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This page show some use of kalgebra in real word

=== Combinatorial example===

   We have 6 people who want to know how to get around a table with 6 chairs.

   We now that 6 people can get around the table with this configuration

   p1 p2 p3 p4 p5 p6
   p1 p2 p3 p4 p6 p5
   p1 p2 p3 p5 p4 p6
   p1 p2 p3 p5 p6 p4

   And so on

   We notice that the last  rotate position by 1, the fifth rotate position by
   2, the fourth rotate position by 3, the third rotate position by 4, the
   second rotate position by 5 and first rotate position by 6.

   So we can write down a simple formula:

   6*5*4*3*2*1

   Let's write this into kalgebra console:

   ((((1*2)*3)*4)*5)*6
	=720      

   This kind of arragenment of things around some position, where position
   number is equal of number of things is called "permutation"

   Let's try to call in kalgebra the permutation function:

   factorial(6)
	=720

   It's the same result as you can see.


=== Probability example ===

   Let's roll a dice, we want to know the probability of one face
      
   We can define positive probability the favourble result of the event to us
   and negative probability the unfavorable result of the event to us

   So you have to pick only one face:

   probability = 1(face picked)/6(total face)

   So now we know that when a dice is rolled there is a 1/6 of probability that
   a face we choice come up

   We can set a simple function in kalgebra to take this formula in a simple 
   way:

   probability:=(favorable,total)->favorable/total



=== Numerical Theory ===

    Let's say that we want to know the sum of all numbers between a bounded
    interval for istance 1 - 100

    we have to do the sum of all numbers from 0 to 100 if we don't know the
    rule to get them
    
    kalgebra offers a great facility to this task. Let's write in console:

    sum(x: x=1.100)
    
    and we get the result

    The syntax indicate this:

    1- Bound x as variable
    2- Take first value of x
    3- Take second value of x and add the previus value of x
    4- Take third value of x and add the previus value of x
    ....
    N- Take the last value of x and add the last value of x
    

=== Eletronic ===

    Example1:

    Let's take a simple circuit a and port with two input and one output

    To resolve it on kalgebra we will write

    and(variable1, variable2)

    we will get the and value of the input as output



    Example2:
   
    We have a simple circuit: a battery of 3V and two eletrical resistence
    (R1 and R2) put on parallel of 3kohm. We want to get the current
    circulating in the circuit.

    We have first to calculate the value of the eletric resistence expressed
    as the law:

    TotalResistence = (1/R1 + 1/R2)^-1
    Current = Voltage/TotalResistence

    Let's write a simple function in kalgebra to do this:

    totalresistence:=(R1,R2)->(1/R1+1/R2)^-1
    current:=(voltage,totalresistence)->voltage/totalresistence

    let's see what we get:

    current(3, totalresistence(3, 3))
   	   =2