>The following statement and the example directly below it... > 
>-------- > Produces a list 
><http://code.jsoftware.com/wiki/Vocabulary/AET#List> > containing 
>all the atoms > <http://code.jsoftware.com/wiki/Vocabulary/AET#Atom> 
>in y, in order. > > An atom 
><http://code.jsoftware.com/wiki/Vocabulary/AET#Atom> is > converted 
>to a 1-atom list > 
><http://code.jsoftware.com/wiki/Vocabulary/AET#List>, a list > 
><http://code.jsoftware.com/wiki/Vocabulary/AET#List> is left > 
>unchanged, and any noun > 
><http://code.jsoftware.com/wiki/Vocabulary/AET#Noun> > of higher 
>rank <http://code.jsoftware.com/wiki/Vocabulary/AET#Rank> is > 
>flattened into a list > 
><http://code.jsoftware.com/wiki/Vocabulary/AET#List> > >     ]z=: 0 
>10 20 +/ i.   NB. sample noun >   0  1  2  3  4 > 10 11 12 13 14 > 
>20 21 22 23 24 > >     ,z > 0 1 2 3 4 10 11 12 13 14 20 21 22 23 
>24 > ------------------- > > ...and 
>also... > >     ,'ace',.'bdf' > > abcdef > > > ...give the first 
>impression that Ravel puts the items into lexical > order, > > which 
>is misleading, as shown by the example 2 under Common Uses: > > > ]a 
>=: 4 4 ?@$ 100 > > 89 91 1 24 > > 88 43 43 32 > > 85 84 27 31 > > 10 
>11 49 90 > > +/ 50 < , a > > 6 > > ,a > > 89 91 1 24 88 43 43 32 85 
>84 27 31 10 11 49 90 > > > Since NuVoc is targeting new users, the 
>'in order' statement should. > IMHO, specify explicitly the order as 
>being <whatever description is appropriate>. > > > 
>Nick > > > > > > > > On Thu, Mar 10, 2016 at 5:48 PM, Roger Hui 
><rogerhui.canada at gmail.com> > wrote: > >>     ,'ace',.'bdf' >> 
>abcdef >>     'ace',@,.'bdf' >> abcdef >> >> >> On Thu, Mar 10, 2016 
>at 2:47 PM, Roger Hui >> <rogerhui.canada at gmail.com> >> 
>wrote: >> >>>     ,|:'ace',:'bdf' >>> abcdef >>>     'ace'([: , 
>|:@,:)'bdf' >>> abcdef >>> >>> >>> On Thu, Mar 10, 2016 at 2:42 PM, 
>Kip Murray <thekipmurray at gmail.com> >>> wrote: >>> >>>> A quickie -- 
>how do you interweave two equal-length lists, so 
>that >>>> >>>>     'ace' itw 'bdf' >>>> abcdef >>>> >>>> --Kip 
>Murray >>>> >>>> >>>> >>>> -- >>>> Sent from Gmail Mobile >>>> 
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