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• Evaluating mathematical expressions in Python

  - by vander

  Hi, I want to tokenize a given mathematical expression into a binary tree like this: ((3 + 4 - 1) * 5 + 6 * -7) / 2 '/' / \ + 2 / \ * * / \ / \ - 5 6 -7 / \ + 1 / \ 3 4 Is there any pure Python way to do this? Like passing as a string to Python and then get back as a tree like mentioned above. Thanks.

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• solve mathematical equation with 1 unknown (equations are dynamically built)

  - by chris-gr

  Hi, I have to built dynamically equations like following: x + x/3 + (x/3)/4 + (x/3/4)/2 = 50 Now I would like to evaluate this equation and get x. The equation is built dynamically. x is the leaf node in a taxonomy, the other 3 nodes are the super concepts. The divisor represents the number of children of the child nodes. Is there a library that allows to build such equations dynamically and resolve x? Thanks, Chris

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• Mathematical problem

  - by coolboycsaba

  I have the following function: function getLevel(points) { var level = -1 + Math.sqrt(4 + points/20); // Round down to nearest level return Math.floor(level); } The above function calculates the level of a player based on their points, my problem is that I need a function like this to calculate the points needed for a given level.

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• Extreme Optimization –Mathematical Constants and Basic Functions

  - by JoshReuben

  Machine constants The MachineConstants class - contains constants for floating-point arithmetic because the CLS System.Single and Double floating-point types do not follow the standard conventions and are useless. machine constants for the Double type: machine precision: Epsilon , SqrtEpsilon CubeRootEpsilon largest possible value: MaxDouble , SqrtMaxDouble, LogMaxDouble smallest Double-precision floating point number that is greater than zero: MinDouble , SqrtMinDouble , LogMinDouble A similar set of constants is available for the Single Datatype  Mathematical Constants The Constants class contains static fields for many mathematical constants and common expressions involving small integers – if you are doing thousands of iterations, you wouldn't want to calculate OneOverSqrtTwoPi , Sqrt17 or Log17 !!! Fundamental constants E - The base for the natural logarithm, e (2.718...). EulersConstant - (0.577...). GoldenRatio - (1.618...). Pi - the ratio between the circumference and the diameter of a circle (3.1415...). Expressions involving fundamental constants: TwoPi, PiOverTwo, PiOverFour, LogTwoPi, PiSquared, SqrPi, SqrtTwoPi, OneOverSqrtPi, OneOverSqrtTwoPi Square roots of small integers: Sqrt2, Sqrt3, Sqrt5, Sqrt7, Sqrt17 Logarithms of small integers: Log2, Log3, Log10, Log17, InvLog10  Elementary Functions The IterativeAlgorithm<T> class in the Extreme.Mathematics namespace defines many elementary functions that are missing from System.Math. Hyperbolic Trig Functions: Cosh, Coth, Csch, Sinh, Sech, Tanh Inverse Hyperbolic Trig Functions: Acosh, Acoth, Acsch, Asinh, Asech, Atanh Exponential, Logarithmic and Miscellaneous Functions: ExpMinus1 - The exponential function minus one, ex-1. Hypot - The hypotenuse of a right-angled triangle with specified sides. LambertW - Lambert's W function, the (real) solution W of x=WeW. Log1PlusX - The natural logarithm of 1+x. Pow - A number raised to an integer power.

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• Infragistics and CenterSpace Software Team Up to Deliver Mathematical Charting Solution

  Princeton, N.J. & Elstree, England & Corvallis, OR – May 5, 2010 — Infragistics, a world leader in user interface (UI) development tools and experts in the User Experience (UX) market, and CenterSpace Software, a leading provider of enterprise class numerical component libraries for the .NET platform, today announced that they have teamed up to bring a complete mathematical charting solution to .NET developers.

