# FindRoot over a function with some constant variables

I would like to perform the FindRoot command over the function func. Suppose:

func = Function[{x,y,z},{x+y+z,3x-y-0.5z}]


I would like to solve func==0 over the variables y, z over a grid of inputs x. Since my actual func is more complicated, I have to resort to using FindRoot rather than Solve.

One way to do this is to execute:

FindRoot[func[x0,y,z], {{y, y0}, {z, z0}}]


where x0 is a numeric input.

However, since my actual y, z consist of a large (and non-constant) number of variables, I wish to execute the following command:

FindRoot[func[x0, variables], {startingvariables}]


This however does not seem to work as either,

• all variables have to be specified manually, or
• the function has to be redefined

Is there a way out?

• Please provide a working example, as FindRoot[func[x0,y,z],{{y,y0},{z,z0}] cannot work (you have one equation func[x0,y,z] == 0, but two unknowns, y and z). – LLlAMnYP Mar 17 '15 at 13:58
• sorry for that! The system has 3 variables and 2 equations. I set one variable as fixed, so that remain 2 eqs + 2 unknowns – Breugem Mar 17 '15 at 14:46

As pointed out in the comments by @LLIAMnYP, FindRoot cannot solve one equation for two unknowns.

You may be able to use FindInstance

func = Plus;

n = 4; (* number of variables *)

var = Array[x, n];

x[1] = 5; (* fixed variable *)

ns = 4; (* number of solutions *)


For Integers

solnI = FindInstance[
func @@ var == 0, Rest[var], Integers, ns]


{{x[2] -> -168, x[3] -> 39, x[4] -> 124}, {x[2] -> 66, x[3] -> -17,
x[4] -> -54}, {x[2] -> 134, x[3] -> -43, x[4] -> -96}, {x[2] -> 199,
x[3] -> -43, x[4] -> -161}}

Domain can be changed to Reals or Complexes (default). Inequalities can be used to constrain the domain.