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  • How to implement Horner's scheme for multivariate polynomials?

    - by gsreynolds
    Background I need to solve polynomials in multiple variables using Horner's scheme in Fortran90/95. The main reason for doing this is the increased efficiency and accuracy that occurs when using Horner's scheme to evaluate polynomials. I currently have an implementation of Horner's scheme for univariate/single variable polynomials. However, developing a function to evaluate multivariate polynomials using Horner's scheme is proving to be beyond me. An example bivariate polynomial would be: 12x^2y^2+8x^2y+6xy^2+4xy+2x+2y which would factorised to x(x(y(12y+8))+y(6y+4)+2)+2y and then evaluated for particular values of x & y. Research I've done my research and found a number of papers such as: staff.ustc.edu.cn/~xinmao/ISSAC05/pages/bulletins/articles/147/hornercorrected.pdf citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.8637&rep=rep1&type=pdf www.is.titech.ac.jp/~kojima/articles/B-433.pdf Problem However, I'm not a mathematician or computer scientist, so I'm having trouble with the mathematics used to convey the algorithms and ideas. As far as I can tell the basic strategy is to turn a multivariate polynomial into separate univariate polynomials and compute it that way. Can anyone help me? If anyone could help me turn the algorithms into pseudo-code that I can implement into Fortran myself, I would be very grateful.

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  • mod,prime -> inverse possible

    - by Piet
    Hi all. I was wondering if one can do the following: We have: X is a product of N-primes, thus I assume unique. C is a constant. We can assure that C is a number that is part of the N-primes or not. Whichever will work best. Thus: X mod C = Z We have Z and C and we know that X was a product of N-primes, where N is restricted lets say first 100 primes. Is there anyway we can get back X?

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  • PHP Find Coordinates between two points

    - by Ozzy
    Hi all, simple question here. Lets say I have two points: point 1 x = 0 y = 0 point 2 x = 10 y = 10 How would i find out all the coordinates inbetween that programmatically, assuming there is a strait line between two points... so the above example would return: 0,0 1,1 2,2 3,3 ... 8,8 9,9 10,10 Thanks :)

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  • Animation with Initial Velocity

    - by abustin
    I've been trying to solve this problem for a number of days now but I must be missing something. Known Variables: vi = Initial Velocity t = Animation Duration d = Distance The function I'm trying to create: D(t) = the current distance for a given time Using this information I want to be able to create a smooth animation curve with varying velocity (ease-in/ease-out). The animation must be able ease-in from an initial velocity. The animation must be exactly t seconds and must be travel exactly d units. The curve should lean towards the average velocity with acceleration occurring at the beginning and the end portions of the curve. I'm open to extra configuration variables. The best I've been able to come up with is something that doesn't factor in the initial velocity. I'm hoping someone smarter can help me out. ;) Thank you! p.s. I'm working with an ECMAScript variant

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  • Mapping Hilbert values to 3D points

    - by Alexander Gladysh
    I have a set of Hilbert values (length from the start of the Hilbert curve to the given point). What is the best way to convert these values to 3D points? Original Hilbert curve was not in 3D, so I guess I have to pick by myself the Hilbert curve rank I need. I do have total curve length though (that is, the maximum value in the set). Perhaps there is an existing implementation? Some library that would allow me to work with Hilbert curve / values? Language does not matter much.

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  • Fibonacci sequence subroutine returning one digit too high...PERL

    - by beProactive
    #!/usr/bin/perl -w use strict; sub fib { my($num) = @_; #give $num to input array return(1) if ($num<=1); #termination condition return($num = &fib($num-1) + &fib($num-2)); #should return sum of first "n" terms in the fibonacci sequence } print &fib(7)."\n"; #should output 20 This subroutine should be outputting a summation of the first "x" amount of terms, as specified by the argument to the sub. However, it's one too high. Does this have something to do with the recursion? Thanks.

