    user&gt; (float (/ 411 125))
    3.288
    user&gt; (double (/ 411 125))
    3.288

    user=&gt; (clojure-version)
    &quot;1.4.0&quot;

    user=&gt; (doc quot)
    -------------------------
    clojure.core/quot
    ([num div])
      quot[ient] of dividing numerator by denominator.
    nil

    user=&gt; (quot 411 125)
    3


As [documented][1], integer division yields rational numbers. Try

    (/ 411.0 125)


  [1]: http://clojure.org/data_structures

If you use a float for the dividend, you&#39;ll get a decimal answer.

    (/ 22.0 7) -&gt; 3.142857142857143

There&#39;s also the [(unchecked-remainder x y)][1] function available.


  [1]: http://clojure.org/api

even this will work: 

    (/ 22. 7) =&gt; 3.142857142857143

`(float 411/125)` is another variant if you are given the numbers directly, which is the case if you are just using the REPL as a calculator. Unfortunately this is a few characters longer than the solution by Jonathan Feinberg and ire_and_curses. ;)

I have recently updated my model, added a BooleanField to it however when I do `python manage.py syncdb`, it doesn&#39;t add the new field to the database for the model. How can I fix this ?

django syncdb and an updated model

Is there some *nix tool or perl/php library that will let you easily create directory tree visualizations that look like the following?

	www
	|-- private
	|    |-- app 
	|    |    |-- php
	|    |    |    |-- classes
	|    |    |    +-- scripts
	|    |    |-- settings
	|    |    +-- sql
	|    +-- lib
	|         +-- ZendFramework-HEAD
	+-- public
		|-- css
		|-- images
		+-- scripts


ASCII Library for Creating &quot;Pretty&quot; Directory Trees?

When I do `(/ 411 125)` , I don&#39;t get it in terms of decimal. How do I do that?

When I divide numbers in clojure I get a fraction , how do I get the decimal?

<p>When I do <code>(/ 411 125)</code> , I don't get it in terms of decimal. How do I do that?</p>


How do you write your own function for finding the most accurate square root of an integer?

After googling it, I found [this][2] (archived from its [original link][1]), but first, I didn&#39;t get it completely, and second, it is approximate too.

Assume square root as nearest integer (to the actual root) or a float.

  [1]: http://nlindblad.org/2007/04/04/write-your-own-square-root-function/
  [2]: //web.archive.org/web/20100330183043/http://nlindblad.org/2007/04/04/write-your-own-square-root-function

Writing your own square root function

This is really weird, and I cannot see why this is happening. In the foreach cycle, I am iterating through a class A collection, and for each class, I call the `Count()` method, where `r1` and `r2` numbers are generated from range [-1,1]. The problem is that  `Random.Next` returns the same &quot;random&quot; numbers for each instance. When the results for the first instance are 0 and -1, the same ones will be returned from following instances. Please, could you tell me why this is happening? Also, I cannot get different results in each class A instance. This is the code:

    class a
    {
     Random rnd = new Random();
     private void Count()
     {
      int r1 = rnd.Next(-1, 1);
      int r2 = rnd.Next(-1, 1);
     }
    }
    class b
    {
     List&lt;a&gt; listofA=new list&lt;a&gt;();
     foreach (a ACLASS in listofA)
     {
      ACLASS.Count();
     }
    }

Random.Next returns always the same values

I want to handle the special case where multiplying two numbers together causes an overflow. The code looks something like this:

    int a = 20;
    long b = 30;
    
    // if a or b are big enough, this result will silently overflow
    long c = a * b;

That&#39;s a simplified version. In the real program `a` and `b` are sourced elsewhere at runtime. What I want to achieve is something like this:

    long c;
    if (a * b will overflow) {
        c = Long.MAX_VALUE;
    } else {
        c = a * b;
    }

How do you suggest I best code this?

Update: `a` and `b` are always non-negative in my scenario.


How can I check if multiplying two numbers in Java will cause an overflow?