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• Documenting mathematical logic in code

  - by Kiril Raychev

  Sometimes, although not often, I have to include math logic in my code. The concepts used are mostly very simple, but the resulting code is not - a lot of variables with unclear purpose, and some operations with not so obvious intent. I don't mean that the code is unreadable or unmaintainable, just that it's waaaay harder to understand than the actual math problem. I try to comment the parts which are hardest to understand, but there is the same problem as in just coding them - text does not have the expressive power of math. I am looking for a more efficient and easy to understand way of explaining the logic behind some of the complex code, preferably in the code itself. I have considered TeX - writing the documentation and generating it separately from the code. But then I'd have to learn TeX, and the documentation will not be in the code itself. Another thing I thought of is taking a picture of the mathematical notations, equations and diagrams written on paper/whiteboard, and including it in javadoc. Is there a simpler and clearer way? P.S. Giving descriptive names(timeOfFirstEvent instead of t1) to the variables actually makes the code more verbose and even harder too read.

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• Layout of mathematical views (iOS)

  - by William Jockusch

  I am trying to figure out the right way to encapsulate graphical information about mathematical objects. It is not simple. For example, a matrix can include square brackets around its entries, or not. Some things carry down to sub-objects -- for example, a matrix might track the font size to be used by its entries. Similarly, the font color and the background color would carry down to the entries. Other things do not carry down. For example, the entries of the matrix do not need to know whether or not the matrix has those square brackets. Based on all of the above, I need to calculate sizes for everything, then frames. All of this can depend on the properties stored above. The size of a matrix depends on the sizes of its entries, and also on whether or not it has those brackets. What I am having a hard time with is not the individual ways to calculate sensible frames for this or that. It is the overall organizational structure of the whole thing. How can I keep track of it all without going crazy. One particular obstacle is worth mentioning -- for reasons I don't want to go into here, I need to calculate the sizes and frames for everything before I instantiate any actual views. So, for example, if I have a Matrix object, I need to calculate its size before I make a MatrixView. If I have an equation, I need to calculate the size of the view for the equation before I create the actual view. So I clearly need separate objects for those calculations. But I can't figure out a sensible class structure for those objects. If I put them all into a single class, I get some advantages because copying then becomes easy. But I also end up with a bloated class that contains info that is irrelevant for some objects -- such as whether or not to include those brackets around the matrix. But if I use a lot of different classes, copying properties becomes a real pain. If it matters, this is all in Objective C, for an iOS environment. Any pointers would be greatly appreciated.

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• Parsing mathematical experssions with two values that have parenthesis and minus signs

  - by user45921

  I'm trying to parse equations like these which only has two values or the square root of a certain value from a text file: 100+100 -100-100 -(100)+(-100) sqrt(100) by the minues signs, parenthesis and the operator symbol in the middle and the square root, and I have no idea how to start off... I've got the file part done and the simple calculation parts except that I couldnt get my program to solve the equations in the above. #include <stdio.h> #include <string.h> #include <stdlib.h> #include <math.h> main(){ FILE *fp; char buff[255], sym,sym2,del1,del2,del3,del4; double num1, num2; int ret; fp = fopen("input.txt","r"); while(fgets(buff,sizeof(buff),fp)!=NULL){ char *tok = buff; sscanf(tok,"%lf%c%lf",&num1,&sym,&num2); switch(sym){ case '+': printf("%lf\n", num1+num2); break; case '-': printf("%lf\n", num1-num2); break; case '*': printf("%lf\n", num1*num2); break; case '/': printf("%lf\n", num1/num2); break; default: printf("The input value is not correct\n"); break; } } fclose(fp); } that is what have I written for the other basic operations without parenthesis and the minus sign for the second value and it works great for the simple ones. I'm using a switch method to calculate the add, sub, mul and divide but I'm not sure how to properly use the sscanf function (if I am not using it properly) or if there is another way using a function like strtok to properly parse the parenthesis and the minus signs. Any kind help?

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• Using NumPy arrays as 2D mathematical vectors?

