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Comments:
<0> lol
<1> ...
<0> Appleman1234: 3*for*large*of*one*values
<0> lol
<0> % int (x^2, x)
<2> Appleman1234: $Failed
<0> % e^(i pi)
<2> Appleman1234: e^(i*pi)
<3> % Exp[i*pi]
<2> Kampen: E^(i*pi)
<3> % E^[I*Pi]
<2> Kampen: $Failed
<3> % E^[i*Pi]
<2> Kampen: $Failed
<3> lame, i'm surprised it can't do that
<4> % E^(I Pi)
<2> Catfive: -1
<3> why didn't mine work with the asterisk?
<4> i =/= I
<3> <3> % E^[I*Pi]
<3> <2> Kampen: $Failed
<3> i used capital I
<4> [] is for function evaluation
<3> ah ok
<5> what's =/= supposed to mean?
<5> i thought != meant not equal...
<6> but != is not what people write, =/= is meant to look like a = with a slash through it which is what we write
<5> ah, not that math people write.
<5> i suppose that makes sense.
<6> err, yes, I write more than I type...
<5> != in written form sometimes gets confused with factorials.
<6> yes, so that's a good reason not to use it
<5> :)
<4> it's also meaningless to anyone who isn't a C programmer
<5> i'm a perl programmer.
<5> it's not quite C
<5> :)
<6> real programmers will only grok .NE.
<5> i'd understand that.
<5> 'ne' is used for string comparison in perl.
<5> g'night
<7> hi, I'm doing some problems relating to factorising, e.g., x^4 + x^3 + x^2 + x + 1 by finding roots of x^5 - 1 = 0 and dividing by (x-1). a pattern exists for only even powers: x^4 + x^2 + 1 = (x^6 - 1)/(x^2-1). I seem to remember that there was also a simple pattern for factorising x + x^3 + x^5, etc. Can anyone tell me if it does exist and if so what it is?
<7> er, finding roots of x^5 - 1 = 0, representing those as factors, then dividing by (x-1) even
<4> x^n - y^n = (x - y)(x^(n-1) + x^(n-2)y + ... + xy^(n-2) + y^(n-1))
<7> ah ok
<7> is it possible to apply that to factorising a polynomial consisting of odd indices?
<8> all the roots come in conjugate pairs, so you can put those together to get a quadratic
<7> that's right
<7> oh silly me. you can just take out x as a factor in the case of x + x^3 + x^5, can't you
<7> simplifying it to an even-index problem like the others
<4> % Factor[x^9 + x^7 + x^5 + x^3 + x]
<2> Catfive: x*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)
<7> well thanks for your input. Catfive, your expansion showed a little more to me than I've had to cover. cool :)
<9> how can a logarithm be computed? is there a known algortithm that a computer can employ? ( considering no ready FPE exists)
<10> yes it can be computed
<11> ('FPE' ?)
<12> revil: why should a logarithm be more difficult than the other functions like sine or exp?
<9> ok, how can any of these be computed?
<10> it doesn't matter what fpe is, the logarithm can be computed in any turing-complete mahine
<10> machine
<12> revil: by approximating them by a power series e.g.
<9> of course it can, FPE does exactly that. The question is, how?
<12> revil: or by numerically solving a differential equation they obey
<12> revil: or by numerically integrating a known function: log x = int_1^x 1/t dt
<9> by trial end error like algorithm? fuzzy guessing?
<10> i thought you asked if it could be computed
<9> no wonder. well, i believe it is a rare question. I can hardly find any references in google
<12> revil: not much trial and error to it. sin x = x -x^3/3! + x^5/5! and so on. the maximum of the error term is known and you can determine the number of terms you need for the precision you require
<9> hm.. the taylor sequnce, right?
<12> revil: well, there are better approximations for fixed precision
<12> revil: but as an example
<9> hm.. i get the idea, thanks!
<13> so i wish to see if a given string has only one | and all other 0s
<13> want to make a nice little input output circuit
<13> now since i do not know the "sizeof"
<13> what could be the best way out?
<10> you're probably asking that in the wrong channel, but you can count the number of | in a string and check if a char is 0 or | with one simple for loop
<14> sizeof ?
