On Thu, Apr 2, 2009 at 6:23 PM, Jason Grout <[email protected]> wrote:
>
> kcrisman wrote:
>>
>>> Incidentally, doing everything with floats would I
>>> think be *very* inappropriate for an undergrad class in linear
>>> algebra, where most of the by hand problems require the students to
>>> use rational numbers.
>>
>> Yes, which is why he only uses Octave for half the semester, I think,
>> or something like that.
>>
>
>
> Remember that both octave and matlab have a "format rat" mode, which
> displays fractions instead of floating point numbers. Rounding to get
> these nice displayed numbers is another issue, but it does look prettier
> and closer to what you do by hand.
>
> Jason
And Octave and Matlab give different answers by default and both
blatantly *lie* whenever there is overflow. Matlab and Octave are in
my opinion totally unsuitable for undergraduate linear algebra
teaching, except in a numerical analysis course. As a person who
actually knows what a rational number is, the behavior of Matlab makes
me cringe.
For example, in Octave:
octave:1> format rat;
octave:2> a = [-86/17,40/29,-68/43,-20/11;-24/17,-1/38,-2/25,49/17]
a =
-86/17 40/29 -68/43 -20/11
-24/17 -1/38 -2/25 49/17
octave:3> rref(a)
ans =
1 0 155/2122 -725/384
0 1 -152/173 -6553/795
and in Matlab:
>> format rat;
>> a = [-86/17,40/29,-68/43,-20/11;-24/17,-1/38,-2/25,49/17]
a =
-86/17 40/29 -68/43 -20/11
-24/17 -1/38 -2/25 49/17
>> rref(a)
ans =
1 0 13/178 -725/384
0 1 -152/173 -1426/173
The truth has little to do with either of the two different outputs above:
sage: a = matrix(2,[-86/17, 40/29, -68/43, -20/11, -24/17, -1/38, -2/25, 49/17])
sage: a.echelon_form()
[ 1 0 306034/4189705 -404710/214357]
[ 0 1 -18405604/20948525 -30037214/3644069]
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