  - by CorundumGames

  Right now I'm using lists as position, velocity, and acceleration vectors in my game. Is that a better option than using NumPy's arrays (not the standard library's) as vectors (with float data types)? I'm frequently adding vectors and changing their values directly, then placing the values in these vectors into a Pygame Rect. The vector is used for position (because Rects can't hold floats, so we can't go "between" pixels), and the Rect is used for rendering (because Pygame will only take in Rects for rendering positions).

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• Non-mathematical Project Euler (or similar)?

  - by Juha Untinen

  I checked the post (Where can I find programming puzzles and challenges?) where there's a lot of programming challenges and such, but after checking several of them, they all seem to be about algorithms and mathematics. Is there a similar site for purely logic/functionality-based challenges? For example: - Retrieve data using a web service - Generate output X from a CSV file - Protect this code against SQL injection - Make this code more secure - What is wrong with this code (where the error is in logic, not syntax) - Make this loop more efficient Does a challenge site like that exist? Especially one that provides hints and/or correct solutions. That would be a very helpful learning site.

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• Can we count Processing as Environment for Mathematical Modelling and Programming?

  - by Ole Jak

  Can we count Processing as Environment for Mathematical Modelling and Programming? And If yes can we do the same for Eclipse (Java)?

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• Building a new cluster for mathematical calculations (Win/Lin)

  - by Muhammad Farhan

  I would like to build a new cluster to perform heavy mathematical calculations in Matlab and Abaqus. One of my friend told me that distributed computing is way faster than parallel computing, which is very true after reading a bit on the internet. However, I have never clustered before. Current workstation I own: Dell Precision T5400 2 x Intel Xeon 2.5 GHz 16 GB RAM (2GB x 8) 1 x Western Digital 1TB HDD 7200 rpm 1 x nVidia Quadro FX4600 768MB GPU 1 x 870W PSU OS: Windows 7 Ultimate 64-bit 2nd WS: I can buy another WS similar configuration to the one I own I am not bothered about OS, I am willing to cluster with either Windows or Linux. However, my software are compatible with windows 64-bit only. Please help me setup a cluster. Thank you.

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• Keyboard layout for mathematical/Greek symbols

  - by David

  I've been wondering about this for a long time but never thought to ask: I do a lot of scientific work so there are many times it would be really handy to be able to type mathematical symbols or Greek letters which, for the most part, aren't part of the ASCII character set. Like "8 µ ? s t ? ? … v ? = = ±" and so on. Is there a keyboard layout (for Linux) that maps simple key combinations to these kinds of characters? (Assuming all the encoding and font issues are worked out properly) I know I could create one myself but it'd be a lot easier if someone's already done the work, or at least if there's a partial solution I could modify.

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• Mathematical annotations in a PDF file

  - by kvaruni

  I like to annotate papers I read in a digital way. Numerous programs exist to help in this process. For example, on OS X one can use programs such as Skim or even Preview. However, making annotations is dreadful when one wishes to add mathematical annotations, such as formulas or greek letters. A cumbersome "solution" is to select the desired symbol one by one using the Special Characters palette, though this considerably slows down the annotation process. Is there any way to add mathematical annotations to a PDF? The only two limitations that I would impose on a solution is that 1) the mathematical text needs to be selectable, i.e. it must be text and 2) I want to limit the number of programs I need to make the process as painless as possible. Some of the more promising solutions I have tried include generating LaTeX with LaTeXiT, but it seems to be impossible to add a PDF on top of another PDF. Another attempt was to use jsMath to generate the symbols and copy-paste these as annotation using one of the jsMath fonts. This results in unreadable, incorrect characters.