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  • Delphi component or library to display mathematical expressions

    - by Svein Bringsli
    I'm looking for a simple component that displays mathematical expressions in Delphi. When I started out I thought it would be easy to find something on the net, but it turns out it was harder than anticipated. There are lots and lots of components that will parse mathematical expressions, but few (none?) that will display them. Ideally I would like a component as simple as a TLabel, where I could set the caption to some expression and it would be displayed correctly, but some sort of library that let's me draw expressions to a canvas would also be sufficient for my needs. Update: I'm not talking about plotting graphs of functions or something like that. I want to display (for instance) (X^2+3)/X like this:

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  • Unique keys for Sphinx along three vectors instead of two

    - by Brendon Muir
    I'm trying to implement thinking-sphinx across multiple 'sites' hosted under a single rails application. I'm working with the developer of thinking-sphinx to sort through the finer details and am making good progress, but I need help with a maths problem: Usually the formula for making a unique ID in a thinking-sphinx search index is to take the id, multiply it by the total number of models that are searchable, and add the number of the currently indexed model: id * total_models + current_model This works well, but now I also through an entity_id into the mix, so there are three vextors for making this ID unique. Could someone help me figure out the equation to gaurantee that the id's will never collide using these three variables: id, total_models, total_entities The entity ID is an integer. I thought of: id * (total_models + total_entities) + (current_model + current_entity) but that results in collisions. Any help would be greatly appreciated :)

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  • Divide and conquer method to compute roots [SOLVED]

    - by hellsoul153
    Hello, Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ? In other words, I'm wondering if (n exp(1/x)) is more efficient to (n exp(1/y)) for x < y and where x and y are integers.

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  • Calculating Length Based on Sensor Data

    - by BSchlinker
    I've got an IR sensor which writes its current information to a token which I then interpret in a C# application. That's all good -- no problems there, heres my code: SetLabelText(tokens [1],label_sensorValue); sensorreading = Int32.Parse(tokens[0]); sensordistance = (mathfunctionhere); Great. So the further away the IR sensor is from an object, the lower the sensor reading (as less light is reflected back and received by the sensor). My problem is in interpreting that length. I can go ahead and get lets say "110" as a value when an object is 5 inches away, and then "70" as a value when an object is 6 inches away. Now I want to be able to calculate the distance of an object using these constants for any length. Any ideas?

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  • Counting problem: possible sudoko tables?

    - by Sorush Rabiee
    Hi, I'm working on a sudoko solver. my method is using a game tree and explore possible permutations for each set of digits by DFS Algorithm. in order to analyzing problem, i want to know what is the count of possible valid and invalid sudoko tables? - a 9*9 table that have 9 one, 9 two, ... , 9 nine. (this isn't exact duplicate by this question) my solution is: 1- First select 9 cells for 1s: (*) 2- and like (1) for other digits (each time, 9 cells will be deleted from remaining available cells): C(81-9,9) , C(81-9*2,9) .... = 3- finally multiply the result by 9! (permutation of 123456789 in (*)) this is not equal to accepted answer of this question but problems are equivalent. what did i do wrong?

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  • Count bits used in int

    - by sigvardsen
    If you have the binary number 10110 how can I get it to return 5? e.g a number that tells how many bits are used? There are some likewise examples listed below: 101 should return 3 000000011 should return 2 11100 should return 5 101010101 should return 9 How can this be obtained the easiest way in Java? I have come up with the following method but can i be done faster: public static int getBitLength(int value) { int l = 1; if (value >> 16 > 0) { value = value >> 16; l += 16; } if (value >> 8 > 0) { value = value >> 8; l += 8; } if (value >> 4 > 0) { value = value >> 4; l += 4; } if (value >> 2 > 0) { value = value >> 2; l += 2; } if (value >> 1 > 0) { value = value >> 1; l += 1; } return l; }

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  • What is the difference between "someValuesFrom" and "allValuesFrom"?

    - by ahmed
    In descriptive logic, what is the difference between "someValuesFrom" and "allValuesFrom"? In other words, the difference between (limited existential quantification) and (value restriction). For example, consider this picture: I have used the photoshop because I can't write some symbols. Is there any way to simplify the concept of somevaluefrom and allvaluesfrom?

