FindInstance

FindInstance[expr, vars]
finds an instance of vars that makes the statement expr be True.

FindInstance[expr, vars, dom]
finds an instance over the domain dom. Common choices of dom are Complexes, Reals, Integers, and Booleans.

FindInstance[expr, vars, dom, n]
finds n instances.

Details and OptionsDetails and Options

  • FindInstance[expr, {x1, x2, ...}] gives results in the same form as Solve: if an instance exists, and if it does not.
  • expr can contain equations, inequalities, domain specifications and quantifiers, in the same form as in Reduce.
  • With exact symbolic input, FindInstance gives exact results.
  • Even if two inputs define the same mathematical set, FindInstance may still pick different instances to return.
  • The instances returned by FindInstance typically correspond to special or interesting points in the set.
  • FindInstance[expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex.
  • FindInstance[expr, vars, Integers] finds solutions to Diophantine equations.
  • FindInstance[expr, vars, Booleans] solves Boolean satisfiability for expr.
  • FindInstance[expr, vars, Reals] assumes that not only vars but also all function values in expr are real. FindInstance[expr&&varsReals, vars] assumes only that the vars are real.
  • FindInstance may be able to find instances even if Reduce cannot give a complete reduction.
  • Every time you run FindInstance with a given input, it will return the same output.
  • Different settings for the option RandomSeed->s may yield different collections of instances.
  • FindInstance[expr, vars, dom, n] will return a shorter list if the total number of instances is less than n.

ExamplesExamplesopen allclose all

Basic Examples (5)Basic Examples (5)

Find a solution instance of a system of equations:

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Find a real solution instance of a system of equations and inequalities:

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Find an integer solution instance:

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Find Boolean values of variables that satisfy a formula:

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Find several instances:

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