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• Recommended books on math for programmers

  - by Anto

  Some programmers do, besides programming, like math (others don't). What books on math do you recommend programmers who like math to read? There are books which present concepts which are applicable in programming and/or computer science, other books about things which will fascinate programmers etc. Books on applying math to programming are okey, but they should be mainly about math (and not programming). Motivate your answers, with focus on why programmers should read the book(s).

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• Good Package for Fitting Polynomial Trend Lines

  - by Rev316

  Given a simple data set, I would like to be able to calculate a trending formula given it's a second order polynomial regression. In fact, it would be great if one could even forecast X periods during calculation (similar to what Excel does). I'm looking for a portable C/C++ package that's relatively easy to use, and allows it to spit out the "best-fit" (highest R^2 value) curve. Any suggestions? Thanks!

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• CPU Architecture and floating-point math

  - by Jo-Herman Haugholt

  I'm trying to wrap my head around some details about how floating point math is performed on the CPU, trying to better understand what data types to use etc. I think I have a fairly good understanding of how integer math is performed. If I've understood correctly, and disregarding SIMD, a 32-bit CPU will generally perform integer math at at least 32-bit precision etc. Is it correct that floating-point math is dependent on the presence of a FPU? And that the FPU on the x86 is 80-bit, so floating point math is performed at this precision unless using SIMD? What about ARM?

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• Math major as a viable degree

  - by Zak O'Keefe

  While I realize there are many topics about CS vs software engineering vs game school programs, I haven't found anything relating to whether pure math degrees (with CS minor and electives) would also be a viable program. By this I mean: Would having a math major, CS minor put one at competitive disadvantage as compared to a pure CS program? This relates specifically to game engine programming, more on the graphics side. Background (for those who care): Currently a math major, CS minor at school and looking to land a career doing graphics engine programming. Admittedly, I love math and if at all possible would like to stay my current program as long as it doesn't put me at a competitive disadvantage trying to land a job post-graduation. That being said, I'm strong in the traditional C/C++ languages, strong concurrent programming skills, and currently produce self-made games for iOS. As an employer, how badly is the math major hurting me? Just want to get some advice from people already in the field!

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• Bad at math, feeling limited

  - by Peter Stain

  Currently I'm a java developer, making websites. I'm really bad at math, in high school I got suspened because of it once. I didn't program then and had no interest in math. I started programming after high school and started feeling that my poor math skills are limiting me. I feel like the programming's not that hard for me. Though web development in general is not that hard, i guess. I've been doing Spring and Hibernate a lot. What i'm trying to ask is : if I understand and can manage these technologies and programming overall, would it mean that I have some higher than average prerequisite for math and details? Would there be any point or would it be easy for me to take some courses in high school math and get a BSc in math maybe? This web development is really starting to feel like not my cup of tea anymore, i would like to do something more interesting. I'm 25 now and feel like stuck. Any help appreciated.

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• What math should all game programmers know?

  - by Tetrad

  Simple enough question: What math should all game programmers have a firm grasp of in order to be successful? I'm not specifically talking about rendering math or anything in the niche areas of game programming, more specifically just things that even game programmers should know about, and if they don't they'll probably find it useful. Note: as there is no one correct answer, this question (and its answers) is a community wiki. Also, if you would like fancy latex math equations, feel free to use http://mathurl.com/.

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• Game Institute Math Courses

  - by W3Geek

  I'm 21 years old and I suck at math, I mean really bad. I don't have the necessary logic to apply it towards programming. I would like to learn the math and logic of applying it. I found Game Institute (http://www.gameinstitute.com) awhile back and heard a lot of praise about them. Are there Math courses any good? Thank you. Edit: My high school was terrible and did not prepare me for any math. I am fairly decent at programming, I just don't have the logic to apply any mathematics to programming, as an example I don't understand the algorithm of finding the size of a user's screen. Yes I have heard of KhanAcademy (http://www.khanacademy.org/) and I have completed a lot of maths on his website but I still don't have the logic to apply any of it to programming.

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• Long term plan of attack to learn math?

  - by zhenka

  I am a web-developer with a desire to expand my skill-set to mathematics relevant to programming. As 2nd career, I am stuck in college doing some of the requirements while working. I was hoping the my education will teach me the needed skills to apply math, however I am quickly finding it to be too much easily-testable breadth-based approach very inefficient for the time invested. For example in my calculus 2 class, the only remotely useful mind expanding experience I had was volumes and areas under the curve. The rest was just monotonous glorified algebra, which while comes easy to me, could be done by software like wolfram alpha within seconds. This is not my idea of learning math. So here I am a frustrated student looking for a way to improve my understanding of math in a way that focuses on application, understanding and maximally removed needless tedium. However I cannot find a good long term study strategy with this approach in mind. So for those of like mind, how would you go about learning the necessary math without worrying too much about stuff a computer can do much better?

