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Find conditions such that symbolic expression is real-valued

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Richard Downey
Richard Downey 2012-6-11
I have a set of symbolic expressions of several variables, and I want Matlab to find the conditions on the variables such that the expressions meet certain criteria, such as being real-valued or one expression being less than another. For example,
syms a b c x;
x = solve(a*x^2 + b*x + c == 0,x)
returns the familiar quadratic formula as a vector:
x =
-(b + (b^2 - 4*a*c)^(1/2))/(2*a)
-(b - (b^2 - 4*a*c)^(1/2))/(2*a)
For these two solutions for x, I'd like to know: (a) the conditions on a, b, and c such that x is real-valued (obviously b^2 > 4*a*c for this example); (b) the conditions on a, b, and c such that x(1) > x(2).
If it helps, I know that all my symbolic variables (a, b, and c in the example) are positive-valued. Also, I'm only interested in positive values of x.
Thanks, Rich
  1 个评论
Walter Roberson
Walter Roberson 2012-6-12
For the quadratic, x(2) >= x(1) provided that both are real-valued. (If they have imaginary components then comparing them is not well defined.)

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Stefan Wehmeier
Stefan Wehmeier 2012-6-26
a)
feval(symengine, 'solve', a*x^2 + b*x + c, x, 'Real', 'IgnoreSpecialCases')
You may omit the IgnoreSpecialCases, which shows you that a<>0 must also be satisfied (obviously).
b) It is better to solve for only one variable:
feval(symengine, 'solve', x(1) > x(2), a, 'Real')
You haven't declared your syms to be real, but the real mode in the solver treats them as reals which I think is what you want.

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