Further Examples: Reduce

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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