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• (int) Math.floor(x / TILESIZE) or just (int) (x / TILESIZE)

  - by Aidan Mueller

  I have a Array that stores my map data and my Tiles are 64X64. Sometimes I need to convert from pixels to units of tiles. So I was doing: int x int y public void myFunction() { getTile((int) Math.floor(x / 64), (int) Math.floor(y / 64)).doOperation(); } But I discovered by using (I'm using java BTW) System.out.println((int) (1 / 1.5)) that converting to an int automatically rounds down. This means that I can replace the (int) Math.floor with just x / 64. But if I run this on a different OS do you think it might give a different result? I'm just afraid there might be some case where this would round up and not down. Should I keep doing it the way I was and maybe make a function like convert(int i) to make it easier? Or is it OK to just do x / 64?

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• Polynomial division overloading operator

  - by Vlad

  Ok. here's the operations i successfully code so far thank's to your help: Adittion: polinom operator+(const polinom& P) const { polinom Result; constIter i = poly.begin(), j = P.poly.begin(); while (i != poly.end() && j != P.poly.end()) { //logic while both iterators are valid if (i->pow > j->pow) { //if the current term's degree of the first polynomial is bigger Result.insert(i->coef, i->pow); i++; } else if (j->pow > i->pow) { // if the other polynomial's term degree is bigger Result.insert(j->coef, j->pow); j++; } else { // if both are equal Result.insert(i->coef + j->coef, i->pow); i++; j++; } } //handle the remaining items in each list //note: at least one will be equal to end(), but that loop will simply be skipped while (i != poly.end()) { Result.insert(i->coef, i->pow); ++i; } while (j != P.poly.end()) { Result.insert(j->coef, j->pow); ++j; } return Result; } Subtraction: polinom operator-(const polinom& P) const //fixed prototype re. const-correctness { polinom Result; constIter i = poly.begin(), j = P.poly.begin(); while (i != poly.end() && j != P.poly.end()) { //logic while both iterators are valid if (i->pow > j->pow) { //if the current term's degree of the first polynomial is bigger Result.insert(-(i->coef), i->pow); i++; } else if (j->pow > i->pow) { // if the other polynomial's term degree is bigger Result.insert(-(j->coef), j->pow); j++; } else { // if both are equal Result.insert(i->coef - j->coef, i->pow); i++; j++; } } //handle the remaining items in each list //note: at least one will be equal to end(), but that loop will simply be skipped while (i != poly.end()) { Result.insert(i->coef, i->pow); ++i; } while (j != P.poly.end()) { Result.insert(j->coef, j->pow); ++j; } return Result; } Multiplication: polinom operator*(const polinom& P) const { polinom Result; constIter i, j, lastItem = Result.poly.end(); Iter it1, it2, first, last; int nr_matches; for (i = poly.begin() ; i != poly.end(); i++) { for (j = P.poly.begin(); j != P.poly.end(); j++) Result.insert(i->coef * j->coef, i->pow + j->pow); } Result.poly.sort(SortDescending()); lastItem--; while (true) { nr_matches = 0; for (it1 = Result.poly.begin(); it1 != lastItem; it1++) { first = it1; last = it1; first++; for (it2 = first; it2 != Result.poly.end(); it2++) { if (it2->pow == it1->pow) { it1->coef += it2->coef; nr_matches++; } } nr_matches++; do { last++; nr_matches--; } while (nr_matches != 0); Result.poly.erase(first, last); } if (nr_matches == 0) break; } return Result; } Division(Edited): polinom operator/(const polinom& P) { polinom Result, temp; Iter i = poly.begin(); constIter j = P.poly.begin(); if (poly.size() < 2) { if (i->pow >= j->pow) { Result.insert(i->coef, i->pow - j->pow); *this = *this - Result; } } else { while (true) { if (i->pow >= j->pow) { Result.insert(i->coef, i->pow - j->pow); temp = Result * P; *this = *this - temp; } else break; } } return Result; } The first three are working correctly but division doesn't as it seems the program is in a infinite loop. Update Because no one seems to understand how i thought the algorithm, i'll explain: If the dividend contains only one term, we simply insert the quotient in Result, then we multiply it with the divisor ans subtract it from the first polynomial which stores the remainder. If the polynomial we do this until the second polynomial( P in this case) becomes bigger. I think this algorithm is called long division, isn't it? So based on these, can anyone help me with overloading the / operator correctly for my class? Thanks!

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• Simple Math Multiplayer game - is Ajax sufficient?

