KAlgebra/Homework: Difference between revisions

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    Revision as of 07:53, 8 December 2010

    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