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  • finding ALL cycles in a huge sparse matrix

    - by Andy
    Hi there, First of all I'm quite a Java beginner, so I'm not sure if this is even possible! Basically I have a huge (3+million) data source of relational data (i.e. A is friends with B+C+D, B is friends with D+G+Z (but not A - i.e. unmutual) etc.) and I want to find every cycle within this (not necessarily connected) directed graph. I've found this thread (http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) which has pointed me to Donald Johnson's (elementary) cycle-finding algorithm which, superficially at least, looks like it'll do what I'm after (I'm going to try when I'm back at work on Tuesday - thought it wouldn't hurt to ask in the meanwhile!). I had a quick scan through the code of the Java implementation of Johnson's algorithm (in that thread) and it looks like a matrix of relations is the first step, so I guess my questions are: a) Is Java capable of handling a 3+million*3+million matrix? (was planning on representing A-friends-with-B by a binary sparse matrix) b) Do I need to find every connected subgraph as my first problem, or will cycle-finding algorithms handle disjoint data? c) Is this actually an appropriate solution for the problem? My understanding of "elementary" cycles is that in the graph below, rather than picking out A-B-C-D-E-F it'll pick out A-B-F, B-C-D etc. but that's not the end of the world given the task. E / \ D---F / \ / \ C---B---A d) If necessary, I can simplify the problem by enforcing mutuality in relations - i.e. A-friends-with-B <== B-friends-with-A, and if really necessary I can maybe cut down the data size, but realistically it is always going to be around the 1mil mark. z) Is this a P or NP task?! Am I biting off more than I can chew? Thanks all, any help appreciated! Andy

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  • Flipping issue when interpolating Rotations using Quaternions

    - by uhuu
    I use slerp to interpolate between two quaternions representing rotations. The resulting rotation is then extracted as Euler angles to be fed into a graphics lib. This kind of works, but I have the following problem; when rotating around two (one works just fine) axes in the direction of the green arrow as shown in the left frame here the rotation soon jumps around to rotate from the opposite site to the opposite visual direction, as indicated by the red arrow in the right frame. This may be logical from a mathematical perspective (although not to me), but it is undesired. How could I achieve an interpolation with no visual flipping and changing of directions when rotating around more than one axis, following the green arrow at all times until the interpolation is complete? Thanks in advance.

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  • How to get bit rotation function to accept any bit size?

    - by calccrypto
    i have these 2 functions i got from some other code def ROR(x, n): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (32 - n)) def ROL(x, n): return ROR(x, 32 - n) and i wanted to use them in a program, where 16 bit rotations are required. however, there are also other functions that require 32 bit rotations, so i wanted to leave the 32 in the equation, so i got: def ROR(x, n, bits = 32): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (bits - n)) def ROL(x, n, bits = 32): return ROR(x, bits - n) however, the answers came out wrong when i tested this set out. yet, the values came out correctly when the code is def ROR(x, n): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (16 - n)) def ROL(x, n,bits): return ROR(x, 16 - n) what is going on and how do i fix this?

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  • Can't get my object to point at the mouse.