  - by Christian Strang

  I'm planning to create a simple math multiplayer game and I plan to just use Ajax for the server/client communication but I'm not sure if this is sufficient or if I need a socket server. The game will look like this: 2-4 users all get a simple math task (like: "37 + 14") they have to solve it as fast as possible first user who solves it is the winner I will track the time for each user, since the game started, on the client side and everytime a user gives an answer, the answer and the passed time will be send to the server. Additionally I'll add a function which will check every 3 seconds if the other users finished, how much time they needed and who won. Do you think this is possible just using Ajax? What alternatives are there?

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• Is there an easy way to type in common math symbols?

  - by srcspider

  Disclaimer: I'm sure someone is going to moan about easy-of-use, for the purpose of this question consider readability to be the only factor that matters So I found this site that converts to easting northing, it's not really important what that even means but here's how the piece of javascript looks. /** * Convert Ordnance Survey grid reference easting/northing coordinate to (OSGB36) latitude/longitude * * @param {OsGridRef} gridref - easting/northing to be converted to latitude/longitude * @returns {LatLonE} latitude/longitude (in OSGB36) of supplied grid reference */ OsGridRef.osGridToLatLong = function(gridref) { var E = gridref.easting; var N = gridref.northing; var a = 6377563.396, b = 6356256.909; // Airy 1830 major & minor semi-axes var F0 = 0.9996012717; // NatGrid scale factor on central meridian var f0 = 49*Math.PI/180, ?0 = -2*Math.PI/180; // NatGrid true origin var N0 = -100000, E0 = 400000; // northing & easting of true origin, metres var e2 = 1 - (b*b)/(a*a); // eccentricity squared var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³ var f=f0, M=0; do { f = (N-N0-M)/(a*F0) + f; var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (f-f0); var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(f-f0) * Math.cos(f+f0); var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(f-f0)) * Math.cos(2*(f+f0)); var Md = (35/24)*n3 * Math.sin(3*(f-f0)) * Math.cos(3*(f+f0)); M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc } while (N-N0-M >= 0.00001); // ie until < 0.01mm var cosf = Math.cos(f), sinf = Math.sin(f); var ? = a*F0/Math.sqrt(1-e2*sinf*sinf); // nu = transverse radius of curvature var ? = a*F0*(1-e2)/Math.pow(1-e2*sinf*sinf, 1.5); // rho = meridional radius of curvature var ?2 = ?/?-1; // eta = ? var tanf = Math.tan(f); var tan2f = tanf*tanf, tan4f = tan2f*tan2f, tan6f = tan4f*tan2f; var secf = 1/cosf; var ?3 = ?*?*?, ?5 = ?3*?*?, ?7 = ?5*?*?; var VII = tanf/(2*?*?); var VIII = tanf/(24*?*?3)*(5+3*tan2f+?2-9*tan2f*?2); var IX = tanf/(720*?*?5)*(61+90*tan2f+45*tan4f); var X = secf/?; var XI = secf/(6*?3)*(?/?+2*tan2f); var XII = secf/(120*?5)*(5+28*tan2f+24*tan4f); var XIIA = secf/(5040*?7)*(61+662*tan2f+1320*tan4f+720*tan6f); var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2; f = f - VII*dE2 + VIII*dE4 - IX*dE6; var ? = ?0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7; return new LatLonE(f.toDegrees(), ?.toDegrees(), GeoParams.datum.OSGB36); } I found that to be a really nice way of writing an algorythm, at least as far as redability is concerned. Is there any way to easily write the special symbols. And by easily write I mean NOT copy/paste them.

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• how to make a function recursive

