st: Mata calls on Stata variables and macros

[Brad Jeffrey Hershbein <bjhersh@umich.edu>]

Dear Statalisters,

I would like to solve a (cubic) polynomial equation where one of the  
coefficients of the polynomial is a variable in my dataset and the  
other coefficients are stored as scalars. That is, I want to solve for  
the roots of Ax^3 + Bx^2 + Cx + D = 0, where D is the variable Z in my  
dataset, and A, B, and C are stored in the scalars a1, b1, and c1,  
respectively. The values of A, B, C, and D are such that there is only  
one positive, real root in all cases, and I would like that root to be  
a new variable in the dataset.

I know the Mata routine polyroots can find the roots of a polynomial,  
but I cannot figure out how to simultaneously pass the scalars and Z  
for polyroots to take as arguments, and how to return the positive  
real root as a new variable to Stata.

Thank you for your consideration.

Brad Hershbein
University of Michigan
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