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LexicographicOrder
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LexicographicOrder

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LexicographicOrder[{a1,a2,…},{b1,b2,…}]

gives Order[ai,bi] for the first non-coinciding pair ai,bi of elements, and 0 if the lists are identical.

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LexicographicOrder[{a1,a2,…},{b1,b2,…},p]

uses the ordering function p to compare ai with bi.

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represents an operator form that compares lists when applied to {a1,a2,…}, {b1,b2,…}.

Details

Examples

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Basic Examples  (1)Summary of the most common use cases

Find whether two lists are ordered lexicographically:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-durabl
Out[1]=1

Shorter lists are ordered first in canonical order:

In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-q26xzf
Out[2]=2

Scope  (6)Survey of the scope of standard use cases

Use an ordering function to order elements of the expressions:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-4pgeqz
Out[1]=1

Canonical order places 0 before -Infinity:

In[2]:=2
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-rorenr
Out[2]=2

Heads other than List can be used:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-s10te4
Out[1]=1

Use LexicographicOrder with two strings:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-4zwqta
Out[1]=1

The computation is equivalent to:

In[2]:=2
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-j3y57i
Out[2]=2

Order associations lexicographically by their values:

In[1]:=1
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-5jsjq1
Out[1]=1

Use LexicographicOrder in Ordering to find the position of the last expression in lexical order:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-12ud4
Out[1]=1

Check whether several lists are sorted lexicographically:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-p8dydf
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Sort subsets lexicographically:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-9cnifv
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-09x1qp
Out[2]=2

Compare two monomials lexicographically:

In[1]:=1
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-t600x8
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-7utndq
Out[2]=2

The first monomial is ordered first:

In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-2by8zx
Out[3]=3

Properties & Relations  (9)Properties of the function, and connections to other functions

Order is determined by the first element that differs, regardless of total length:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-htexle
Out[1]=1

LexicographicOrder returns 0 when the lists have the same elements:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-fkd8qf
Out[1]=1

When all elements coincide up to the shortest length, the shorter list is ordered first:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-syl24g
Out[1]=1

The empty list is sorted before any other list:

In[1]:=1
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-oxvuss
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-1pl2gk
Out[2]=2

LexicographicSort[list] is equivalent to Sort[list,LexicographicOrder]:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-gk3m9j
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-5ngtdw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-haxngg
Out[3]=3

Compare with canonical order:

In[4]:=4
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-2xccfr
Out[4]=4

For lists of the same length, LexicographicOrder is equivalent to Order:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-2il30x
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-zeaquz
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-533grv
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-zuvo9h
Out[4]=4

LexicographicOrder with strings of letters is equivalent to AlphabeticOrder with default options:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-v4wd85
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-lfbimv
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-l5f5po
Out[3]=3

AlphabeticOrder and Order are not lexicographic when the strings contain letters and numbers:

In[4]:=4
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-ky90hb
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-jibe02
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-sjh3ce
Out[6]=6

Compare with the ordering of the first characters:

In[7]:=7
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-5y4btw
Out[7]=7

For numeric vectors of equal length, LexicographicOrder[NumericalOrder] is equivalent to NumericalOrder:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-gvasjk
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-kfsv2k
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-cjk3bk
Out[3]=3

VectorLess and related functions are similar to LexicographicOrder[NumericalOrder]:

In[1]:=1
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-httl5m
In[2]:=2
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-dys4wd
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-zv54tz
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0nx3iwmxgpx2rbgy6-dcs606
Out[4]=4
Wolfram Research (2021), LexicographicOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/LexicographicOrder.html.
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Wolfram Research (2021), LexicographicOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/LexicographicOrder.html.

Text

Wolfram Research (2021), LexicographicOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/LexicographicOrder.html.

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Wolfram Research (2021), LexicographicOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/LexicographicOrder.html.

CMS

Wolfram Language. 2021. "LexicographicOrder." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LexicographicOrder.html.

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Wolfram Language. 2021. "LexicographicOrder." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LexicographicOrder.html.

APA

Wolfram Language. (2021). LexicographicOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LexicographicOrder.html

✖
Wolfram Language. (2021). LexicographicOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LexicographicOrder.html

BibTeX

@misc{reference.wolfram_2025_lexicographicorder, author="Wolfram Research", title="{LexicographicOrder}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/LexicographicOrder.html}", note=[Accessed: 18-May-2025 ]}

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@misc{reference.wolfram_2025_lexicographicorder, author="Wolfram Research", title="{LexicographicOrder}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/LexicographicOrder.html}", note=[Accessed: 18-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_lexicographicorder, organization={Wolfram Research}, title={LexicographicOrder}, year={2021}, url={https://reference.wolfram.com/language/ref/LexicographicOrder.html}, note=[Accessed: 18-May-2025 ]}

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@online{reference.wolfram_2025_lexicographicorder, organization={Wolfram Research}, title={LexicographicOrder}, year={2021}, url={https://reference.wolfram.com/language/ref/LexicographicOrder.html}, note=[Accessed: 18-May-2025 ]}