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:[email protected]] On Behalf Of Henry
Rich Sent: Thursday, March 10, 2016 6:58 PM To:
[email protected] 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
<[email protected]> > wrote: > >> ,'ace',.'bdf' >>
abcdef >> 'ace',@,.'bdf' >> abcdef >> >> >> On Thu, Mar 10, 2016
at 2:47 PM, Roger Hui >> <[email protected]> >>
wrote: >> >>> ,|:'ace',:'bdf' >>> abcdef >>> 'ace'([: ,
|:@,:)'bdf' >>> abcdef >>> >>> >>> On Thu, Mar 10, 2016 at 2:42 PM,
Kip Murray <[email protected]> >>> 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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