I'd buy a handheld Plouffe Inverter. On Fri, May 6, 2011 at 10:29 AM, Henry Baker <hbaker1@pipeline.com> wrote:
You know that the Casio performs an inverse lookup for sure?
As an aside, there is an interesting trend in symbolic algebra that's been going on for 35 years or so: doing less traditional algebra & more numerical calculations. E.g., instead of using bignums to compute the inverse of an integer determinant, compute the determinant mod p for enough p's; using "black box programs" to compute polynomials & computing the coefficients (if you really want them) by interpolating enough point values.
Part of this trend is driven by necessity: modern computers are far better at numerical calculations than symbolic calculations, & part is driven by good mathematics & computational complexity.
Mathematicians & physicists have a long history of doing numerical calculations & then guessing the correct symbolic formula. In some cases (Newton springs to mind), the data are then fudged to make the symbolic formula look even better.
At 10:20 AM 5/6/2011, Adam P. Goucher wrote:
Yes, but MuMath *actually* performs symbolic calculation (or that's the impression I got, anyway), whereas the Casio must perform an inverse lookup to convert from a decimal approximation to a symbolic expression.
Sincerely,
Adam P. Goucher
Your Casio is not the first "symbolic hand calculator"; MuMath was really the first:
http://en.wikipedia.org/wiki/MuMATH
At 09:46 AM 5/6/2011, Adam P. Goucher wrote:
Today I received a Casio fx-85GT calculator as a present from a couple of my friends. It gives expressions in exact forms as an alternative to the ordinary decimal output. For example, enter:
sqrt(8)
and it will output:
2*sqrt(2)
Of course, I believed that the calculator was performing symbolic manipulation -- very impressive for a handheld scientific calculator!
However, I then decided to test it:
ln(640320^3+744)/sqrt(163)
Instead of displaying the correct answer, 3.14159265..., a prominent image of the Greek letter pi was rendered!
Hmm...
I'm waiting for a version that prints "stop trying to test my symbolic calculation facilities with well-known near-miss identities!"
On this topic, there is this comic:
Sincerely,
Adam P. Goucher
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