# A question on parametrically solving systems of equalities and inequalities

Posted 4 months ago
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 Dear Members of the community, I am experimenting with Solve[] for the solutions of systems of equalities and inequalities containing parameters. For example Solve[10 x1 + 3 L1 - L2 - L3 == 0 && L1 (3 x1 - y1 - y2) == 0 && L2 (-x1 + 1/10 y2 + 0.25 y3) == 0 && L3 (0.2 - x1) == 0 && 3 x1 - y1 - y2 <= 0 && -x1 + 0.1 y2 + 0.25 y3 <= 0 && 0.2 - x1 <= 0 && L1 >= 0 && L2 >= 0 && L3 >= 0, {x1, L1, L2, L3}, Reals] My variables are { x1,L1,L2,L3} and I am including the parameters {y1,y2,y3}. Mathematica seems to handle this rather complicated solution but also displays the following message:Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.Could someone help me to interpret this?Is there information concerning the number of parameters I could include in the set of equations? In this case, the functionality given by Solve[] seems very powerful, but not many examples can be found that consider parametric solutions. I will appreciate any help. CheersJesus
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Posted 4 months ago
 Jesus,The message is only a warning. You have numbers that are floats in your expression (for example, 0.1 and 0.25). The message will go away if you make these numbers fractions like 1/4 or give them exact precision such as 0.25` (prime symbol to designate precision). Mathematica does this for you, solves the expression and converts the answer back to floats. The warning is there because it is possible for small errors to crop in if you use floating point numbers.Regards,Neil