<15> or match it with a regex: 0*\|0* in perl style ;-P
<14> what language are we talking here ?
<13> yuck sorje :)
<13> know i basically was thinking about the good ol 11110000 kind
<13> and realised i can view it as a square wave with the 1->0 edge
<13> and 000100000 seems like a pulse
<13> but i wish to ensure the pulse is just "once"
<9> zaphyBeeble, i believe you need some flip flops
<13> wonder if mr fourier did something in discreet for it
<15> hehe, seems like nobody really understands the question ;-)
<13> :)
<13> sorry maybe batty
<13> say i wanted to make this with simple ol relay switches/ or any other mechainical device
<13> 0 being "nothing" when the cog wheel is there, 1 being there is something
<13> but i have to make sure there is only 1 "1" else ring a bell with a hammer that goes down hehe
<15> hmm "real" switches are really bad at emitting exactly one signal. Keep that in mind ;-)
<13> ummm yeah
<13> they all have blurred vision
<13> ;)
<16> WOOT
<16> p***ed discrete math!
<16> big thx to cale and all the others :P
<16> its indeed a miracle for a retard like me to p*** it
<16> unbelieveable
<16> :D
<4> @arrr
<2> May the clap make ye incapable of Cracking Jenny's Tea Cup.
<17> What is the discussion here about?
<18> tea cups
<17> Antique or newage?
<18> general form has been around for some time
<19> you know, the ones that you can actually use :)
<17> % Solve[x^2+1==0]
<2> hiker13526: {{x -> -I}, {x -> I}}
<17> anyone understand that? :)
<4> % I::usage
<2> Catfive: "I represents the imaginary unit Sqrt[-1]."
<16> sure, it has imaginary roots :P
<17> yeah but whats that -> thingy
<4> % I::usage
<2> Catfive: "I represents the imaginary unit Sqrt[-1]."
<4> % x /. {x -> 5}
<2> Catfive: 5
<4> % x /. Solve[x^2 + 1 == 0] //First
<2> Catfive: -I
<17> % Solve[x + 2 == 0]
<2> hiker13526: {{x -> -2}}
<17> I'm good with this thing
<14> % Sqrt[-1]::usage
<2> kmh: MessageName[Sqrt[-1], "usage"]
<14> bah
<17> % Solve[x == I^2]
<2> hiker13526: {{x -> -1}}
<17> wow mbot's good :)
<20> hello, dunno how to formulate my question, it would sound like: can some computer-generated random numbers be "more random" or "have a better randomness" than others?
<21> yes, some are more random than others
<21> in computer, most random generators will give you pseudorandom numbers anyway
<12> weeze: http://en.wikipedia.org/wiki/Kolmogorov_complexity
<21> to gain more 'randomness' you need to introduce something that is not dependant on the machine state
<19> weeze: pseudorandom means that the "random" number is actually generated in a very deterministic way, so that it has relatively many properties of truely random numbers
<20> thank you for answering... I wonder how one can determine a numbers's randomness' validity
<19> weeze: heh, one of the easiest ways is to try to compress it using zip/gzip/bzip/whatever :). If you are able to compress the number, it's not really random, because the compression algorithm found some regularities it could use :)
<20> lol ! I see, it's funny though
<19> Of course that's not the "cleanest" method, but it works and is clever =)
<20> and, the way a deterministic algorithm comes with different numbers every time.. kinda beats me
<20> then one could define a number's randomness by the proportion of "zipping" that can be done on it? lol
<19> weeze: Really, the pseudorandom numbers repeat themselves if you run them long enough. The trick is, it's somewhat simple to make them repeat only after 2^64 numbers or whatever you like
<20> which is considerably enough for my everyday life...
<21> in some mainframes, special chips were used for random numbers
<21> there are natural processes that can be used for random number generation, like radioactivity of some isotopes
<19> Yeah, and I recall there are special devices recording the ambient radiation and extracting randomness from there. That's already pretty good random
<20> the reason I came to ask is (aside from being unable to formulate it properly on google) I'm trying to generate random numbers for a tiny educational program and I somewhat felt that the random numbers between X and Y tended to "hit "more often near the average of X and Y, and less often near the boundaries themselves
<19> Actually, I guess simply using the noise you get from a soundcard's unconnected mic-in might work too
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