Hi, 

I need to know which softwares/authors to cite in writing my manuscript. I 
use the sage function to solve multi-variable systems of nonlinear 
inequalities. For example, if I have 12 variables defined in set 'vars' and 
8 inequality constraints, I simply use the following command to know if 
there is or is not a solution to this problem: 

solve(['k_31 > g_3 *t_32','k_21 + k_22 < g_2 *t_21','k_11 > g_1 
*t_11','k_11 < g_1 *t_12','k_31 > g_3 *t_32','k_31 < g_3 *t_33','k_21 + 
k_22 > 0','k_21 + k_22 < g_2 *t_21'],vars)

My questions are: 

1) What is the mathematical method used to solve this set of inequalities? 
Is it linear/nonlinear programming? Or something more advanced like QEPCAD? 
Where can I find more information on these methods?
2) What is the main program for symbolic computation? Is it MAXIMA?

Thanks, 

-Diana 

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