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I was wondering if this question should be posted in this forum or in Stack Exchange, but reading both "What kind of questions can I ask here?", in Math I found

Software that mathematicians use

So I guess it should fit here.

I have a TI-89 (a --powerful, I guess-- Texas Instruments calculator) which I've had since high-school days; I very rarely use it anymore. Of course, for more advanced mathematical computations there is great software for the PC, but maybe some of it (the most simple of it) has been done for the TI-89, and I thought it might be cool finding some use for it again.

Most notably while studying Galois theory lately, I've been using Wolfram Alpha to quickly determine the discriminant of a polynomial of degree >= 3. Of course one could just use the formula (it's not that cumbersome for degrees 3 and 4), but I thought there might be a program that would do it for you.

So, the question is: what good, useful "advanced" (advanced undergraduate and forth) math software do you know for the TI-89?

In particular, do you know of one to compute the discriminant of a polynomial?

I hope the question is well-posed and suited for this forum. If not, please redirect me.

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up vote 1 down vote accepted

The discriminant can be computed as a (Sylvester) determinant (or resultant), e.g. see Wikipedia Thus you need merely find a program that computes determinants.

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The TI calculates determinants. But for $n=4$ I'd have to input a 7x7 matrix, probably erring on the way. Of course, using the det function it must be really easy to make a program to compute discriminants using the Sylvester determinant, but I completely lack TI-programming skills (nor does my curiosity go so far as to start learning it). – Bruno Stonek Nov 13 '10 at 21:30
@Bruno: Ah, I see. Perhaps you could find a TI-89 programmer to help you in this forum. Why do you need to calculate such discriminants? – Bill Dubuque Nov 13 '10 at 21:36
To classify the Galois group of irreducible polynomials of degree 3 or 4 over $\mathbb{Q}$. I'll try asking there, thank you! – Bruno Stonek Nov 13 '10 at 22:30
@Bruno: You have the option of computing the Bezout determinant instead of the Sylvester determinant... that should make for a less space-intensive method. – J. M. Nov 14 '10 at 0:55

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