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ExpandNumerator
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ExpandNumerator

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expands out products and powers that appear in the numerator of expr.

Details and Options

  • ExpandNumerator works on terms that have positive integer exponents.
  • ExpandNumerator applies only to the top level in expr.
  • ExpandNumerator automatically threads over lists, as well as equations, inequalities, and logic functions.

Examples

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Basic Examples  (2)Summary of the most common use cases

Expand the numerator of a fraction:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-zcun
Out[1]=1

Expand a numerator involving multiple variables:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-5q2vie
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

Expand the numerator of a rational function:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-lfx4a
Out[1]=1

ExpandNumerator threads over sums:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-cukby
Out[1]=1

ExpandNumerator threads over Boolean combinations of equations and inequalities:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-g61ofw
Out[1]=1

ExpandNumerator does not separate the fraction; Expand does:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-glq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8c90ddq2-wif
Out[2]=2

Expand numerator of a fraction involving arbitrary functions:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-qrjodg
Out[1]=1

Expand the numerator using expansion formulas for trigonometric functions:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-xbw69m
Out[1]=1

Expand the numerator over the integers modulo :

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-jet5lj
Out[1]=1

Options  (2)Common values & functionality for each option

Modulus  (1)

Expand the numerator over the integers modulo 3:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-c6u1su
Out[1]=1

Trig  (1)

Expand the numerator using expansion formulas for trigonometric functions:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-sv8zu
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

ExpandNumerator can be used to verify that two expressions are equal:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-l491wt
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8c90ddq2-7o4nyj
Out[2]=2

Properties & Relations  (5)Properties of the function, and connections to other functions

ExpandNumerator leaves the denominator unexpanded:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-fs3xqa
Out[1]=1

ExpandDenominator expands the denominator, leaving the numerator unexpanded:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-ysarr
Out[1]=1

Expand expands the numerator and expands the fraction into a sum of fractions:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-i55yj4
Out[1]=1

ExpandAll expands the numerator, the denominator, and the fraction:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-tzh2s
Out[1]=1

Use Factor, Numerator, and Denominator to factor the numerator back:

In[1]:=1
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https://wolfram.com/xid/0b8c90ddq2-u5qrd
Out[1]=1
Wolfram Research (1988), ExpandNumerator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandNumerator.html (updated 2007).
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Wolfram Research (1988), ExpandNumerator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandNumerator.html (updated 2007).

Text

Wolfram Research (1988), ExpandNumerator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandNumerator.html (updated 2007).

✖
Wolfram Research (1988), ExpandNumerator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandNumerator.html (updated 2007).

CMS

Wolfram Language. 1988. "ExpandNumerator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ExpandNumerator.html.

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Wolfram Language. 1988. "ExpandNumerator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ExpandNumerator.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_expandnumerator, author="Wolfram Research", title="{ExpandNumerator}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpandNumerator.html}", note=[Accessed: 28-April-2025 ]}

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@misc{reference.wolfram_2025_expandnumerator, author="Wolfram Research", title="{ExpandNumerator}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpandNumerator.html}", note=[Accessed: 28-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_expandnumerator, organization={Wolfram Research}, title={ExpandNumerator}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpandNumerator.html}, note=[Accessed: 28-April-2025 ]}

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@online{reference.wolfram_2025_expandnumerator, organization={Wolfram Research}, title={ExpandNumerator}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpandNumerator.html}, note=[Accessed: 28-April-2025 ]}