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CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , specifically in ring theory , an algebra over a commutative ring is a generalization of the concept of an algebra over a field , where the base field K is replaced by a commutative ring R . In this article, all rings are assumed to be unital . 1 Formal definition 2 Example 2.1 Split-biquaternions 3 Associative algebras 4 Non-associative algebras 5 See also 6 References 7 Further reading Formal definition [ edit ] Let R be a commutative ring. An R -algebra is an R -module A together with a binary operation [·, ·] called A - multiplication , which satisfies the following axiom: Bilinearity : for all scalars , in R and all elements x , y , z in A . Example [ edit ] Split-biquaternions [ edit ] The split-biquaternions are an example of a...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search For numbers "constructible" in the sense of set theory , see Constructible universe . For example, the square root of 2 is constructible : from the length unit, we can construct a line segment of length with straightedge and compass. A point in the Euclidean plane is a constructible point if, given a fixed coordinate system (or a fixed line segment of unit length ), the point can be constructed with unruled straightedge and compass . A complex number is a constructible number if its corresponding point in the Euclidean plane is constructible from the usual x - and y -coordinate axes. It can then be shown that a real number r is constructible if and only if , given a line segment of unit length, a line segment of length | r | can be constructed with compass and straightedge. [ 1 ] It...

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CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search The Chinese remainder theorem was proved by Gauss with his 1801 book Disquisitiones Arithmeticae . [ 1 ] The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra . It was first published in the 3rd to 5th centuries by the Chinese mathematician Sun Tzu . In its basic form, the Chinese remainder theorem will determine a number n that, when divided by some given divisors, leaves given remainders. For example, what is the lowest number n that when divided by 3 leaves a remainder of 2, when divided by 5 leaves a remainder of 3, and when divided by 7 leaves a remainder of 2? 1 Theorem statement 2 Existence and uniqueness 2.1 Case of two equations ( k = 2 ) 2.2 General case 3 Finding the solution with basic algebra ...

we're hiring! blog about imgur imgur store uploading tools developer api need help? terms privacy upload images 23 Upload Images Video to GIF Make a Meme sign in sign up #secondary-nav .header-center #topbar Loading... browse your computer drag and drop here Ctrl + V paste from your clipboard gallery submit vars publish to Imgur create album Start Upload Blog Horizontal Grid (0) By uploading, you agree to our terms of service Optimizing your large GIFs... That file type is not supported! Supported formats: JPEG, GIF, PNG, APNG, TIFF, BMP, PDF, XCF share Created 2 minutes ago · 2 images · 0 views · stats View ful...

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This is a dumb hack, we should only have one or the other from the the template context, so only one of the following will be rendered. ...

January 21, 2012 Mike Bostock Or, why random comparators are bad (in addition to being slow). This matrix diagram visualizes the probability of each element i being placed in position j at the end of a random shuffle. Red cells represent negative bias ; green cells represent positive bias . A good shuffling algorithm is unbiased ; you should see a uniform grey matrix with only a bit of white noise. A bad algorithm will show streaks in the matrix, indicating an un­even distribution. For more details, read my previous post on the Fisher–Yates shuffle . Also see screenshots of different browsers . Built with d3.js . Choose an algorithm: Or write your own: refresh auto-refresh Comments? Discuss on HN! January 21, 2012 Mike Bostock ...

January 14, 2012 Mike Bostock Say you had a fresh pack of cards: If you want to play a game of Texas Hold ‘em with friends, you should shuffle the deck first to randomize the order and insure a fair game. But how? A quick way of seeing an algorithm’s bias is a matrix diagram . A simple but effective way of doing this is to pull a random card from the deck repeatedly and set it aside, incrementally building a new stack. As long as you pick each remaining card from the deck with equal probability, you’ll have a perfectly-unbiased random stack when you’re done: Click to shuffle! But let’s say instead of a physical deck of cards, you wanted to write code to perform this same task with an in-memory array of n elements. Sounds straightforward (in part), but how would you pick a random remaining element from the original deck, exactly? One slow option—gotta start somewhere: pick a ran...

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Menubar This keeps the margins nice Toggle navigation PCG, A Better Random Number Generator /.navbar-header Download Docs Paper Video Blog /.navbar-collapse /.container End of Menubar Body content PCG, A Family of Better Random Number Generators PCG is a family of simple fast space-efficient statistically good algorithms for random number generation. Unlike many general-purpose RNGs, they are also hard to predict. comment founded on the idea of permutation functions on tuples. First column header is not rotated Following headers are rotated Statistical Quality Prediction Difficulty Reproducible Results Multiple Streams Period Useful Features Time Perfomance Space Usage Code Size & Complexity k -Dimensional Equidistribution PCG Family Excellent Challenging Yes Yes (e.g. 2 63 ) Arbitrary Jump ahead, Distance ...

Battle.net Forums Battle.net Forums Battle.net Desktop App Technical Support Linux battlenet desktop "This application failed to start" SOLVED Log in or Create an Account Shop Account Support Knowledge Center Browse our support articles Your Support Tickets View your active tickets (login required). [if IE 6]> <iframe id="support-shim" src="javascript:false;" frameborder="0" scrolling="no" style="display: block; position: absolute; top: 0; left: 9px; width: 297px; height: 400px; z-index: -1;"></iframe> <script type="text/javascript"> //<![CDATA[ (function(){ var doc = document; var shim = doc.getElementById('support-shim'); shim.style.filter = 'progid:DXImageTransform.Microsoft.Alpha(style=0,opacity=0)'; shim.style.display = 'block'; })(); //]]> ...

Skip to content Sign up Sign in This repository Explore Features Enterprise Blog Watch 225 Star 3,704 Fork 812 mongodb / node-mongodb-native /.container /.repohead Code Pull requests Wiki Pulse Graphs HTTPS Subversion You can clone with HTTPS or Subversion . Download ZIP /.repository-sidebar Permalink blob contrib key: blob_contributors:v21:2c26a39e7d359adee7a7ceafae34ee11 tag: V1.1.7 Switch branches/tags Branches Tags 0.9.7-dev 1.1.12-dev 1.2-dev 1.3.10-dev 1.3.20 1.3-dev 1.3-dev-write-command 2.0 2.0-crud 2.0-dev 3.0 V0.9.6.5 V0.9.7.3-dev V0.9.7.4-dev attemptReplSetRefactoring cursorReworkingToAvoidNextTick development-1.1 gh-pages ha integra master ne...

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