Recent content by tmccullough

Both of those quantities are the minimum distance from the origin to the plane, meaning the distance from the origin to the plane traveling in the direction of the normal vector (actually times the length of the normal vector, which is typically chosen to be norm 1 for simplicity). To see...

Dimension theory (krull dimension anyways) is very much a fundamental part of algebraic geometry, and that's where I first learned it. Polynomial rings (finite number of variables) over a field are very "homogeneous", so every maximal tower of ideals has the same length. This will then hold...

Consider that k[x^2,x^3] = k[t,u]/(t^2-u^3). The polynomial t^2-u^3 is irreducible, so it's principle ideal is prime. Then, your ring is noetherian and dimension 1.

Because it's calculus - an integral and all.

That's not modified at all, that is the argument. I didn't want to give everything away.

I think I understand the statement, but I'm not totally sure. I suppose that you mean what is the measure of the set of all vectors which are rationally dependent (if this is even measurable)? I've never heard of rationally dependent before... I think this is the answer: Suppose...

If H is the klein-4 group, and N = <g> where g\in A4\setminus H, then the product NH=A4 just based on index.

Functions don't have a "limit" at a simple pole (like this one), they have aribitarily large norm. At poles, the values "wrap around" the complex plane at infinity, in other words, the function hits all complex numbers with arbitarily large norm. You always see a complex function going to the...

GargleBlast42, I presume that you are associated with a university. Most math departments (that I've seen) have magma available for free. It's awesome for this, and many other, symbolic algebra problems. If you continue with algebra, it's a really good tool to have at your disposal.

You can absolutely solve this by hand. First, follow mr. vodka's advice and apply long division, sp that you rewrite your function as ax + b + \frac{cx+d}{x^2+2x} I'm struggling to remember the name of the next step (partial fraction decomposition?), write it as ax+b + \frac{g}{x+2} +...

I assume that you mean S_n is the number of ways to express n as a sum of positive integers, where orders matters. Consider the different cases for the last integer in the sum, all of which are disjoint, since order matters. There are n different cases. Explicitly: if the last integer is...

Stated in a different way, \log_2(t) is an increasing function. Inequalities remain true if you apply an increasing function.

There are a millions way to fiddle with the logic of this problem, so I will just edit what you have here to make it more python-like. The end result will still be an array of length 101, where counts[x] will be the number of times score x appeared, as well as the other desired quantities...

Where did you get the function e^{x/y^2}? I'm confused a little by your latex formatting - use { and not ( for enclosing the things in the super/subscript. Are you sure that's the right function? If so, what you've shown in the post looks correct. Unfortunately, I don't think you're...

I'm pretty sure people that draw such things use xy-pic. I know why you ask about one that's not too much trouble :wink: