Damm algorithm - Revision history

Randomdude121: Reverted edits by 2603:8001:4500:1199:D4A5:3404:C186:3731 (talk) (AV)

2025-06-08T01:47:42Z

Reverted edits by 2603:8001:4500:1199:D4A5:3404:C186:3731 (talk) (AV)

← Previous revision		Revision as of 01:47, 8 June 2025
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	is needed. Such a quasigroup can be constructed from any totally anti-symmetric quasigroup by rearranging the columns in such a way that all zeros lay on the diagonal. And, on the other hand, from any weak totally anti-symmetric quasigroup a totally anti-symmetric quasigroup can be constructed by rearranging the columns in such a way that the first row is in natural order.<ref name="dhmd" />		is needed. Such a quasigroup can be constructed from any totally anti-symmetric quasigroup by rearranging the columns in such a way that all zeros lay on the diagonal. And, on the other hand, from any weak totally anti-symmetric quasigroup a totally anti-symmetric quasigroup can be constructed by rearranging the columns in such a way that the first row is in natural order.<ref name="dhmd" />

	== ~~Damm~~ Algorithm ==		== Algorithm ==
	The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111).<ref name="dhmd" /> It is useful if each main diagonal entry is {{math\|0}},<ref name=fenwick2014 /> because it simplifies the check digit calculation.		The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111).<ref name="dhmd" /> It is useful if each main diagonal entry is {{math\|0}},<ref name=fenwick2014 /> because it simplifies the check digit calculation.

2603:8001:4500:1199:D4A5:3404:C186:3731: /* Algorithm */

2025-06-08T01:44:10Z

Algorithm

← Previous revision		Revision as of 01:44, 8 June 2025
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	is needed. Such a quasigroup can be constructed from any totally anti-symmetric quasigroup by rearranging the columns in such a way that all zeros lay on the diagonal. And, on the other hand, from any weak totally anti-symmetric quasigroup a totally anti-symmetric quasigroup can be constructed by rearranging the columns in such a way that the first row is in natural order.<ref name="dhmd" />		is needed. Such a quasigroup can be constructed from any totally anti-symmetric quasigroup by rearranging the columns in such a way that all zeros lay on the diagonal. And, on the other hand, from any weak totally anti-symmetric quasigroup a totally anti-symmetric quasigroup can be constructed by rearranging the columns in such a way that the first row is in natural order.<ref name="dhmd" />

	== Algorithm ==		== Damm Algorithm ==
	The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111).<ref name="dhmd" /> It is useful if each main diagonal entry is {{math\|0}},<ref name=fenwick2014 /> because it simplifies the check digit calculation.		The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111).<ref name="dhmd" /> It is useful if each main diagonal entry is {{math\|0}},<ref name=fenwick2014 /> because it simplifies the check digit calculation.

CanonNi: /* Validating a number against the included check digit */ rm extra col

2024-12-02T10:35:45Z

Validating a number against the included check digit: rm extra col

← Previous revision		Revision as of 10:35, 2 December 2024
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	\|style="width:1.5em"\| 7		\|style="width:1.5em"\| 7
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	\|style="width:1.5em"\| 4		\|style="width:1.5em"\| 4
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	\| 7		\| 7
	\| 4		\| 4
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	\| '''0'''		\| '''0'''
	\|}		\|}

CanonNi: Removed {{Dark mode problems}} tag: fixed; feel free to revert if there are more

2024-12-02T10:35:21Z

Removed {{Dark mode problems}} tag: fixed; feel free to revert if there are more

← Previous revision		Revision as of 10:35, 2 December 2024
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	{{Dark mode problems}}
	{{Short description\|Check digit algorithm}}		{{Short description\|Check digit algorithm}}
	In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''		In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''

CanonNi: /* Example */ fix for dark mode

2024-12-02T10:35:13Z

Example: fix for dark mode

← Previous revision		Revision as of 10:35, 2 December 2024
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	== Example ==		== Example ==
	The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math\|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math\|1=''φ'' = (1 2 9 5 4 8 6 7 3)}} and defining {{math\|1=''x'' ⋅ ''y'' = ''φ''<sup>−1</sup>(''φ''(''x'') ∗ ''y'')}}.		The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math\|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math\|1=''φ'' = (1 2 9 5 4 8 6 7 3)}} and defining {{math\|1=''x'' ⋅ ''y'' = ''φ''<sup>−1</sup>(''φ''(''x'') ∗ ''y'')}}.
	{\| class="wikitable" style="text-align:center;color:#E000E0"		{\| class="skin-invert wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	\|style="width:1.5em"\| {{math\|1=⋅}}		\|style="width:1.5em"\| {{math\|1=⋅}}
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	=== Calculating the check digit ===		=== Calculating the check digit ===
	{\| class="wikitable" style="text-align:center;color:#E000E0"		{\| class="skin-invert wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index		!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index
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	=== Validating a number against the included check digit ===		=== Validating a number against the included check digit ===
	{\| class="wikitable" style="text-align:center;color:#E000E0"		{\| class="skin-invert wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index		!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index