    - by melignus
    I'm using a combination of SDL and OpenGL in a sort of crash course project to teach myself how this all works. I'm really only interested in OpenGL as a way to use acceleration in 2D games so I just need this to work in a 2D plane. I have been having a lot of problems today with my current issue, I would like an object to point towards the mouse while the mouse button is clicked and then of course stay pointing in that direction after the mouse is lifted. void Square::handle_input() { //If a key was pressed if( event.type == SDL_KEYDOWN ) { //Adjust the velocity switch( event.key.keysym.sym ) { case SDLK_UP: upUp = false; yVel = -1; break; case SDLK_DOWN: downUp = false; yVel = 1; break; case SDLK_LEFT: leftUp = false; xVel = -1; break; case SDLK_RIGHT: rightUp = false; xVel = 1; break; case SDLK_w: wUp = false; sAng = 1; break; case SDLK_s: sUp = false; sAng = -1; break; } } //If a key was released else if( event.type == SDL_KEYUP ) { //Adjust the velocity switch( event.key.keysym.sym ) { case SDLK_UP: upUp = true; yVel = 0; break; case SDLK_DOWN: downUp = true; yVel = 0; break; case SDLK_LEFT: leftUp = true; xVel = 0; break; case SDLK_RIGHT: rightUp = true; xVel = 0; break; case SDLK_w: wUp = true; sAng = 0; break; case SDLK_s: sUp = true; sAng = 0; break; } } //If a mouse button was pressed if( event.type == SDL_MOUSEBUTTONDOWN ) { switch ( event.type ) { case SDL_MOUSEBUTTONDOWN: mouseUp = false; mousex == event.button.x; mousey == event.button.y; break; case SDL_MOUSEBUTTONUP: mouseUp = true; break; } } } And then this is called at the end of my Object::Move call which also handles x and y translation if (!mouseUp) { xVect = mousex - x; yVect = mousey - y; radAng = atan2 ( mousey - y, mousex - x ); sAng = radAng * 180 / 3.1415926l; } Right now when I click the object turns and faces down to the bottom left but then no longer changes direction. I'd really appreciate any help I could get here. I'm guessing there might be an issue here with state versus polled events but from all the tutorials that I've been through I was pretty sure I had fixed that. I've just hit a wall and I need some advice!

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  • Audio Detection in Matlab

    - by insane-36
    I am writing a matlab code that would be able to read the audio file and then compare it to the another audio and recognize if those audio are the voice of the same person. In both type of the audio, would have the same word utterance and the audio is about 1 minutes long. I have come to know that the approach of sliding windows using hamming window would work best on this approach but have a very little idea on this. The simple code to read an audio file and then display a portion of 10s is as below : [x,fs, nbits]= wavread('01-AudioTrack 01.wav'); subplot(211) plot(x) title('Entire Wave') smallRange = 1:100000; subplot(212) plot(smallRange,x(smallRange)) How do I make Hamming window each of 10ms in this case and what approaches should I take to deal with this problem ?

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  • Single dimension peak fitting

    - by bufferz
    I have a single dimensional array of floating point values (c# doubles FYI) and I need to find the "peak" of the values ... as if graphed. I can't just take the highest value, as the peak is actually a plateau that has small fluctuations. This plateau is in the middle of a bunch of noise. I'm looking find a solution that would give me the center of this plateau. An example array might look like this: 1,2,1,1,2,1,3,2,4,4,4,5,6,8,8,8,8,7,8,7,9,7,5,4,4,3,3,2,2,1,1,1,1,1,2,1,1,1,1 where the peak is somewhere in the bolded section. Any ideas?

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  • CenterPoint in CGContextAddArc ?

    - by Mikhail Naimy
    Hi , i am drawing Arc through CGCOntext.I want to draw a string in the center Point of Arc.how can i fond the center point in the Arc which has been drawn through CGContext. CGContextSetAlpha(ctx, 0.5); CGContextSetRGBFillColor(ctx, color.red, color.green, color.blue, color.alpha ); CGContextMoveToPoint(ctx, cX, cY); CGContextAddArc(ctx, cX, cY, radious+10, (startDeg-90)*M_PI/180.0, (endDeg-90)*M_PI/180.0, 0); CGContextClosePath(ctx); CGContextFillPath(ctx);

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  • floor of double(time_t)

    - by plok
    I cannot understand why this throws undefined reference to `floor'": double curr_time = (double)time(NULL); return floor(curr_time); Hasn't it been casted to double, which is what floor receives?

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  • multidimensional vector rotation and angle computation -- how?

    - by macias
    Input: two multidimensional (for example dim=8) vectors a and b. I need to find out the "directed" angle (0-2*Pi, not 0-Pi) between those vectors a and b. And if they are not parallel I need to rotate vector b in plane a,b by "directed" angle L. If they are parallel, plane does not matter, but angle of rotation is still the same L. For 2d and 3d this is quite easy, but for more dimensions I am lost, I didn't find anything on google, and I prefer using some already proved&tested equations (avoiding errors introduced by my calculations :-D). Thank you in advance for tips, links, etc. Edit: dimension of the space is the same as dimension of the vectors.

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