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Aug
24
comment Pre-Calculus - Solving for $x^3$
When you used the quadratic formula and got the two roots $a=\frac{-1+i\sqrt{3}}{2}$ and $b=\frac{-1-i\sqrt{3}}{2}$ you should be replacing $x^2+x+1$ with $(x-a)(x-b)$, not what you did.
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Minor math error (forgot dA)
Aug
24
comment Green's theorem for conservative fields - are partials equal?
No problem. Glad to help. FYI, subscripts, in this context, mean partials - $\frac{\partial f}{\partial x}=f_x$.
Aug
24
comment Integer combination
Will the formula always be less than or equal to? And that simple? (i.e., in the form $a x + b y \le c$ for integers a, b, and c)?
Aug
24
comment Green's theorem for conservative fields - are partials equal?
There. I hope my edit was what you were looking for.
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Missed a period, added a proof, put more LaTeX in.
Aug
24
comment Green's theorem for conservative fields - are partials equal?
@alkamid $P_y$ and $f_{xy}$ are the same thing (if $f$ exists). The actual Young's Theorem says $f_{xy}=f{yx}$. As for the typo, it was just a missing period, right?
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Missed a period.
Aug
24
answered Green's theorem for conservative fields - are partials equal?
Aug
24
comment Is the vector cross product only defined for 3D?
Why don't you get a vector in the end? Using Mathematica's Cross[] function is allowed over any number of vectors, so long as there's one more dimension than the number of vectors. Playing around with using matrices to find the cross product and using Cross[], I found the result only differed by factors of -1 occasionally.
Aug
24
comment Find all ways to factor a number
As to your consideration of 2*2 as distinct with 4, I guess that's true if you're looking for ALL representations of a number. But that being said, if you're looking into quantifying how many partitions a number has, then look to the answer below. I was talking about an approach to explicitly writing out all of these possible factors.
Aug
24
comment Find all ways to factor a number
@dj18 "Finding all combinations of the prime factorization of a number" is the same thing as "finding all (UNIQUE) subsets - the union of subsets - of the set of its prime factors."
Aug
23
comment Is the vector cross product only defined for 3D?
@rschwieb WRI guys, or at least the ones that I talked to, use the MMA abbreviation. However, I think I'll be using yours as much as possible from now on.
Aug
23
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Aug
23
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Aug
23
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Aug
23
comment Is the vector cross product only defined for 3D?
Thanks for the reply. That was what I was looking for. I was only familiar with the wedge product through Stroke's Theorem, and I have yet to find out what the "exterior algebra" is. That's why I couldn't make the connection on my own.
Aug
23
accepted Is the vector cross product only defined for 3D?
Aug
23
comment Is the vector cross product only defined for 3D?
Thanks. That explains why there is only a 3D and 7D cross product, and any other pattern I saw can be explained with the wedge product and exterior algebra of the system.
Aug
23
comment Is the vector cross product only defined for 3D?
@Will Jagy Sorry about that if there were repeats. Perhaps I didn't search well enough before questioning.