Reduce
 Usage
Notes
 Further Examples
Here x needs to be real. Because x appears in an inequality, it will be assumed to be real. There is no restriction on y.
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Here x, y, and  need to be real.
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This allows complex values of x as long as both sides of the inequality are real and the inequality is true.
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Since y appears after x in the variable list, Reduce may use x to express the solution for y.
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When  , Reduce replaces x in the solution for y with its  possible values.
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Reduce may use new parameters to express a solution.
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When  , the new parameters introduced by Reduce are  .
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The options Cubics and Quartics tell Reduce whether it should use radicals to solve cubic and quartic equations. The default setting is False.
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Reduce eliminates quantifiers from quantified polynomial systems. Here we compute conditions for a quartic to have all roots equal.
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Here we find the vertical asymptotes of  directly using the definition of limit.
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This solves a system of equations over the integers modulo  .
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Reduce can solve some systems involving compositions of polynomials and simple transcendental functions.
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Here Reduce uses a composition of transcendental and Diophantine solvers.
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Reduce looks for parameters at the algebraic level, so Log[a] and Log[2 a] in this equation are treated as independent parameters.
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If we tell Reduce that a is a variable it will know that Log[a] and Log[2 a] are dependent.
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