Viktor T. Toth wrote:
> This discussion made me wonder: what is the rationale for not having
> keepfloat:true by default?
>
>
> Viktor
>
1. Historical. Macsyma's rational function package assumes exact
coefficients, necessary for computing GCD, factorization, avoiding
overflow, underflow, and any other issues related to approximate
representation of floats. It was written initially in 1967-68.
keepfloat was added later because of coefficient explosion when floats
were rationalized in the process of rat(), as already
mentioned. But keepfloat also invalidates an important part of rat, ratsimp,
etc. Namely GCDs go away. (Though there are ways to put it back, according
to recent researchers who would have you believe in approximate GCDs.)
2. Why not have keepfloat:true be the default?
(a) A bias in favor of exact arithmetic
(b) keepfloat could give you wrong answers... though it works well for polynomials
as long as the numbers are modest: that is, no numbers
overflow or underflow
3. I can see the argument for keepfloat:true .... Someone put a float
in there. So it is already an indication that floats are being used.
But what if the float is the output of, say, allroots, and what someone
needs is a rational approximation to a root (not a float?). It is
harder to read the intention.
(I'm neutral on this, I guess).
RJF
>
> -----Original Message-----
> From: maxima-admin@math.utexas.edu [mailto:maxima-admin at math] On
> Behalf Of C Y
> Sent: Tuesday, February 22, 2005 3:39 PM
> To: macrakis@alum.mit.edu; James Amundson; gesslein@panix.com
> Cc: Maxima List
> Subject: Re: [Maxima] [Fwd: Two bugs in one (fwd)]
>
>
> --- Stavros Macrakis wrote:
>
>
>>The conversion of floats to fractions is controlled by the global
>>parameter ratepsilon. By default, this is 2.0e-8. I have argued for
>>a long time that this should be much smaller, perhaps 1.0e-15 (5
>>ulps).
>
>
> Are there any downsides anyone can see to this? If not, I move we
> change it pronto.
>
> CY
>
>
>
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