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.

FindInstance[expr, , , ... ] 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 && vars Reals, 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 -> n may yield different collections of instances.

See Section 3.4.8 and Section 3.4.9.

See also: Solve, Reduce, FindRoot, Minimize, Random.

New in Version 5.0.

Further Examples