network profile
| bio | website | |
|---|---|---|
| location | Amherst, MA | |
| age | ||
| visits | member for | 11 months |
| seen | 17 hours ago | |
| stats | profile views | 13 |
I'm an about-to-retire mathematics professor who's used numerous programming languages over the years, including FORTRAN, Pascal, and APL. I've dabbled a bit with Java. My current programming interests are in Mathematica and J (the jsoftware.com free product).
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23h |
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In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes? Yeah, underdetermined seems to be the case. |
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1d |
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In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes? But that property of determinants is not part of Browne's axioms. Note that he doesn't use the more familiar approach of defining exterior powers in terms of tensor powers, etc., but instead is trying to lay down a set of axioms for wedge product. |
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1d |
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In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes? @TedShifrin: No, unfortunately, what you guess in included in the axioms in Browne's treatment is not in fact there. Unless there's something much more subtle, I think what's missing is one or another version of what's called Axiom 4 in William Schulz's document cefns.nau.edu/~schulz/grassmann.pdf (pages 50-51). |
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May 15 |
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Solve $(x^2 + 5)^2 - 15(x^2 + 5) + 54 = 0$ I wasn't objecting to the procedure, but to the manifest logic of its description. As I said, a write-up indicating that the answer you obtain consists of roots and only roots, you need "if and only if" connectives, not "if ... then" connectives. What you have (thrice) is the latter. |
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May 15 |
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Solve $(x^2 + 5)^2 - 15(x^2 + 5) + 54 = 0$ This answer has one-way implications. Presumably they should be two-way implications, i.e., logical equivalences; otherwise, you could be obtaining extraneous roots or numbers that are not roots at all. |
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Mar 12 |
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Evaluating $f(z)=\sqrt{z^2-1}$, given the branch I am on. There's also the issue of what branch of log is being used in your symbolic evaluation. |
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Jan 9 |
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Is the term true? $\frac{\theta}{\theta - 1 } = \frac{1} {\theta-1} + 1$ It's not true for theta = 1. |
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Oct 5 |
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What might be meant by “closed form explicit analytical solution” to an ordinary differential equation? Yes, "closed-form" generally implies only a finite number of operations, but the issue remains as to what the functions operated upon are. Thus "closed-form" is mathematically ambiguous; "elementary" is not. |
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Oct 4 |
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What might be meant by “closed form explicit analytical solution” to an ordinary differential equation? The never actually said "elementary", just "analytic", "closed form", and "useful". |
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Oct 4 |
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What might be meant by “closed form explicit analytical solution” to an ordinary differential equation? Since my original post, I looked at the company's page where they give details on pricing. And they charge US $200 more if the client does not supply a numerical solution. So I now believe that all they do is to provide a closed-form analytic function that fits well the numeric solution. |
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Sep 15 |
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Why these line integrals have the same value? In fact, the standard parameterization of the circle gives integral 0. But parameterizing each side of the square by x or y, as appropriate, gives sum of integrals on the sides to be 4 i. |
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May 28 |
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Another limit related to pi number According to Mathematica, the tail-end of the infinite series -- after the terms through $k = n$, sums to a rational function of factorials and the hypergeometric $_2F_1(1, n + 2, n + 5/2; 1/2)$. So my answer to the original question would still be no -- at least assuming there's no simplification that avoids the hypergeometric function or some combination of gamma function expressions. |
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May 28 |
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Another limit related to pi number Sorry, missed that square on the $k!$. |
