Previous: Minimization, Up: Numerical Solutions

10.7.3 Systems of Equations

The a R command can also solve systems of equations. In this case, the equation should instead be a vector of equations, the guess should instead be a vector of numbers (intervals are not supported), and the variable should be a vector of variables. You can omit the brackets while entering the list of variables. Each equation must be differentiable by each variable for this mode to work. The result will be a vector of two vectors: The variable values that solved the system of equations, and the differences between the sides of the equations with those variable values. There must be the same number of equations as variables. Since only plain numbers are allowed as guesses, the Hyperbolic flag has no effect when solving a system of equations.

It is also possible to minimize over many variables with a N (or maximize with a X). Once again the variable name should be replaced by a vector of variables, and the initial guess should be an equal-sized vector of initial guesses. But, unlike the case of multidimensional a R, the formula being minimized should still be a single formula, not a vector. Beware that multidimensional minimization is currently very slow.