Gaffer on Games has a [great article][1] about using [RK4 integration][2] for better game physics. The implementation is straightforward, but the math behind it confuses me. I understand derivatives and integrals on a conceptual level, but haven&#39;t manipulated equations in a long while.

Here&#39;s the brunt of Gaffer&#39;s implementation:

    void integrate(State &amp;state, float t, float dt)
    {
         Derivative a = evaluate(state, t, 0.0f, Derivative());
         Derivative b = evaluate(state, t+dt*0.5f, dt*0.5f, a);
         Derivative c = evaluate(state, t+dt*0.5f, dt*0.5f, b);
         Derivative d = evaluate(state, t+dt, dt, c);

         const float dxdt = 1.0f/6.0f * (a.dx + 2.0f*(b.dx + c.dx) + d.dx);
         const float dvdt = 1.0f/6.0f * (a.dv + 2.0f*(b.dv + c.dv) + d.dv)

         state.x = state.x + dxdt * dt;
         state.v = state.v + dvdt * dt;
    }

Can anybody explain in simple terms how RK4 works? Specifically, why are we averaging the derivatives at `0.0f`, `0.5f`, `0.5f`, and `1.0f?` How is averaging derivatives up to the 4th order different from doing a simple euler integration with a smaller timestep?

----------

After reading the accepted answer below, and several other articles, I have a grasp on how RK4 works. To answer my own questions:

**Can anybody explain in simple terms how RK4 works?**

&gt; RK4 takes advantage of the fact that
&gt; we can get a much better approximation
&gt; of a function if we use its
&gt; higher-order derivatives rather than
&gt; just the first or second derivative.
&gt; That&#39;s why the [Taylor series][3]
&gt; converges much faster than Euler
&gt; approximations. (take a look at the
&gt; animation on the right side of that
&gt; page)

**Specifically, why are we averaging the derivatives at `0.0f`, `0.5f`, `0.5f`, and `1.0f`?**

&gt; The Runge-Kutta method is an
&gt; approximation of a function that
&gt; samples derivatives of several points
&gt; within a timestep, unlike the Taylor
&gt; series which only samples derivatives
&gt; of a single point. After sampling
&gt; these derivatives we need to know how
&gt; to weigh each sample to get the
&gt; closest approximation possible. An
&gt; easy way to do this is to pick
&gt; constants that coincide with the
&gt; Taylor series, which is how the
&gt; constants of a Runge-Kutta equation
&gt; are determined.
&gt; 
&gt; [This article][4] made it clearer for
&gt; me. Notice how `(15)` is the Taylor
&gt; series expansion while `(17)` is the
&gt; Runge-Kutta derivation.

**How is averaging derivatives up to the 4th order different from doing a simple euler integration with a smaller timestep?**

&gt; Mathematically, it converges much
&gt; faster than doing many Euler
&gt; approximations. Of course, with enough
&gt; Euler approximations we can gain equal
&gt; accuracy to RK4, but the computational
&gt; power needed doesn&#39;t justify using
&gt; Euler.


  [1]: http://gafferongames.com/game-physics/integration-basics/
  [2]: http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
  [3]: http://en.wikipedia.org/wiki/Taylor_series
  [4]: http://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node5.html

Runge-Kutta (RK4) integration for game physics

I have a variable that will sometimes be negative and sometimes positive.

Before I use it I need to make it positive. How can I accomplish this?

making a variable value positive

I tried the following in Clojure, expecting to have the class of a non-lazy sequence returned:

    (.getClass (doall (take 3 (repeatedly rand))))

However, this still returns `clojure.lang.LazySeq`.  My guess is that `doall` does evaluate the entire sequence, but returns the original sequence as it&#39;s still useful for memoization.

So what is the idiomatic means of creating a non-lazy sequence from a lazy one?
 

How to convert lazy sequence to non-lazy in Clojure

I want to transform one map of values to another map with the same keys but with a function applied to the values. I would think there was a function for doing this in the clojure api, but I have been unable to find it. 

