Introductory examples:
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| (7) |
| (8) |
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Nested and mixed radicals / RootOfs are handled as well:
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| (11) |
| (12) |
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| (15) |
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Algebraic functions in the coefficients are not accepted:
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Floats are not accepted:
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Leading coefficients and denominators are not rationalized:
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An attempt is made to simplify the expression by freezing algebraic numbers and canceling the greatest common divisor of the numerator and denominator of the result. To fully simplify the output, use Normal instead:
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Non-algebraic subexpressions are first handled recursively (unless option 'recursive'=false is present) and then temporarily replaced by new variables:
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Non-algebraic subexpressions may evaluate to something algebraic after recursive treatment:
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Partial factorizations in the inputs are preserved, unless option 'expanded'=true is given:
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If there is a zero divisor in the denominator, it will be reduced, if possible:
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In this example, there is a RootOf whose leading coefficient is not invertible, so it is not possible to reduce a positive power of of it. This is because there is no way for Reduce to know whether without an index represents or :
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| (30) |
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However, if option 'symbolic'=true, then it chooses one possibility. Here, option 'symbolic'=true picks , so the leading coefficient of the outer RootOf no longer contains a zero divisor, and its power can be reduced:
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Using option characteristic, powers can be reduced over finite fields:
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The polynomial defining a RootOf will also be reduced modulo the characteristic:
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Reductions can sometimes, but not always, be computed in composite characteristic:
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With option 'makeindependent'=true, the input will be checked for algebraic dependencies even if there are more than algebraic objects in the input:
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| (37) |
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| (38) |
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| (39) |
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| (40) |
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| (41) |
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| (42) |
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| (43) |
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With option 'makeindependent'=false, the input will never be checked for algebraic dependencies:
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| (45) |