  - by tom smith

  i have this huge function and i am wondering how to make it recursive. i have the base case which should never come true, so it should always go to else and keep calling itself with the variable t increases. any help would be great thanks def draw(x, y, t, planets): if 'Satellites' in planets["Moon"]: print ("fillcircle", x, y, planets["Moon"]['Radius']*scale) else: while True: print("refresh") print("colour 0 0 0") print("clear") print("colour 255 255 255") print("fillcircle",x,y,planets['Sun']['Radius']*scale) print("text ", "\"Sun\"",x+planets['Sun']['Radius']*scale,y) if "Mercury" in planets: r_Mercury=planets['Mercury']['Orbital Radius']*scale; print("circle",x,y,r_Mercury) r_Xmer=x+math.sin(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury r_Ymer=y+math.cos(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury print("fillcircle",r_Xmer,r_Ymer,3) print("text ", "\"Mercury\"",r_Xmer+planets['Mercury']['Radius']*scale,r_Ymer) if "Venus" in planets: r_Venus=planets['Venus']['Orbital Radius']*scale; print("circle",x,y,r_Venus) r_Xven=x+math.sin(t*2*math.pi/planets['Venus']['Period'])*r_Venus r_Yven=y+math.cos(t*2*math.pi/planets['Venus']['Period'])*r_Venus print("fillcircle",r_Xven,r_Yven,3) print("text ", "\"Venus\"",r_Xven+planets['Venus']['Radius']*scale,r_Yven) if "Earth" in planets: r_Earth=planets['Earth']['Orbital Radius']*scale; print("circle",x,y,r_Earth) r_Xe=x+math.sin(t*2*math.pi/planets['Earth']['Period'])*r_Earth r_Ye=y+math.cos(t*2*math.pi/planets['Earth']['Period'])*r_Earth print("fillcircle",r_Xe,r_Ye,3) print("text ", "\"Earth\"",r_Xe+planets['Earth']['Radius']*scale,r_Ye) if "Moon" in planets: r_Moon=planets['Moon']['Orbital Radius']*scale; print("circle",r_Xe,r_Ye,r_Moon) r_Xm=r_Xe+math.sin(t*2*math.pi/planets['Moon']['Period'])*r_Moon r_Ym=r_Ye+math.cos(t*2*math.pi/planets['Moon']['Period'])*r_Moon print("fillcircle",r_Xm,r_Ym,3) print("text ", "\"Moon\"",r_Xm+planets['Moon']['Radius']*scale,r_Ym) if "Mars" in planets: r_Mars=planets['Mars']['Orbital Radius']*scale; print("circle",x,y,r_Mars) r_Xmar=x+math.sin(t*2*math.pi/planets['Mars']['Period'])*r_Mars r_Ymar=y+math.cos(t*2*math.pi/planets['Mars']['Period'])*r_Mars print("fillcircle",r_Xmar,r_Ymar,3) print("text ", "\"Mars\"",r_Xmar+planets['Mars']['Radius']*scale,r_Ymar) if "Phobos" in planets: r_Phobos=planets['Phobos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Phobos) r_Xpho=r_Xmar+math.sin(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos r_Ypho=r_Ymar+math.cos(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos print("fillcircle",r_Xpho,r_Ypho,3) print("text ", "\"Phobos\"",r_Xpho+planets['Phobos']['Radius']*scale,r_Ypho) if "Deimos" in planets: r_Deimos=planets['Deimos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Deimos) r_Xdei=r_Xmar+math.sin(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos r_Ydei=r_Ymar+math.cos(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos print("fillcircle",r_Xdei,r_Ydei,3) print("text ", "\"Deimos\"",r_Xpho+planets['Deimos']['Radius']*scale,r_Ydei) if "Ceres" in planets: r_Ceres=planets['Ceres']['Orbital Radius']*scale; print("circle",x,y,r_Ceres) r_Xcer=x+math.sin(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres r_Ycer=y+math.cos(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres print("fillcircle",r_Xcer,r_Ycer,3) print("text ", "\"Ceres\"",r_Xcer+planets['Ceres']['Radius']*scale,r_Ycer) if "Jupiter" in planets: r_Jupiter=planets['Jupiter']['Orbital Radius']*scale; print("circle",x,y,r_Jupiter) r_Xjup=x+math.sin(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter r_Yjup=y+math.cos(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter print("fillcircle",r_Xjup,r_Yjup,3) print("text ", "\"Jupiter\"",r_Xjup+planets['Jupiter']['Radius']*scale,r_Yjup) if "Io" in planets: r_Io=planets['Io']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Io) r_Xio=r_Xjup+math.sin(t*2*math.pi/planets['Io']['Period'])*r_Io r_Yio=r_Yjup+math.cos(t*2*math.pi/planets['Io']['Period'])*r_Io print("fillcircle",r_Xio,r_Yio,3) print("text ", "\"Io\"",r_Xio+planets['Io']['Radius']*scale,r_Yio) if "Europa" in planets: r_Europa=planets['Europa']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Europa) r_Xeur=r_Xjup+math.sin(t*2*math.pi/planets['Europa']['Period'])*r_Europa r_Yeur=r_Yjup+math.cos(t*2*math.pi/planets['Europa']['Period'])*r_Europa print("fillcircle",r_Xeur,r_Yeur,3) print("text ", "\"Europa\"",r_Xeur+planets['Europa']['Radius']*scale,r_Yeur) if "Ganymede" in planets: r_Ganymede=planets['Ganymede']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Ganymede) r_Xgan=r_Xjup+math.sin(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede r_Ygan=r_Yjup+math.cos(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede print("fillcircle",r_Xgan,r_Ygan,3) print("text ", "\"Ganymede\"",r_Xgan+planets['Ganymede']['Radius']*scale,r_Ygan) if "Callisto" in planets: r_Callisto=planets['Callisto']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Callisto) r_Xcal=r_Xjup+math.sin(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto r_Ycal=r_Yjup+math.cos(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto print("fillcircle",r_Xcal,r_Ycal,3) print("text ", "\"Callisto\"",r_Xcal+planets['Callisto']['Radius']*scale,r_Ycal) if "Saturn" in planets: r_Saturn=planets['Saturn']['Orbital Radius']*scale; print("circle",x,y,r_Saturn) r_Xsat=x+math.sin(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn r_Ysat=y+math.cos(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn print("fillcircle",r_Xsat,r_Ysat,3) print("text ", "\"Saturn\"",r_Xsat+planets['Saturn']['Radius']*scale,r_Ysat) if "Mimas" in planets: r_Mimas=planets['Mimas']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Mimas) r_Xmim=r_Xsat+math.sin(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas