cubic polynomial with variables
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Hello everyone,
This is probably a fairly easy question to answer.
I am trying to solve a 3rd degree polynomial with 4 variables, a b c d, each functions of k1, k2, Tr, Tf (or some of those).
Is it possible to obtain the roots of the polynomial in terms of k1, k2, Tf, Tr?
Thanks for your help,
Mark
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Walter Roberson
2012년 7월 4일
syms x k1 k2 Tr Tf
a = SomeFunction(k1,k2,Tr,Tf);
b = SomeOtherFunction(k1,k2,Tr,Tf);
c = AThirdFunction(k1,k2,Tr,Tf);
d = FourthFunction(k1,k2,Tr,Tf);
CubeRoots = solve( a*x^3 + b*x^2 + c*x + d, x);
You might also want to simplify() each of the roots.
I will caution you that the results you get out are likely to be messy to read: the generalized solution for a cubic is not fun to make mental sense of. (Quadratic can be a lot worse though!)
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mark wentink
2012년 7월 4일
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Walter Roberson
2012년 7월 5일
Only about 10 lines? Then MuPAD has already done quite a good job of simplifying: the result that I find is over 4000 characters, about 30 lines each over 128 characters long.
Symbolic forms of cube roots are long, period. There isn't much in the way of simplification available. There is common sub-expression optimization, which gives you efficiencies but often isn't much more readable.
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