Together

Together[expr]

puts terms in a sum over a common denominator, and cancels factors in the result.

Details and Options

  • 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.
  • Together automatically threads over lists, as well as equations, inequalities and logic functions.

Examples

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Basic Examples  (2)

Combine terms over a common denominator:

Cancel common factors between the numerator and the denominator:

Scope  (8)

Combine a sum of any number of terms:

Here all factors of the denominator divide the numerator:

Together threads over lists:

Together threads over equations and inequalities:

Compute over the algebraic extension generated by the coefficients:

Compute over the integers modulo :

Compute over a finite field:

Use trigonometric identities:

Options  (6)

Extension  (2)

By default, Together treats algebraic numbers as independent variables:

With Extension->Automatic, Together recognizes algebraically dependent coefficients:

Modulus  (2)

Computations over rational numbers:

The same computations over integers modulo 2:

Trig  (2)

By default, Together treats trigonometric functions as independent variables:

With Trig->True, Together recognizes dependencies between trigonometric functions:

Applications  (1)

Test whether a function is a rational function:

Properties & Relations  (3)

Apart acts as a partial inverse of Together:

Together combines terms over a common denominator and cancels common factors:

Cancel only cancels common factors between numerators and denominators:

Use Numerator and Denominator to extract numerators and denominators:

Wolfram Research (1988), Together, Wolfram Language function, https://reference.wolfram.com/language/ref/Together.html (updated 2023).

Text

Wolfram Research (1988), Together, Wolfram Language function, https://reference.wolfram.com/language/ref/Together.html (updated 2023).

CMS

Wolfram Language. 1988. "Together." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/Together.html.

APA

Wolfram Language. (1988). Together. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Together.html

BibTeX

@misc{reference.wolfram_2024_together, author="Wolfram Research", title="{Together}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Together.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_together, organization={Wolfram Research}, title={Together}, year={2023}, url={https://reference.wolfram.com/language/ref/Together.html}, note=[Accessed: 22-December-2024 ]}