r_Ymim=r_Ysat+math.cos(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas print("fillcircle",r_Xmim,r_Ymim,3) print("text ", "\"Mimas\"",r_Xmim+planets['Mimas']['Radius']*scale,r_Ymim) if "Enceladus" in planets: r_Enceladus=planets['Enceladus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Enceladus) r_Xenc=r_Xsat+math.sin(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus r_Yenc=r_Ysat+math.cos(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus print("fillcircle",r_Xenc,r_Yenc,3) print("text ", "\"Enceladus\"",r_Xenc+planets['Enceladus']['Radius']*scale,r_Yenc) if "Tethys" in planets: r_Tethys=planets['Tethys']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Tethys) r_Xtet=r_Xsat+math.sin(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys r_Ytet=r_Ysat+math.cos(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys print("fillcircle",r_Xtet,r_Ytet,3) print("text ", "\"Tethys\"",r_Xtet+planets['Tethys']['Radius']*scale,r_Ytet) if "Dione" in planets: r_Dione=planets['Dione']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Dione) r_Xdio=r_Xsat+math.sin(t*2*math.pi/planets['Dione']['Period'])*r_Dione r_Ydio=r_Ysat+math.cos(t*2*math.pi/planets['Dione']['Period'])*r_Dione print("fillcircle",r_Xdio,r_Ydio,3) print("text ", "\"Dione\"",r_Xdio+planets['Dione']['Radius']*scale,r_Ydio) if "Rhea" in planets: r_Rhea=planets['Rhea']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Rhea) r_Xrhe=r_Xsat+math.sin(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea r_Yrhe=r_Ysat+math.cos(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea print("fillcircle",r_Xrhe,r_Yrhe,3) print("text ", "\"Rhea\"",r_Xrhe+planets['Rhea']['Radius']*scale,r_Yrhe) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Titan) r_Xtit=r_Xsat+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytit=r_Ysat+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtit,r_Ytit,3) print("text ", "\"Titan\"",r_Xtit+planets['Titan']['Radius']*scale,r_Ytit) if "Iapetus" in planets: r_Iapetus=planets['Iapetus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Iapetus) r_Xiap=r_Xsat+math.sin(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus r_Yiap=r_Ysat+math.cos(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus print("fillcircle",r_Xiap,r_Yiap,3) print("text ", "\"Iapetus\"",r_Xiap+planets['Iapetus']['Radius']*scale,r_Yiap) if "Uranus" in planets: r_Uranus=planets['Uranus']['Orbital Radius']*scale; print("circle",x,y,r_Uranus) r_Xura=x+math.sin(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus r_Yura=y+math.cos(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus print("fillcircle",r_Xura,r_Yura,3) print("text ", "\"Uranus\"",r_Xura+planets['Uranus']['Radius']*scale,r_Yura) if "Puck" in planets: r_Puck=planets['Puck']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Puck) r_Xpuc=r_Xura+math.sin(t*2*math.pi/planets['Puck']['Period'])*r_Puck r_Ypuc=r_Yura+math.cos(t*2*math.pi/planets['Puck']['Period'])*r_Puck print("fillcircle",r_Xpuc,r_Ypuc,3) print("text ", "\"Puck\"",r_Xpuc+planets['Puck']['Radius']*scale,r_Ypuc) if "Miranda" in planets: r_Miranda=planets['Miranda']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Miranda) r_Xmira=r_Xura+math.sin(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda r_Ymira=r_Yura+math.cos(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda print("fillcircle",r_Xmira,r_Ymira,3) print("text ", "\"Miranda\"",r_Xmira+planets['Miranda']['Radius']*scale,r_Ymira) if "Ariel" in planets: r_Ariel=planets['Ariel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Ariel) r_Xari=r_Xura+math.sin(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel r_Yari=r_Yura+math.cos(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel print("fillcircle",r_Xari,r_Yari,3) print("text ", "\"Ariel\"",r_Xari+planets['Ariel']['Radius']*scale,r_Yari) if "Umbriel" in planets: r_Umbriel=planets['Umbriel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Umbriel) r_Xumb=r_Xura+math.sin(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel r_Yumb=r_Yura+math.cos(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel print("fillcircle",r_Xumb,r_Yumb,3) print("text ", "\"Umbriel\"",r_Xumb+planets['Umbriel']['Radius']*scale,r_Yumb) if "Titania" in planets: r_Titania=planets['Titania']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Titania) r_Xtita=r_Xura+math.sin(t*2*math.pi/planets['Titania']['Period'])*r_Titania r_Ytita=r_Yura+math.cos(t*2*math.pi/planets['Titania']['Period'])*r_Titania print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titania\"",r_Xtita+planets['Titania']['Radius']*scale,r_Ytita) if "Oberon" in planets: r_Oberon=planets['Oberon']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Oberon) r_Xober=r_Xura+math.sin(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon r_Yober=r_Yura+math.cos(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon print("fillcircle",r_Xober,r_Yober,3) print("text ", "\"Oberon\"",r_Xober+planets['Oberon']['Radius']*scale,r_Yober) if "Neptune" in planets: r_Neptune=planets['Neptune']['Orbital Radius']*scale; print("circle",x,y,r_Neptune) r_Xnep=x+math.sin(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune r_Ynep=y+math.cos(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune print("fillcircle",r_Xnep,r_Ynep,3) print("text ", "\"Neptune\"",r_Xnep+planets['Neptune']['Radius']*scale,r_Ynep) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xnep,r_Ynep,r_Titan) r_Xtita=r_Xnep+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytita=r_Ynep+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titan\"",r_Xtita+planets['Titan']['Radius']*scale,r_Ytita) t += 0.003 print(draw(x, y, t, planets))