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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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• String manipulation of type String substitution in mathematical expression

  - by Peterstone

  Imagine something like exp(49/200)+(x-49/200) I want to pass as argument of the function "roundn" whatever operation that is not a addtion or a subtraction So my expresion became roundn(exp(roundn(49/200,n)),n)+(x - roundn(49/200,n) Well the expression I want to manipulate is this: exp(49/200)+exp(49/200)*(x-49/200)+1/2*exp(49/200)*(x-49/200)^2+1/6*exp(49/200)*(x- 49/200)^3+1/24*exp(49/200)*(x-49/200)^4+1/120*exp(49/200)*(x-49/200)^5+1/720*exp(49/200)*(x-49/200)^6+1/5040*exp(49/200)*(x-49/200)^7+1/40320*exp(49/200)*(x-49/200)^8+1/362880*exp(49/200)*(x-49/200)^9+1/3628800*exp(49/200)*(x-49/200)^10+1/39916800*exp(49/200)*(x-49/200)^11 I´m looking for a method (That include whatever program) not based in lenguage programming, as much batch or somithing like that... Thank you!

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• Mathematical modulus in c#

  - by penguat

  Is there a library function in c# for the mathematical modulus of a number - by this I specifically mean that a negative integer modulo a positive integer should yield a positive result.

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• iPhone App Development - mathematical sysmbols

  - by mcglynnconsultancy

  I am quite the beginner - but I have a lot of experience with respect to Electrical Engineering and formulas - over 30 years worth! Trying to construct an app for the iPhone. Loaded the SDK, bought myself a Mac, got a couple of "Chapter" pages written by John at Alpha Aviation - who recomended I try this site. How do I - well for example I enetered 400/1.732 - it came out like it was a web address with an underline! How can I get mathematical symbols like - sqare root, to the power of, subscript, superscript. I'd like to insert a few "calculator" pages but don't know how to. Appreciate I have only been doing this for the last week or so - so I am still quite rusty compared to what I wrote many years ago. Can anyone help? cheers

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• syntax to express mathematical formula concisely in your language of choice

  - by aaa

  hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. Right now my language looks something like this: // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible. Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them Thank you

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• Question about the mathematical properties of hashes

  - by levand

  Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value. Let A be the set of all possible 256 bit binary values. A is extremely large, but finite. Let B be the set of all possible binary values. B is infinite. Let C be the set of values obtained by running SHA-256 on every member of B. Obviously this can't be done in practice, but I'm guessing we can still do mathematical analysis of it. My Question: By necessity, C ? A. But does C = A?

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• Lazy sequence or recur for mathematical power function?

  - by StackedCrooked

  As an exercise I implemented the mathematical power function. Once using recur: (defn power [a n] (let [multiply (fn [x factor i] (if (zero? i) x (recur (* x factor) factor (dec i))))] (multiply a a (dec n)))) And once with lazy-seq: (defn power [a n] (letfn [(multiply [a factor] (lazy-seq (cons a (multiply (* a factor) factor))))] (nth (multiply a a) (dec n)))) Which implementation do you think is superior? I truly have no idea.. (I'd use recur because it's easier to understand.) I read that lazy-seq is fast because is uses internal caching. But I don't see any opportunities for caching in my sample. Am I overlooking something?

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• Code bacteria: evolving mathematical behavior

  - by Stefano Borini

  It would not be my intention to put a link on my blog, but I don't have any other method to clarify what I really mean. The article is quite long, and it's in three parts (1,2,3), but if you are curious, it's worth the reading. A long time ago (5 years, at least) I programmed a python program which generated "mathematical bacteria". These bacteria are python objects with a simple opcode-based genetic code. You can feed them with a number and they return a number, according to the execution of their code. I generate their genetic codes at random, and apply an environmental selection to those objects producing a result similar to a predefined expected value. Then I let them duplicate, introduce mutations, and evolve them. The result is quite interesting, as their genetic code basically learns how to solve simple equations, even for values different for the training dataset. Now, this thing is just a toy. I had time to waste and I wanted to satisfy my curiosity. however, I assume that something, in terms of research, has been made... I am reinventing the wheel here, I hope. Are you aware of more serious attempts at creating in-silico bacteria like the one I programmed? Please note that this is not really "genetic algorithms". Genetic algorithms is when you use evolution/selection to improve a vector of parameters against a given scoring function. This is kind of different. I optimize the code, not the parameters, against a given scoring function.