Here&#39;s an example implementation of what I&#39;m looking for

    (defn map-function-on-map-vals [m f]
      (reduce (fn [altered-map [k v]] (assoc altered-map k (f v))) {} m))
    (println (map-function-on-map-vals {:a &quot;test&quot; :b &quot;testing&quot;} #(.toUpperCase %)))
    {:b TESTING, :a TEST}

Does anybody know if `map-function-on-map-vals` already exists? I would think it did (probably with a nicer name too).

Mapping a function on the values of a map in Clojure

Let&#39;s say I have a **LazySeq** of *java.lang.Character* like

    (\b \ \! \/ \b \ \% \1 \9 \/ \. \i \% \$ \i \space \^@)

How can I convert this to a String? I&#39;ve tried the obvious

    (String. my-char-seq)

but it throws

    java.lang.IllegalArgumentException: No matching ctor found for class java.lang.String (NO_SOURCE_FILE:0)
    [Thrown class clojure.lang.Compiler$CompilerException]

I think because the String constructor expects a primitive **char[]** instead of a **LazySeq**. So then I tried something like

    (String. (into-array my-char-seq))

but it throws the same exception. The problem now is that **into-array** is returning a **java.lang.Character[]** instead of a primitive **char[]**. This is frustrating, because I actually generate my character sequence like this

    (map #(char (Integer. %)) seq-of-ascii-ints)

Basically I have a seq of ints representing ASCII characters; 65 = A, etc. You can see I explicitly use the primitive type coercion function **(char x)**.

What this means is that my **map** function is returning a primitive **char** but the Clojure **map** function overall is returning the *java.lang.Character* object.
 






How can I convert a LazySeq of Characters to a String in Clojure?

Given a function object or name, how can I determine its arity? Something like `(arity func-name)` .

I hope there is a way, since arity is pretty central in Clojure

Clojure: How to find out the arity of function at runtime?

*Thanks a lot for all the beautiful answers! Cannot mark just one as correct*  

*Note: Already a wiki*

I am new to functional programming and while I can read simple functions in Functional programming, for e.g. computing the factorial of a number, I am finding it hard to read big functions.
Part of the reason is I think because of my inability to figure out the smaller blocks of code within a function definition and also partly because it is becoming difficult for me to match `( )` in code. 

It would be great if someone could walk me through reading some code and give me some tips on how to quickly decipher some code. 

*Note: I can understand this code if I stare at it for 10 minutes, but I doubt if this same code had been written in Java, it would take me 10 minutes. So, I think to feel comfortable in Lisp style code, I must do it faster*

*Note: I know this is a subjective question. And I am not seeking any provably correct answer here. Just comments on how you go about reading this code, would be welcome and highly helpful* 

    (defn concat
      ([] (lazy-seq nil))
      ([x] (lazy-seq x))
      ([x y]
        (lazy-seq
          (let [s (seq x)]
            (if s
              (if (chunked-seq? s)
                (chunk-cons (chunk-first s) (concat (chunk-rest s) y))
                (cons (first s) (concat (rest s) y)))
              y))))
      ([x y &amp; zs]
         (let [cat (fn cat [xys zs]
                     (lazy-seq
                       (let [xys (seq xys)]
                         (if xys
                           (if (chunked-seq? xys)
                             (chunk-cons (chunk-first xys)
                                         (cat (chunk-rest xys) zs))
                             (cons (first xys) (cat (rest xys) zs)))
                           (when zs
                             (cat (first zs) (next zs)))))))]
           (cat (concat x y) zs))))



How to read mentally Lisp/Clojure code

When I convert an unsigned 8-bit int to string then I know the result will always be at most 3 chars (for 255) and for an signed 8-bit int we need 4 chars for e.g. &quot;-128&quot;.

Now what I&#39;m actually wondering is the same thing for floating-point values. What is the maximum number of chars required to represent any &quot;double&quot; or &quot;float&quot; value as a string?

Assume a regular C/C++ double (IEEE 754) and normal decimal expansion (i.e. no %e printf-formatting).