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• Why isn't my operator overloading working properly?

  - by Mithrax

  I have the following Polynomial class I'm working on: #include <iostream> using namespace std; class Polynomial { //define private member functions private: int coef[100]; // array of coefficients // coef[0] would hold all coefficients of x^0 // coef[1] would hold all x^1 // coef[n] = x^n ... int deg; // degree of polynomial (0 for the zero polynomial) //define public member functions public: Polynomial::Polynomial() //default constructor { for ( int i = 0; i < 100; i++ ) { coef[i] = 0; } } void set ( int a , int b ) //setter function { //coef = new Polynomial[b+1]; coef[b] = a; deg = degree(); } int degree() { int d = 0; for ( int i = 0; i < 100; i++ ) if ( coef[i] != 0 ) d = i; return d; } void print() { for ( int i = 99; i >= 0; i-- ) { if ( coef[i] != 0 ) { cout << coef[i] << "x^" << i << " "; } } } // use Horner's method to compute and return the polynomial evaluated at x int evaluate ( int x ) { int p = 0; for ( int i = deg; i >= 0; i-- ) p = coef[i] + ( x * p ); return p; } // differentiate this polynomial and return it Polynomial differentiate() { if ( deg == 0 ) { Polynomial t; t.set ( 0, 0 ); return t; } Polynomial deriv;// = new Polynomial ( 0, deg - 1 ); deriv.deg = deg - 1; for ( int i = 0; i < deg; i++ ) deriv.coef[i] = ( i + 1 ) * coef[i + 1]; return deriv; } Polynomial Polynomial::operator + ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] += b.coef[i]; c.deg = c.degree(); return c; } Polynomial Polynomial::operator += ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] += b.coef[i]; c.deg = c.degree(); for ( int i = 0; i < 100; i++) a.coef[i] = c.coef[i]; a.deg = a.degree(); return a; } Polynomial Polynomial::operator -= ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i]; c.deg = c.degree(); for ( int i = 0; i < 100; i++) a.coef[i] = c.coef[i]; a.deg = a.degree(); return a; } Polynomial Polynomial::operator *= ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) for ( int j = 0; j <= b.deg; j++ ) c.coef[i+j] += ( a.coef[i] * b.coef[j] ); c.deg = c.degree(); for ( int i = 0; i < 100; i++) a.coef[i] = c.coef[i]; a.deg = a.degree(); return a; } Polynomial Polynomial::operator - ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i]; c.deg = c.degree(); return c; } Polynomial Polynomial::operator * ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) for ( int j = 0; j <= b.deg; j++ ) c.coef[i+j] += ( a.coef[i] * b.coef[j] ); c.deg = c.degree(); return c; } }; int main() { Polynomial a, b, c, d; a.set ( 7, 4 ); //7x^4 a.set ( 1, 2 ); //x^2 b.set ( 6, 3 ); //6x^3 b.set ( -3, 2 ); //-3x^2 c = a - b; // (7x^4 + x^2) - (6x^3 - 3x^2) a -= b; c.print(); cout << "\n"; a.print(); cout << "\n"; c = a * b; // (7x^4 + x^2) * (6x^3 - 3x^2) c.print(); cout << "\n"; d = c.differentiate().differentiate(); d.print(); cout << "\n"; cout << c.evaluate ( 2 ); //substitue x with 2 cin.get(); } Now, I have the "-" operator overloaded and it works fine: Polynomial Polynomial::operator - ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i]; c.deg = c.degree(); return c; } However, I'm having difficulty with my "-=" operator: Polynomial Polynomial::operator -= ( Polynomial b ) { Polynomial a = *this; //a is the poly on the L.H.S Polynomial c; for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i]; for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i]; c.deg = c.degree(); // overwrite value of 'a' with the newly computed 'c' before returning 'a' for ( int i = 0; i < 100; i++) a.coef[i] = c.coef[i]; a.deg = a.degree(); return a; } I just slightly modified my "-" operator method to overwrite the value in 'a' and return 'a', and just use the 'c' polynomial as a temp. I've put in some debug print statement and I confirm that at the time of computation, both: c = a - b; and a -= b; are computed to the same value. However, when I go to print them, their results are different: Polynomial a, b; a.set ( 7, 4 ); //7x^4 a.set ( 1, 2 ); //x^2 b.set ( 6, 3 ); //6x^3 b.set ( -3, 2 ); //-3x^2 c = a - b; // (7x^4 + x^2) - (6x^3 - 3x^2) a -= b; c.print(); cout << "\n"; a.print(); cout << "\n"; Result: 7x^4 -6x^3 4x^2 7x^4 1x^2 Why is my c = a - b and a -= b giving me different results when I go to print them?

