I've been reading your answer again and I learned a lot from your power verb
(but wonder what it is)
However I have two little verbs that are quite nice based on your work. It
seems like they should be able to be combined into one verb but I can't seem to
do that.
f=: 13 : 'y,+/_2{.y'
f 14
14 14
g=: 13 :'f^:(<:y) 1'
g 14
1 1 2 3 5 8 13 21 34 55 89 144 233 377
Your examples were very helpful. Thanks. Linda
-----Original Message-----
From: Programming [mailto:[email protected]] On Behalf
Of Don Guinn
Sent: Monday, February 27, 2017 1:06 PM
To: Programming forum
Subject: Re: [Jprogramming] Explicit fib
If I were teaching this I would first build some terms of the series manually.
Put on the board (or in a J session displayed on a screen in front of the
class):
1 1
Ask the class what is the sum of the last two numbers. Hopefully, someone says
"2". Then write "2" after the numbers on the board.
1 1 2
Ask again what the sum of the last two digits is. Answer: "3"
1 1 2 3
Repeat a couple of more times getting something like the following and give it
a name:
y=:1 1 2 3 5 8
This demonstrates what the series is and how to build it.
Now ask the class how to get the last two digits of y. (This is assuming you
have already introduced some J expressions like {. and +/ to the class
earlier.) In J that would be:
_2{.y
5 8
Now ask how to add the digits in J:
+/5 8
Then put it together:
+/_2{.y
13
Then concatenate it to the list built so far:
y,+/_2{.y
1 1 2 3 5 8 13
Now define a verb to do this, maybe called "f". Simply wrap what you have above
giving:
f =: 3 : 'y,+/_2{.y'
If you are doing this on a computer it would be easy to simply add the
characters around the expression already used.
Then go back to the beginning:
f 1 1
1 1 2
Then add an "f":
f f 1 1
1 1 2 3
And repeat for a while to something like:
f f f f f 1 1
1 1 2 3 5 8 13
power=:2 : 'v^:m y' NB. To repeat verb v m times A conjunction "power", which
you don't have to explain how it works to the class, simply have it already
defined.
Now use it with f:
f 1 1
1 1 2
1 power f 1 1
1 1 2
2 power f 1 1
1 1 2 3
5 power f 1 1
1 1 2 3 5 8 13
12 power f 1 1
1 1 2 3 5 8 13 21 34 55 89 144 233 377
It might be fun to ask them what the 100th fibonacci number is.
{:98 power f 1 1x
354224848179261915075
Then explain that since you started with 2 terms already you only needed to do
it 98 more times.
Okay, so this is not how to program in the tradition of C or whatever, but it
is J-like and should be easy for students to see what's happening. A way for
them to approach solving problems themselves by testing as they go.
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