I&#39;m not even sure if the really small number (i.e. 0.234234) will be longer than the really huge numbers (doubles representing integers)?

What is the maximum length in chars needed to represent any double value?

I tried this:

    float a = 1.4123;
    a = a &amp; (1 &lt;&lt; 3);

I get a compiler error saying that the operand of `&amp;` cannot be of type float.

When I do:

    float a = 1.4123;
    a = (int)a &amp; (1 &lt;&lt; 3);

I get the program running. The only thing is that the bitwise operation is done on the integer representation of the number obtained after rounding off.

The following is also not allowed.

    float a = 1.4123;
    a = (void*)a &amp; (1 &lt;&lt; 3);

I don&#39;t understand why `int` can be cast to `void*` but not `float`.

I am doing this to solve the problem described in Stack Overflow question *[How to solve linear equations using a genetic algorithm?][1]*.

  [1]: https://stackoverflow.com/questions/1692418/how-to-solve-linear-equations-using-genetic-algorithm


How to perform a bitwise operation on floating point numbers

What is the biggest &quot;no-floating&quot; integer that can be stored in an IEEE 754 double type without losing precision ?

biggest integer that can be stored in a double

Is there a built in MATLAB function to find out if a matrix contains a certain value?
(ala PHP&#39;s `in_array()`)

Function for &#39;does matrix contain value X?&#39;

Is it possible to set the display precision of a float in Ruby?

Something like:

    z = 1/3
    z.to_s    #=&gt; 0.33333333333333
    z.to_s(3) #=&gt; 0.333
    z.to_s(5) #=&gt; 0.33333

Or do I have to override the `to_s` method of `Float`?

Set the display precision of a float in Ruby

I have a variable which contains the value `1234567`.

I would like it to contain exactly 8 digits, i.e. `01234567`.

Is there a PHP function for that?


Formatting a number with leading zeros in PHP

I want to check if a `string` contains only digits. I used this:

    var isANumber = isNaN(theValue) === false;

    if (isANumber){
        ..
    }

But realized that it also allows `+` and `-`. Basically, I want to make sure an `input` contains ONLY digits and no other characters. Since `+100` and `-5` are both numbers, `isNaN()` is not the right way to go.
Perhaps a regexp is what I need? Any tips?

Check if string contains only digits

How do I parse and evaluate a mathematical expression in a string (e.g. `&#39;1+1&#39;`) without invoking `eval(string)` to yield its numerical value?

With that example, I want the function to accept `&#39;1+1&#39;` and return `2`.

Evaluating a string as a mathematical expression in JavaScript

I am looking for an easy way in JavaScript to check if a number has a decimal place in it (in order to determine if it is an integer).  For instance,

&lt;!-- language: lang-js --&gt;

    23 -&gt; OK
    5 -&gt; OK
    3.5 -&gt; not OK
    34.345 -&gt; not OK

&lt;pre&gt;&lt;code&gt;if(number is integer) {...}&lt;/code&gt;&lt;/pre&gt;


Check if a number has a decimal place/is a whole number

How can I generate some **unique random** numbers between 1 and 100 using JavaScript?

Content Type	Original Author	Original Content on Stackoverflow
Question	unj2	View Question on Stackoverflow
Solution 1 - Math	Brian Carper	View Answer on Stackoverflow
Solution 2 - Math	Jacek Laskowski	View Answer on Stackoverflow
Solution 3 - Math	Jonathan Feinberg	View Answer on Stackoverflow
Solution 4 - Math	ire_and_curses	View Answer on Stackoverflow
Solution 5 - Math	Samir	View Answer on Stackoverflow
Solution 6 - Math	user1460043	View Answer on Stackoverflow

When I divide numbers in clojure I get a fraction , how do I get the decimal?

Math Problem Overview

Math Solutions

Solution 1 - Math

Solution 2 - Math

Solution 3 - Math

Solution 4 - Math

Solution 5 - Math

Solution 6 - Math

ASCII Library for Creating "Pretty" Directory Trees?

django syncdb and an updated model

Attributions