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| This page show some use of kalgebra in real word
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| === Combinatorial example===
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| We have 6 people who want to know how to get around a table with 6 chairs.
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| We now that 6 people can get around the table with this configuration
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| p1 p2 p3 p4 p5 p6
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| p1 p2 p3 p4 p6 p5
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| p1 p2 p3 p5 p4 p6
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| p1 p2 p3 p5 p6 p4
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| And so on
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| We notice that the last rotate position by 1, the fifth rotate position by
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| 2, the fourth rotate position by 3, the third rotate position by 4, the
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| second rotate position by 5 and first rotate position by 6.
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| So we can write down a simple formula:
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| 6*5*4*3*2*1
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| Let's write this into kalgebra console:
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| ((((1*2)*3)*4)*5)*6
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| =720
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| This kind of arragenment of things around some position, where position
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| number is equal of number of things is called "permutation"
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| Let's try to call in kalgebra the permutation function:
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| factorial(6)
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| =720
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| It's the same result as you can see.
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| === Probability example ===
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| Let's roll a dice, we want to know the probability of one face
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| We can define positive probability the favourble result of the event to us
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| and negative probability the unfavorable result of the event to us
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| So you have to pick only one face:
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| probability = 1(face picked)/6(total face)
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| So now we know that when a dice is rolled there is a 1/6 of probability that
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| a face we choice come up
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| We can set a simple function in kalgebra to take this formula in a simple
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| way:
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| probability:=(favorable,total)->favorable/total
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| === Numerical Theory ===
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| Let's say that we want to know the sum of all numbers between a bounded
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| interval for istance 1 - 100
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| we have to do the sum of all numbers from 0 to 100 if we don't know the
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| rule to get them
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| kalgebra offers a great facility to this task. Let's write in console:
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| sum(x: x=1.100)
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| and we get the result
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| The syntax indicate this:
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| 1- Bound x as variable
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| 2- Take first value of x
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| 3- Take second value of x and add the previus value of x
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| 4- Take third value of x and add the previus value of x
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| ....
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| N- Take the last value of x and add the last value of x
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| === Eletronic ===
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| Example1:
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| Let's take a simple circuit a and port with two input and one output
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| To resolve it on kalgebra we will write
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| and(variable1, variable2)
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| we will get the and value of the input as output
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| Example2:
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| We have a simple circuit: a battery of 3V and two eletrical resistence
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| (R1 and R2) put on parallel of 3kohm. We want to get the current
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| circulating in the circuit.
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| We have first to calculate the value of the eletric resistence expressed
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| as the law:
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| TotalResistence = (1/R1 + 1/R2)^-1
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| Current = Voltage/TotalResistence
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| Let's write a simple function in kalgebra to do this:
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| totalresistence:=(R1,R2)->(1/R1+1/R2)^-1
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| current:=(voltage,totalresistence)->voltage/totalresistence
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| let's see what we get:
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| current(3, totalresistence(3, 3))
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| =2
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