The problem was a^4*a^-6, I said a^-2, my software
(http://www.theoryyalgebra.com/) said it was not simplest form, but
1/a^2 was.
Who is right?!!!
Mind you the target is an educational setting, if that matters.
I think my software is right, but I started to wonder.
cheers, kenny
---
http://www.theoryyalgebra.com/
From: Don Geddis
Subject: Re: Is a^-2 in simplest form? (Hoist on my own petard!)
Date:
Message-ID: <87vdy0fhlz.fsf@geddis.org>
Kenny <·········@gmail.com> wrote on Sat, 16 Aug 2008:
> The problem was a^4*a^-6, I said a^-2, my software
> (http://www.theoryyalgebra.com/) said it was not simplest form, but 1/a^2
> was. Who is right?!!! Mind you the target is an educational setting, if
> that matters. I think my software is right, but I started to wonder.
Do you think "simplest form" has a precise definition, over all possible
mathematical expressions? That there is always a single, correct answer?
I suspect that, in some corner cases, the "correct" answer may depend on
context.
-- Don
_______________________________________________________________________________
Don Geddis http://don.geddis.org/ ···@geddis.org
I think there are some things you can only learn by experience. Like, never
put an ice cube down the back of somebody who's shooting a bow and arrow.
-- Deep Thoughts, by Jack Handey [1999]
Don Geddis wrote:
> Kenny <·········@gmail.com> wrote on Sat, 16 Aug 2008:
>
>>The problem was a^4*a^-6, I said a^-2, my software
>>(http://www.theoryyalgebra.com/) said it was not simplest form, but 1/a^2
>>was. Who is right?!!! Mind you the target is an educational setting, if
>>that matters. I think my software is right, but I started to wonder.
>
>
> Do you think "simplest form" has a precise definition, over all possible
> mathematical expressions? That there is always a single, correct answer?
I thought that was 42.
Anyway, you are right, I neglected option three, aka "both acceptable".
I have a lot of different rewrites I try to identify acceptable
alternative forms, so one option is indeed to create another such
rewrite. We will have new ballots printed and hold new elections.
>
> I suspect that, in some corner cases, the "correct" answer may depend on
> context.
Yeah. I think a^-2 is cool, but if it were a^-2 * b^3 I would like to
see b^3 / a^2.
Ah, Just checked my Gustafson&Frisk "Beginning Algebra": 1/a^2 is The
One Correct Answer. :)
kt
Kenny escribi�:
> Don Geddis wrote:
>> Kenny <·········@gmail.com> wrote on Sat, 16 Aug 2008:
>>
>>> The problem was a^4*a^-6, I said a^-2, my software
>>> (http://www.theoryyalgebra.com/) said it was not simplest form, but
>>> 1/a^2
>>> was. Who is right?!!! Mind you the target is an educational
>>> setting, if
>>> that matters. I think my software is right, but I started to wonder.
>>
>>
>> Do you think "simplest form" has a precise definition, over all possible
>> mathematical expressions? That there is always a single, correct answer?
>
> I thought that was 42.
>
> Anyway, you are right, I neglected option three, aka "both acceptable".
> I have a lot of different rewrites I try to identify acceptable
> alternative forms, so one option is indeed to create another such
> rewrite. We will have new ballots printed and hold new elections.
>
>>
>> I suspect that, in some corner cases, the "correct" answer may depend on
>> context.
>
> Yeah. I think a^-2 is cool, but if it were a^-2 * b^3 I would like to
> see b^3 / a^2.
>
> Ah, Just checked my Gustafson&Frisk "Beginning Algebra": 1/a^2 is The
> One Correct Answer. :)
>
> kt
But if you want to be absolutely helpful to your prospective users,
accept any of both answers as good and show the alternative, in order to
reinforce the learning of the relationship between a^-2 and 1/a^2.
And if possible, explain why it is so.
And if you can, go *personally* to explain why... Sorry. Leaving user
mode right now.
Leandro
Kenny wrote:
> The problem was a^4*a^-6, I said a^-2, my software
> (http://www.theoryyalgebra.com/) said it was not simplest form, but
> 1/a^2 was.
Simplest form is ill-defined. Personally, I'd accept both. Some
educators prefer 1/a^2 since it avoids negative exponents while others
prefer a^-2 since it avoids the fraction, hence being marginally simpler.
Just be sure to document what your software expects and/or provide a
config option for the teacher to set.
That's my two cents. You might also query sci.math.symbolic -- its
not completely dead -- or ask the developers of Axiom/FriCAS/OpenAxiom
or Maxima or Sage or...
- Daniel
On Sat, 16 Aug 2008 23:25:59 -0400, D Herring
<········@at.tentpost.dot.com> wrote:
>Kenny wrote:
>> The problem was a^4*a^-6, I said a^-2, my software
>> (http://www.theoryyalgebra.com/) said it was not simplest form, but
>> 1/a^2 was.
>
>Simplest form is ill-defined. Personally, I'd accept both. Some
>educators prefer 1/a^2 since it avoids negative exponents while others
>prefer a^-2 since it avoids the fraction, hence being marginally simpler.
