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#math
<Kampen> http://pastebin.com/886362 well, there's the code, if anyone feels like taking a look :p
<TRWBW> Kampen: code, ugh, why not explain the problem and your solution
<Kampen> the problem is time complexity. i am not an experienced programmer.
<Kampen> so i don't know the solution. that's what i was looking for, for someone to be able to quickly spot the problem, if one exists.
<Kampen> it's no big deal
<TRWBW> Kampen: let me repeat what i said
<Kampen> you mean to say what the program was about and the approach i took?
<TRWBW> Kampen: if it's a code bug, ugh, but if it's a conceptual issue, that's fair game
<Kampen> it's more of a computational issue
<Kampen> so a bit conceptual
<Kampen> i'm concerned with the time complexity of it
<TRWBW> it=?
<Kampen> it is a rudimentary CAS, in the sense that it performs polynomial operations while storing the polynomials in memory still, using linked lists
<TRWBW> k, sounds pretty n^2
<Kampen> is that good or bad
<Kampen> for that kind of thing
<TRWBW> meh
<Kampen> it performs differentiation, addition, subtraction, division, multiplication, and integration, all using linked lists
<Kampen> then writes the resultant polynomial to a new polynomial
<hedos> Is there a software that solves differential equations, such as A*d^2(x)/dt^2 + B*dx/dt + C*x = 0 ?
<Kampen> yes
<Kampen> i beleive mbot will do it even
<Kampen> believe*
<hedos> ok
<TRWBW> Kampen: k, those are alls O(n), cept division wichih is N^3 maybe, you didn't mention multiplication, N^2. you can do better on those two i think if you want to be complexity theory guy
<Kampen> as an aside, can someone tell me the difference between T_3 spaces, T_3 1/2 spaces, and T_pi for tychonoff spaces?
<Kampen> i don't want to be time completity (girl), but we get graded on it
<TRWBW> hedos: factor a*u^2+b*u+c=0
<arrenlex> *screams* this seems SO OBVIOUS but I'm completely stuck! How do you prove that a continuous function that never exceeds its average value must be constant?
<me22> arrenlex: because if it can't go below either
<Kampen> yeah
<Kampen> or just consider the negative of the continuous function
<Kampen> and use that
<Kampen> since they would be continuous positive or negative
<Golfgeo> Perpaps my question wasn't a proper one, but I'm looking to transforming my worksheet into a function so I can use it further. But this doesn't seem possible automagicly...
<me22> formally iirc you need the mvt or somethign
<TRWBW> arrenlex: if it's continuous and there is a point where it is below "c" then it's below "c" for some delta>0 wide interval.
<TRWBW> arrenlex: or what me22 said
<me22> or maybe use integrals and bounds
<TRWBW> arrenlex: that's another way. average is really an integral property.
<arrenlex> TRWBW: Yeah, A=(1/(b-a))integral(f,a,b). But I can't figure out how to use that.
<me22> Abs[min value of function] <= (integral over width) / width <= Abs[max value of function]
<TRWBW> arrenlex: if f(x)<=c then integral is <= (b-a)*c. if f(x0)<c then |f(x)-f(x0)|<(c-f(x0))/2 for x in some |x-x0|<delta.
<Kampen> if anyone is able, could they look up and answer my question about the notation for tychonoff spaces?
<TRWBW> arrenlex: integrate [a,x0-delta] [x0-delta,x0+delta] [x0+delta,b] and add them up
<TRWBW> arrenlex: you'll get the average is less than the average, proof by contradiction
<TRWBW> arrenlex: anotherway, use g(x)=f(x)-(average of f(x)). same problem, but it might be clearer to you see how you can show that if g(x)<=0 and for some x0 g(x)<0, then integral g(x)<0
<arrenlex> I've considered g(x)=A-f(x). I worked out that integral(g)=0 because integral(A)=A(b-a)=((b-a)/(b-a))int(f)=int(f) and int(f)-int(f)=0.
<arrenlex> Does that relate to what you're suggesting?
<arrenlex> (A is the average value of f)
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