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• suggestions on syntax to express mathematical formula concisely

  - by aaa

  hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. I post prototype in the comment, it is about 2 hundred lines long. Right now my language looks something like this (well, actually is going to look like): // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible (in any language, not just C++). Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them. Thank you just to clarify and give actual formula, my short-term goal is to express the following expression concisely where values in <> are already computed as 4-dimensional array

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• How to parse mathematical expressions involving parentheses

  - by Rob P.

  Please forgive my title, I really don't know how to phrase it better. This isn't a school assignment or anything, but I realize it's a mostly academic question. But, what I've been struggling to do is parse 'math' text and come up with an answer. For Example - I can figure out how to parse '5 + 5' or '3 * 5' - but I fail when I try to correctly chain operations together. (5 + 5) * 3 It's mostly just bugging me that I can't figure it out. If anyone can point me in a direction, I'd really appreciate it. EDIT Thanks for all of the quick responses. I'm sorry I didn't do a better job of explaining. First - I'm not using regular expressions. I also know there are already libraries available that will take, as a string, a mathematical expression and return the correct value. So, I'm mostly looking at this because, sadly, I don't "get it". Second - What I've tried doing (is probably misguided) but I was counting '(' and ')' and evaluating the deepest items first. In simple examples, this worked; but my code is not pretty and more complicated stuff crashes. When I 'calculated' the lowest level, I was modifying the string. So... (5 + 5) * 3 Would turn into 10 * 3 Which would then evaluate to 30 But it just felt 'wrong'. I hope that helps clarify things. I'll certainly check out the links provided.

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• Code Golf: Evaluating Mathematical Expressions

  - by Noldorin

  Challenge Here is the challenge (of my own invention, though I wouldn't be surprised if it has previously appeared elsewhere on the web). Write a function that takes a single argument that is a string representation of a simple mathematical expression and evaluates it as a floating point value. A "simple expression" may include any of the following: positive or negative decimal numbers, +, -, *, /, (, ). Expressions use (normal) infix notation. Operators should be evaluated in the order they appear, i.e. not as in BODMAS, though brackets should be correctly observed, of course. The function should return the correct result for any possible expression of this form. However, the function does not have to handle malformed expressions (i.e. ones with bad syntax). Examples of expressions: 1 + 3 / -8 = -0.5 (No BODMAS) 2*3*4*5+99 = 219 4 * (9 - 4) / (2 * 6 - 2) + 8 = 10 1 + ((123 * 3 - 69) / 100) = 4 2.45/8.5*9.27+(5*0.0023) = 2.68... Rules I anticipate some form of "cheating"/craftiness here, so please let me forewarn against it! By cheating, I refer to the use of the eval or equivalent function in dynamic languages such as JavaScript or PHP, or equally compiling and executing code on the fly. (I think my specification of "no BODMAS" has pretty much guaranteed this however.) Apart from that, there are no restrictions. I anticipate a few Regex solutions here, but it would be nice to see more than just that. Now, I'm mainly interested in a C#/.NET solution here, but any other language would be perfectly acceptable too (in particular, F# and Python for the functional/mixed approaches). I haven't yet decided whether I'm going to accept the shortest or most ingenious solution (at least for the language) as the answer, but I would welcome any form of solution in any language, except what I've just prohibited above! My Solution I've now posted my C# solution here (403 chars). Update: My new solution has beaten the old one significantly at 294 chars, with the help of a bit of lovely regex! I suspected that this will get easily beaten by some of the languages out there with lighter syntax (particularly the funcional/dynamic ones), and have been proved right, but I'd be curious if someone could beat this in C# still. Update I've seen some very crafty solutions already. Thanks to everyone who has posted one. Although I haven't tested any of them yet, I'm going to trust people and assume they at least work with all of the given examples. Just for the note, re-entrancy (i.e. thread-safety) is not a requirement for the function, though it is a bonus. Format Please post all answers in the following format for the purpose of easy comparison: Language Number of characters: ??? Fully obfuscated function: (code here) Clear/semi-obfuscated function: (code here) Any notes on the algorithm/clever shortcuts it takes.

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