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• Small-o(n^2) implementation of Polynomial Multiplication

  - by AlanTuring

  I'm having a little trouble with this problem that is listed at the back of my book, i'm currently in the middle of test prep but i can't seem to locate anything regarding this in the book. Anyone got an idea? A real polynomial of degree n is a function of the form f(x)=a(n)x^n+?+a1x+a0, where an,…,a1,a0 are real numbers. In computational situations, such a polynomial is represented by a sequence of its coefficients (a0,a1,…,an). Assuming that any two real numbers can be added/multiplied in O(1) time, design an o(n^2)-time algorithm to compute, given two real polynomials f(x) and g(x) both of degree n, the product h(x)=f(x)g(x). Your algorithm should **not** be based on the Fast Fourier Transform (FFT) technique. Please note it needs to be small-o(n^2), which means it complexity must be sub-quadratic. The obvious solution that i have been finding is indeed the FFT, but of course i can't use that. There is another method that i have found called convolution, where if you take polynomial A to be a signal and polynomial B to be a filter. A passed through B yields a shifted signal that has been "smoothed" by A and the resultant is A*B. This is supposed to work in O(n log n) time. Of course i am completely unsure of implementation. If anyone has any ideas of how to achieve a small-o(n^2) implementation please do share, thanks.

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• How to learn the math behind the code?

  - by Solomon Wise

  I am a 12 year old who has recently gotten into programming. (Although I know that the number of books you have read does not determine your programming competency or ability, just to paint a "map" of where I am in terms of the content I know...) I've finished the books: Python 3 For Absolute Beginners Pro Python Python Standard Library by Example Beautiful Code Agile Web Development With Rails and am about halfway into Programming Ruby. I have written many small programs (One that finds which files have been updated and deleted in a directory, one that compares multiple players' fantasy baseball value, and some text based games, and many more). Obviously, as I'm not some sort of child prodigy, I can't take a formal Computer Science course until high school. I really want to learn computer science to increase my knowledge about the code, and the how the code runs. I've really become interested in the math part after reading the source code for Python's random module. Is there a place where I can learn CS, or programming math online for free, at a level that would be at least partially understandable to a person my age?

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• Algorithm for computing the inverse of a polynomial

  - by Neville

  I'm looking for an algorithm (or code) to help me compute the inverse a polynomial, I need it for implementing NTRUEncrypt. An algorithm that is easily understandable is what I prefer, there are pseudo-codes for doing this, but they are confusing and difficult to implement, furthermore I can not really understand the procedure from pseudo-code alone. Any algorithms for computing the inverse of a polynomial with respect to a ring of truncated polynomials?