>
>Just be sure to document what your software expects and/or provide a
>config option for the teacher to set.
Or make sure the software accepts both.
>That's my two cents. You might also query sci.math.symbolic -- its
>not completely dead -- or ask the developers of Axiom/FriCAS/OpenAxiom
>or Maxima or Sage or...
>
>- Daniel
George
From: Frederick Williams
Subject: Re: Is a^-2 in simplest form? (Hoist on my own petard!)
Date:
Message-ID: <48A7F3EF.E8B67E1A@tesco.net>
Kenny wrote:
>
> The problem was a^4*a^-6, I said a^-2, my software
> (http://www.theoryyalgebra.com/) said it was not simplest form, but
> 1/a^2 was.
>
> Who is right?!!!
"Simplest form" has no precise definition so the question is not
answerable. In the context of formalized languages "simplest" could be
defined to mean "that which has the smallest number of symbols", but
that is of no relevance here.
--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day.
Frederick Williams wrote:
> Kenny wrote:
>
>>The problem was a^4*a^-6, I said a^-2, my software
>>(http://www.theoryyalgebra.com/) said it was not simplest form, but
>>1/a^2 was.
>>
>>Who is right?!!!
>
>
> "Simplest form" has no precise definition so the question is not
> answerable.
If you gave a test and said reduce to simplest form... well, one book I
have explicitly says to rewrite without negative exponents. I imagine
before any test we would spell that out, or on the test likewise make
the requirmeent explicit.
I think I will let the community complain, and it may well end up a
preference.
> In the context of formalized languages "simplest" could be
> defined to mean "that which has the smallest number of symbols", but
> that is of no relevance here.
>
I heard that suggestion on my last such suggestion. Ironically 1/a^2 has
more symbols than a^-2.
thx to all for the input.
kenny
---
http://www.theoryyalgebra.com/
From: Frederick Williams
Subject: Re: Is a^-2 in simplest form? (Hoist on my own petard!)
Date:
Message-ID: <48A835B2.98CE415@tesco.net>
Kenny wrote:
>
> Frederick Williams wrote:
> > Kenny wrote:
> >
> >>The problem was a^4*a^-6, I said a^-2, my software
> >>(http://www.theoryyalgebra.com/) said it was not simplest form, but
> >>1/a^2 was.
> >>
> >>Who is right?!!!
> >
> >
> > "Simplest form" has no precise definition so the question is not
> > answerable.
>
> If you gave a test and said reduce to simplest form...
If I was in that position (luckily I'm not) I'd accept both 1/a^2 and
a^-2 as correct.
> well, one book I
> have explicitly says to rewrite without negative exponents. I imagine
> before any test we would spell that out, or on the test likewise make
> the requirmeent explicit.
--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day.
From: hostlocal
Subject: Re: Is a^-2 in simplest form? (Hoist on my own petard!)
Date:
Message-ID: <g8g6o5$p9e$1@news.albasani.net>
"Kenny" <·········@gmail.com> wrote in message
······························@cv.net...
> The problem was a^4*a^-6, I said a^-2, my software
> (http://www.theoryyalgebra.com/) said it was not simplest form, but 1/a^2
> was.
>
> Who is right?!!!
>
> Mind you the target is an educational setting, if that matters.
>
> I think my software is right, but I started to wonder.
>
> cheers, kenny
> ---
> http://www.theoryyalgebra.com/
a^-2 is, least number of symbols -- from Ga Tech Math dept
hostlocal wrote:
> "Kenny" <·········@gmail.com> wrote in message
> ······························@cv.net...
>
>>The problem was a^4*a^-6, I said a^-2, my software
>>(http://www.theoryyalgebra.com/) said it was not simplest form, but 1/a^2
>>was.
>>
>>Who is right?!!!
>>
>>Mind you the target is an educational setting, if that matters.
>>
>>I think my software is right, but I started to wonder.
>>
>>cheers, kenny
>>---
>>http://www.theoryyalgebra.com/
>
>
>
> a^-2 is, least number of symbols -- from Ga Tech Math dept
>
>
Yeah, I think the instructions to elim neg expons has to be explicit or
this is acceptable. But I think the /math/ denoted by 1/a^2 is much
simpler than that denoted by a^-2. The latter goes through a^0-2 to a
def of division of a^m/a^n = a^m-n to get to the idea that a^-2 is the
inverse of a^2, while 1/a^2 Just Says It. So symbol-counting may not be
the right criterion.
kt
From: Kaz Kylheku
Subject: Re: Is a^-2 in simplest form? (Hoist on my own petard!)
Date:
Message-ID: <20080820122401.253@gmail.com>
On 2008-08-17, Kenny <·········@gmail.com> wrote:
> The problem was a^4*a^-6, I said a^-2, my software
> (http://www.theoryyalgebra.com/) said it was not simplest form, but
> 1/a^2 was.
>
> Who is right?!!!
The Harrop complexities H of these formulae are:
H(a^-2) = 4
H(1/a^2) = 5
So according to this metric, the former is the simpler.