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Together
Together[
expr
] puts terms in a sum over a common denominator, and cancels factors in the result.
Example: Together[1/x + 1/(1-x)] .
Together makes a sum of terms into a single rational function.
The denominator of the result of Together is typically the lowest common multiple of the denominators of each of the terms in the sum.
Together avoids expanding out denominators unless it is necessary.
Together is effectively the inverse of Apart.
Together[
expr
,
Modulus->
p
] generates a result modulo p.
Together[
expr
,
Extension->Automatic] allows operations to be performed on algebraic numbers in expr.
Together[
expr
,
Trig
->
True] treats trigonometric functions as rational functions of exponentials, and manipulates them accordingly.
See the Mathematica book: Section 1.4.5, Section 3.3.3.
See also: Cancel, Collect, Factor, PolynomialGCD.
Further Examples
Here is a simple example.
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Here is another simple example.
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Together explicitly makes it clear that this expression is indeterminate.
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1
Power::infy: Infinite expression - encountered.
0
Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered.
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Together simplifies this nasty expression.
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No cancellation is done here.
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You can cancel out a common factor by setting Extension
->
Automatic.
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Here are two modular examples.
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The setting Trig
->
True here gives a better result.
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Here is a more dramatic difference.
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We want to show that this expression is zero, verifying an identity of Dedekind.
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We want to show that this expression is zero, verifying an identity of Dedekind.
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Seeing that the result is in terms of algebraic numbers leads us to set the Extension option to Automatic.
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