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• NTRU Pseudo-code for computing Polynomial Inverses

  - by Neville

  Hello all. I was wondering if anyone could tell me how to implement line 45 of the following pseudo-code. Require: the polynomial to invert a(x), N, and q. 1: k = 0 2: b = 1 3: c = 0 4: f = a 5: g = 0 {Steps 5-7 set g(x) = x^N - 1.} 6: g[0] = -1 7: g[N] = 1 8: loop 9: while f[0] = 0 do 10: for i = 1 to N do 11: f[i - 1] = f[i] {f(x) = f(x)/x} 12: c[N + 1 - i] = c[N - i] {c(x) = c(x) * x} 13: end for 14: f[N] = 0 15: c[0] = 0 16: k = k + 1 17: end while 18: if deg(f) = 0 then 19: goto Step 32 20: end if 21: if deg(f) < deg(g) then 22: temp = f {Exchange f and g} 23: f = g 24: g = temp 25: temp = b {Exchange b and c} 26: b = c 27: c = temp 28: end if 29: f = f XOR g 30: b = b XOR c 31: end loop 32: j = 0 33: k = k mod N 34: for i = N - 1 downto 0 do 35: j = i - k 36: if j < 0 then 37: j = j + N 38: end if 39: Fq[j] = b[i] 40: end for 41: v = 2 42: while v < q do 43: v = v * 2 44: StarMultiply(a; Fq; temp;N; v) 45: temp = 2 - temp mod v 46: StarMultiply(Fq; temp; Fq;N; v) 47: end while 48: for i = N - 1 downto 0 do 49: if Fq[i] < 0 then 50: Fq[i] = Fq[i] + q 51: end if 52: end for 53: {Inverse Poly Fq returns the inverse polynomial, Fq, through the argument list.} The function StarMultiply returns a polynomial (array) stored in the variable temp. Basically temp is a polynomial (I'm representing it as an array) and v is an integer (say 4 or 8), so what exactly does temp = 2-temp mod v equate to in normal language? How should i implement that line in my code. Can someone give me an example. The above algorithm is for computing Inverse polynomials for NTRUEncrypt key generation. The pseudo-code can be found on page 28 of this document. Thanks in advance.

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• Java Math.cos() Method Does Not Return 0 When Expected

  - by dimo414

  Using Java on a Windows 7 PC (not sure if that matters) and calling Math.cos() on values that should return 0 (like pi/2) instead returns small values, but small values that, unless I'm misunderstanding, are much greater than 1 ulp off from zero. Math.cos(Math.PI/2) = 6.123233995736766E-17 Math.ulp(Math.cos(Math.PI/2)) = 1.232595164407831E-32 Is this in fact within 1 ulp and I'm simply confused? And would this be an acceptable wrapper method to resolve this minor inaccuracy? public static double cos(double a){ double temp = Math.abs(a % Math.PI); if(temp == Math.PI/2) return 0; return Math.cos(a); }

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• MathType and LibreOffice Math comparison

  - by Agmenor

  In my office my team and I are going to type texts in the future which will include mathematical signs. Two programs are being proposed: LibreOffice Writer + Math or Microsoft Office + MathType. I would like to advocate for the first solution, but I need to know what technical advantages and disadvantages each program has. Compatibility with Ubuntu is an evident and important characteristic for LibreOffice, but could you give some other aspects? As a side question, do you advice any other program, even if not WYSIWYG and thus not my preference in this case?

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• Getting to math applications gradually

  - by den-javamaniac

  I'm currently getting a formal degree related to computation, in particular my current focus is numerical programming, scientific computing and machine learning. I'd love to apply that knowledge in game dev and expand it with statistics, probability theory, and graph theory (probably even linear algebra). The question is: which spheres of gamedev are filled with such math stuff, is it possible to advance in those without being a part of a group of people and how to get to it gradually? P.S.: I've got experience with commercial java dev and am getting my hands on C/C++ at the moment, however, I'm opened to go ahead and try Unity3D and etc.

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• Understanding math used to determine if vector is clockwise / counterclockwise from your vector

  - by MTLPhil

  I'm reading Programming Game AI by Example by Mat Buckland. In the Math & Physics primer chapter there's a listing of the declaration of a class used to represent 2D vectors. This class contains a method called Sign. It's implementation is as follows //------------------------ Sign ------------------------------------------ // // returns positive if v2 is clockwise of this vector, // minus if anticlockwise (Y axis pointing down, X axis to right) //------------------------------------------------------------------------ enum {clockwise = 1, anticlockwise = -1}; inline int Vector2D::Sign(const Vector2D& v2)const { if (y*v2.x > x*v2.y) { return anticlockwise; } else { return clockwise; } } Can someone explain the vector rules that make this hold true? What do the values of y*v2.x and x*v2.y that are being compared actually represent? I'd like to have a solid understanding of why this works rather than just accepting that it does without figuring it out. I feel like it's something really obvious that I'm just not catching on to. Thanks for your help.

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• Polynomial.Net

  Polynomial Class Library - An easy way to working with polynomials

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