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FindInstance

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

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

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

FilledSmallSquare FindInstance[expr, , , ... ] gives results in the same form as Solve: -> , -> , ... if an instance exists, and {} if it does not.

FilledSmallSquare expr can contain equations, inequalities, domain specifications and quantifiers, in the same form as in Reduce.

FilledSmallSquare With exact symbolic input, FindInstance gives exact results.

FilledSmallSquare Even if two inputs define the same mathematical set, FindInstance may still pick different instances to return.

FilledSmallSquare The instances returned by FindInstance typically correspond to special or interesting points in the set.

FilledSmallSquare FindInstance[expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex.

FilledSmallSquare FindInstance[expr, vars, Integers] finds solutions to Diophantine equations.

FilledSmallSquare FindInstance[expr, vars, Booleans] solves Boolean satisfiability for expr.

FilledSmallSquare 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.

FilledSmallSquare FindInstance may be able to find instances even if Reduce cannot give a complete reduction.

FilledSmallSquare Every time you run FindInstance with a given input, it will return the same output.

FilledSmallSquare Different settings for the option RandomSeed -> n may yield different collections of instances.

FilledSmallSquare See Section 3.4.8 and Section 3.4.9.

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

FilledSmallSquare New in Version 5.0.

Further Examples