Simulating rational number addition/subtraction

Simulating rational number addition/subtraction

[Lawrence Bottorff]

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With guile (and a few other Schemes/Lisps) you can directly add fractions
or rational numbers:

(+ 1/2 1/12)
=> 7/12

It's like magic, no? Anyway, I'm trying -- for educational purposes -- to
reproduce this functionality. But right out of the blocks I'm stuck trying
to figure out how to handle incoming parameters. So far I've got

(define (myrat a b)
   . . .)

(define (myrat a b c d)
   . . .)

where numerator and denominator are given separately, as well as

(define (myrat . fracparams)
   . . .)

which still has my basic problem, namely, can one parameter hold both parts
of a rational number, then allow the numerator and denominator to be peeled
off and worked on, i.e., something like

(let ((num1 numepeeler(a))
       (denom1 denompeeler(a)


LB

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Re: Simulating rational number addition/subtraction

[dsmich]

---- Lawrence Bottorff <borgauf@gmail.com> wrote: 
> With guile (and a few other Schemes/Lisps) you can directly add fractions
> or rational numbers:
> 
> (+ 1/2 1/12)
> => 7/12
> 
> It's like magic, no? Anyway, I'm trying -- for educational purposes -- to
> reproduce this functionality. But right out of the blocks I'm stuck trying
> to figure out how to handle incoming parameters. So far I've got
> 
> (define (myrat a b)
>    . . .)
> 
> (define (myrat a b c d)
>    . . .)
> 
> where numerator and denominator are given separately, as well as
> 
> (define (myrat . fracparams)
>    . . .)
> 
> which still has my basic problem, namely, can one parameter hold both parts
> of a rational number, then allow the numerator and denominator to be peeled
> off and worked on, i.e., something like
> 
> (let ((num1 numepeeler(a))
>        (denom1 denompeeler(a)
> 
> 
> LB

This https://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html might be enlightening....

-Dale

Re: Simulating rational number addition/subtraction

[Jan Wedekind]

On 24. Februar 2016 22:27:45 GMT+00:00, Lawrence Bottorff <borgauf@gmail.com> wrote:
>With guile (and a few other Schemes/Lisps) you can directly add
>fractions
>or rational numbers:
>
>(+ 1/2 1/12)
>=> 7/12
>
>It's like magic, no? Anyway, I'm trying -- for educational purposes --
>to
>reproduce this functionality. But right out of the blocks I'm stuck
>trying
>to figure out how to handle incoming parameters. So far I've got
>
>(define (myrat a b)
>   . . .)
>
>(define (myrat a b c d)
>   . . .)
>
>where numerator and denominator are given separately, as well as
>
>(define (myrat . fracparams)
>   . . .)
>
>which still has my basic problem, namely, can one parameter hold both
>parts
>of a rational number, then allow the numerator and denominator to be
>peeled
>off and worked on, i.e., something like
>
>(let ((num1 numepeeler(a))
>       (denom1 denompeeler(a)
>
>
>LB

You can use GOOPS (*) to represent the rational numbers.

(*) http://www.gnu.org/software/guile/manual/html_node/GOOPS.html
-- 
Jan Wedekind
http://www.wedesoft.de/

Re: Simulating rational number addition/subtraction

[tomas]

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On Wed, Feb 24, 2016 at 06:32:12PM -0500, dsmich@roadrunner.com wrote:

[representing rationals]

> This https://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html might be enlightening....

Yes. "Structure and Interpretation of Computer Programs" (here affectionately
known as "SICP") *very* *warmly* recommended.

- -- t
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Re: Simulating rational number addition/subtraction

[Alex Vong]

<tomas@tuxteam.de> writes:

> On Wed, Feb 24, 2016 at 06:32:12PM -0500, dsmich@roadrunner.com wrote:
>
> [representing rationals]
>
>> This https://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html
>> might be enlightening....

There are also video lectures recorded in 1986 in addition to the book
<http://cynic.cc/blog/posts/2015-01-17_uploading_sicp_to_youtube/>.
Lecture 2B talks about implementing rational numbers using CONS, CAR and
CDR as an example of data abstraction. Then, to "terrify" you by showing
CONS, CAR and CDR can be built from "air". Watch the lecture or the book
(the link of enlightenment given by Dale) to find out what does it mean
:)

>
> Yes. "Structure and Interpretation of Computer Programs" (here affectionately
> known as "SICP") *very* *warmly* recommended.
>
> -- t