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Comments:
<0> > let primesUpTo n = takeWhile (<= n) primes; primes = 2 : 3 : [n | n <- [5,7..], all (\p -> mod n p /= 0) (takeWhile (\p -> p*p <= n) primes)] in primesUpTo 100
<1> [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
<2> Hello everyone
<3> hi... how do i solve 3080^3 mod 8999 using my normal calculator? i'm trying to use fast exponantiation, but it doesn't get easier :)
<2> when multiplying two matricies -- ie. a 4 x 2 and a 2 x 4 -- what is the size of the result matrix ?
<0> 4x4
<2> ok - thanks
<2> hrrm
<2> but a 2 x 3 and a 3 x 2 produces a 2 x 2 matrix ?
<2> hrm
<4> a n x m matrix times a m x p matrix will result in a n x p matrix
<2> ok
<2> ty
<2> Ok one other stupid question ;)
<2> What's the difference between a free variable and a basic variable?
<0> % {{1,2,3},{4,5,6}} . {{0,1},{2,1},{3,0}}
<1> xerox: {{13, 3}, {28, 9}}
<2> Is a free varaible just a variable that is not defined in the given set?
<2> so like if we had ehh....
<5> Is the dot product defined for complex vectors?
<2> x1 = 5 + x2
<2> and x2 + x3 = 5
<2> x2 and x1 can be defined in terms of what is given - so they are basic (or bound - or whatever)
<2> And x3 is free ?
<6> Knight_Lord2: i don't see why not....there is no law says you can't use it that way
<7> how would you indicate subscript in plain old ascii?
<2> x_2
<2> s sub 2
<2> err x sub 2
<7> ahh neato, thanks
<8> raz0: That way g(0) = 0 and g(1) = 1, which is not necessarily true for your suggested alternative.
<9> hi
<3> hi... how do i solve 3080^3 mod 8999 using my normal calculator? i'm trying to use fast exponantiation, but it doesn't get easier :) 8999 is a prime number btw
<10> I don't know, but you'll end up with 5817.
<11> drizzd_, Oh right.
<9> i am woundering a2+b2=c2 how do i solve for a triangle
<6> fortytwo: yea you can use mathematics here!
<12> atown, c is the one in front of the 90 degrees angle
<6> % Mod[13,12]
<1> seb-: 1
<6> % Mod[3080^3, 8999]
<1> seb-: 5817
<6> fortytwo: there ya go
<10> seb-: That doesn't actually answer his question though, y'know.
<9> will c always be infront of the 90
<10> That answer he got from me already.
<12> atown, well, thats the only way a^2+b^2=c^2 works :-)
<12> if c is in front of the 90 degrees angle
<9> so the right triangle is here and the teacher wants me to draw atriangle on the one or two side that it will fit and put it in a square root with a2+b2=c2
<9> dose any one get it
<12> youre in a lesson?
<9> what
<12> just curious :-)
<12> so she wants you to find out what c is?
<9> yes
<7> mbot does plotting too?
<7> that's super fancy
<12> its a triangle, there are only two other sides except for c :-)
<12> anyway, theres some seirously disturbing stuff on the news, i gotta go turn on the tv and watch 6 news channels in the same time :-( cya
<13> some event medfly ? or just the general horror show?
<12> exchange of fire
<12> between the IDF and lebanon army, in case youre curious :-)
<13> ah
<13> I don't have TV just net, thinks for mentioning
<14> folks, is there a notion of dot-product if the two vectors are not the same size?
<15> that question doesn't make sense to me
<16> me neither...
<14> yeah me neither. I am trying to understand something and it looks like they're taking a dot product of 2 vectors which aren't of the same size
<14> by size i mean like one has N elements and one has N+1
<15> that doesn't make sense either lol
<14> why not?
<15> two vectors typically exist in the same number of dimensions if you are taking a dot product
<14> right
<14> can you plz see section 1a at this link: http://www.cs.nyu.edu/~mohri/ml07/sol2.pdf it sounds to me like the bottom part is doing a dot product of two things of diff dimensions
<17> ed : you need to be able to measure the angle between the two vectors
<14> but does it even make sense what's written there?
<17> remember, a.b = |a||b|sin(theta)
<17> uh actually it's cos(theta)
<14> i am not sure I need the geometric sense of dot product for this particular thing
<14> it's just matrix stuff, i THINK
<17> ed : yes this is more general
<17> i'm not sure i can help here, maybe someone else with more experience
<14> but you see on the bottom of that section where it says : w . X0... it seems to me that w has n+1 items in it, but X0 is a vector in n-dimensional space!
<17> i see your confusion
<17> they have defined n+1 labels
<17> whereas x_0 is just the vector of n real numbers, where all the real numbers are 0
<14> yeah
<17> maybe they mean w = (y1,y2,...,yn) ?
<17> i.e. no y0
<17> after all, the 0th entry of a vector doesn't make much sense
<16> sure it does......
<17> enlighten me
<16> if you can have a zeroth bit, its not a strech to have a zeroth entry of a vector
<17> these are vectors in R^n
<17> i.e. n points
<16> analpear: so, the indices are just labels
<17> ok
<16> you could say (x_a,x_b,x_c....) etc
<14> yeah plus if you look at the page, there's actually n+1 points in R^n
<17> there shouldn't be? surely?
<14> what?
<17> well for a start there are not n+1 points in R^n
<17> maybe you mean there are n+1 points in x where x in R^n
<17> but there aren't
<17> there are n
<14> yes that's exactly what i meant, there're n+1 points which are in R^n space
<14> you're right, n+1 points in x
<18> hi all
<17> [23:18] <17> but there aren't
<17> [23:18] <17> there are n
<14> why do you say that
<18> i want to convert 1.2818030*2^(-16) into a number with factor*10^x where x is a integer number
<18> what is the best way to do that?
<17> take R^2
<19> hey when peiple say counter clockwise what is it 12 11 10 9 8 or 8 9 10 11 12
<17> that is the real line cartesian producted with itself
<17> i.e. set of all ordered pairs (x,y) with x and y in R
<18> analpear: huh?
<20> Kidpunkx: http://en.wikipedia.org/wiki/Clockwise_and_counterclockwise
<14> analpear: are you disputing the fact that n+1 points can be selected in R^n space?
<17> no
<14> good :)
<18> analpear: i don't understand you
<17> litb : maybe because i wasn't talking to you
<18> oh
<17> ed : we were discussing the possibility of a 0th entry of a vector
<17> i thought you meant there were n+1 numbers in a R^n vector
<17> (clearly false)
<17> anyway
<17> w is a vector containing n numbers, y1,y2,...,yn
<17> so w.x0 makes sense
<14> I think W contains y0..yn
<17> ok
<17> "Let w be the vector whose ith coordinate is yi."
<17> that is quoted from the text
<17> let i=0 and see if that statement makes sense
<17> it will not
<14> well
<14> you know, I am a computer programmer. So I can easily say that a[0] is the zeroths element of a
<18> i must have factor to be the right number so that factor*10^x approximates 1.2818030*2^
<18> (-16) as good as it can
<17> vectors are not arrays like in C!
<17> they do not have a 0th index (using the symbols we're familiar with anyway)
<14> analpear: but right above, in the text, they are defining y0 to yn
<17> ed : yes, they use y0 for other things
<21> if e_1, e_2 are a basis in V and e'_1, e'_2 are another basis in V then if I want to represent a vector in the basis e1, e2 with the vectors from the second basis, I need a matrix
<14> hmm ok
<17> ed : but still, it is strange
<14> analpear: so you think W has n elements
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