100 Equations, 101 Variables, Systems of Equations Shortcuts?

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Matthew 2011-4-27

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I have 100 equations and 101 variables. I'm trying to find all variables as a function of one variable i.e. x = f(t); y = g(t); ......, etc. I already have all the equations on a text file in linear form (i.e. y = x + 3t, etc). I was wondering how I would be able to solve it using one of these two ways: 1) I can make a matrix of coefficents and solve it using one of Matlab's functions. However, a 100x100 matrix means I would have to input 1,000 cells. The possibility of human error is quite high. Is there any function that allows me to translate my already made equations into a matrix of coefficents? 2) About 80 of the equations are 3 variable equations (i.e. x = 10y - 6z), isn't there anything in the symbolic toolbox that allows me to simply start solving them as a function of t without having to go through annoying matrix methods?

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Answer 1

Walter Roberson 2011-4-27

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You can use sym2poly to extract expressions.

To solve as functions of t, use subs() to convert your plain x and y and so on in to x(t), y(t) and so on. Then use solve() or dsolve()

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Matthew 2011-4-27

While the sym2poly definitely can speed up the process, Matlab says that it can't have more than one input variable. Therefore, to use it I would have to rearrange all 100 equations so they only have 1 input variable. That's harder than just manually inputting all 10,000 coefficents.

The subs function seems promising, but its a bit more intensive. I'll comment when I figure out how to implement it best.

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