AutoHotkey Community

[k3ph]

[ description ]
This script returns the maximum multipliers incognitas and supports N numbers of variables.
Examples: a * x = s1 ... a * x + b * y = s2 ... a * x + b * y + c * z = s3 ... N number of sum of multipliers.
It's known that big Z values makes the perfomance decrease but the main objective is to show a PoC of the transforming of a Finite State Automata through REgex

[ explanation ]
Transforming FSA into RE- by Model Engineering College

The idea behind the construction is the following: (assuming states are enumerated) we will give an algorithm by which we can calculate a regular expression Ti,j(k) which describes all the strings which can take us from state i in the FSA to state j via states 1, 2, ... k. The language described by an FSA with n states, and where the start state is named 1 is then the union of all strings which take us from state 1 to a final state f through any of the states: the sum of all regular expressions T1,f(n) where f ranges over the final states.

The algorithm to calculate Ti,j(k) is stated inductively over variable k:
Base case: k=0 . We subdivide this into two cases, when i is the same as j and when they are not:

· Ti,i(0) =1+a+...+z where a to z are the labels on transition arcs going from state i to itself. Note that if no such arcs exist, the expression becomes simply 1.

· Ti,j(0) =a+...+z where a to z are the labels on transition arcs going from state i to state j (which are not equal). Note that if no such arcs exist, the expression becomes simply 0.

Inductive case: When the third parameter (k) is larger than 0, we use the following equation to calculate the desired result:

Ti,j(k+1) = Ti,j(k) + Ti,k+1(k)(Tk+1,k+1(k))*Tk+1,j(k)

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[ examples ]

example 1:

[Laszlo]

Interesting idea. I would explicitly write * for multiplication (or at least a mandatory space, because Ax, By, or even 7x are valid AHK variable names, and there seem to be no reason to restrict the system of equations to handle only single letters for the parameters.

For larger systems of equations one can consider writing the coefficients in an array, without the variable names. These array can be conveniently initialized with StringSplit.

[k3ph]

Thanks for the reply, I appreciate it. As guessed, I plan to design a finite-dimensional linear solver with it, and an array-like notation would be very useful for it, thanks again for sharing your ideas.

I had so much fun thinking in the possibilities with this PoC. If you do have more, please share with me. I hope more people join it ;) yay.
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[Jex]

You don't like math homework.

Are you planning to add curves?
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Woot.

Please read forum etiquette

[k3ph]

(lol)

Maybe some graphical functions will be added. But actually I can't see how to get better than Laszlo's Popup Calculator and I'm a little bit concerned about speed perfomance. Testing this version out with a Z with 5 digits length took me some long seconds to calculate the answers.

Does someone have any ideas of accelerate it? I guess I should look for a way to replace the loop...

Also I've take a look into [VxE]'s Laplace Expansion to find Matrix Determinant and I'm plan to communicate with it.
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[Laszlo]

[k3ph]

I've updated this script to support N number of sums and put an little explanation of it. Enjoy!
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