LOGO-L> min max

[neuwirth <neuwirth@smc.univie.ac.at>]

i have to talk about my favorite set of tools in logo again:
thanks to brian we have map and friends

map applies a function to a list of arguments.
rseq (now in ucblogo and mswlogo)
gives equally spaced sequences.

let us look for the maximum of x*x*(1-x) on the interval from 0 to 1

map [? * ? * (1 - ?)] rseq 0 1 21
gives the list of values for
0, 0.05, 0.1, 0,15 ....

we want to see the input producaing a value and tha value itself,
therefore we do:

map [list ? (? * ? * (1 - ?))] rseq 0 1 21

now we want to find the input-value pair with the maximal value

iwill reuse some of the things from the pirate project

we need max of a list of values

to max :a :b
output ifelse :a < :b [:b] [:a]
end

to max.list :l
if (count :l) = 2 [output first :l]
output reduce "max :l
end

to maxfind :funlist
localmake "ourmax max.list map [first butfirst ?] :funlist
output filter [:ourmax = first butfirst ?] :funlist
end


with these tools

maxfind map [list ? (? * ? * (1 - ?))] rseq 0 1 21

will give the maximal value
if you need functions with an arugment of x
(or any other named argument)
you also can do

maxfind map [[x] list :x (:x * :x * (1 - :x))] rseq 0 1 21

this is rather close to how one would express the
definition of a maximum in mathematical notation,
and at the same time it works.

there si one programming language which
gets even closer to mathematical notation
for this type of example, it is ISETL


--
Erich Neuwirth <neuwirth@smc.univie.ac.at>
Computer Supported Didactics Working Group, Univ. Vienna
Visit our SunSITE at http://sunsite.univie.ac.at



---------------------------------------------------------------
Please post messages to the Logo forum to logo-l@gsn.org.  Mail
questions about the list administration to logofdn@gsn.org.  To
unsubscribe send    unsubscribe logo-l    to majordomo@gsn.org.