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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Equation Solving  /
Reduce

  • Reduce[ eqns , vars ] simplifies the equations eqns, attempting to solve for the variables vars. The equations generated by Reduce are equivalent to eqns, and contain all the possible solutions.
  • Reduce[ eqns , vars , elims ] simplifies the equations, trying to eliminate the variables elims.
  • The equations given to Reduce are in the form lhs == rhs. Simultaneous equations can either be given in a list, or combined with &&.
  • Example: Reduce[a x + b == 0, x].
  • Reduce generates equations (==) and nonequalities (!=), combined with && and ||.
  • Reduce primarily deals with polynomial equations.
  • See the Mathematica book: Section 1.5.7Section 3.4.6.
  • See also: Solve, Eliminate, LogicalExpand, ToRules.

    Further Examples

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    This is an example of the three-argument form. We eliminate y and z, and attempt to solve for r and b; conditions are imposed on the remaining parameters.

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    In the previous example the denominators were removed by cross multiplication. The presence of denominators makes this a harder problem.

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