Daniel Quinlan: tag with {{Dark mode problems}}

2024-10-23T00:51:14Z

tag with {{Dark mode problems}}

← Previous revision		Revision as of 00:51, 23 October 2024
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			{{Dark mode problems}}
	{{Short description\|Check digit algorithm}}		{{Short description\|Check digit algorithm}}
	In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''		In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''

Daniel Quinlan: remove background styling that frequently causes unreadable text in dark mode (via WP:JWB)

2024-10-23T00:50:21Z

remove background styling that frequently causes unreadable text in dark mode (via WP:JWB)

← Previous revision		Revision as of 00:50, 23 October 2024
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	== Example ==		== Example ==
	The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math\|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math\|1=''φ'' = (1 2 9 5 4 8 6 7 3)}} and defining {{math\|1=''x'' ⋅ ''y'' = ''φ''<sup>−1</sup>(''φ''(''x'') ∗ ''y'')}}.		The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math\|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math\|1=''φ'' = (1 2 9 5 4 8 6 7 3)}} and defining {{math\|1=''x'' ⋅ ''y'' = ''φ''<sup>−1</sup>(''φ''(''x'') ∗ ''y'')}}.
	{\| class="wikitable" style="text-align:center~~;background:none~~;color:#E000E0"		{\| class="wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	\|style="width:1.5em"\| {{math\|1=⋅}}		\|style="width:1.5em"\| {{math\|1=⋅}}
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	=== Calculating the check digit ===		=== Calculating the check digit ===
	{\| class="wikitable" style="text-align:center~~;background:none~~;color:#E000E0"		{\| class="wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index		!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index
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	=== Validating a number against the included check digit ===		=== Validating a number against the included check digit ===
	{\| class="wikitable" style="text-align:center~~;background:none~~;color:#E000E0"		{\| class="wikitable" style="text-align:center;color:#E000E0"
	\|- style="color:#00A000"		\|- style="color:#00A000"
	!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index		!style="color:black"\| <span style="color:#00A000">digit to be processed</span> → column index

Tuckertwo: Adding local short description: "Check digit algorithm", overriding Wikidata description "check digit algorithm presented by H. Michael Damm"

2024-10-14T11:05:04Z

Adding local short description: "Check digit algorithm", overriding Wikidata description "check digit algorithm presented by H. Michael Damm"

← Previous revision		Revision as of 11:05, 14 October 2024
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			{{Short description\|Check digit algorithm}}
	In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''		In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''

W96: URL of the link to Singapore patent application numbers

2024-02-04T06:55:18Z

URL of the link to Singapore patent application numbers

← Previous revision		Revision as of 06:55, 4 February 2024
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	{{Wikibooks\|Algorithm Implementation/Checksums/Damm Algorithm}}		{{Wikibooks\|Algorithm Implementation/Checksums/Damm Algorithm}}
	*[[b:Algorithm Implementation/Checksums/Damm Algorithm\|Damm validation & generation code in several programming languages]]		*[[b:Algorithm Implementation/Checksums/Damm Algorithm\|Damm validation & generation code in several programming languages]]
	*[https://~~web.archive.org/web/20160418222701/https://blog~~.cantab-ip.com/2014/01/20/new-format-for-singapore-ip-application-numbers-at-ipos/ Practical application in Singapore]		*[https://www.cantab-ip.com/blog/2014/01/20/new-format-for-singapore-ip-application-numbers-at-ipos/ Practical application in Singapore]
	*[http://www.md-software.de/math/DAMM_Quasigruppen.txt Quasigroups for the Damm algorithm up to order 64]		*[http://www.md-software.de/math/DAMM_Quasigruppen.txt Quasigroups for the Damm algorithm up to order 64]
	*[https://rosettacode.org/wiki/Damm_algorithm At RosettaCode.org, Implementations of the Damm algorithm in many programming languages]		*[https://rosettacode.org/wiki/Damm_algorithm At RosettaCode.org, Implementations of the Damm algorithm in many programming languages]

CygnetRiver: Replace broken link with archive.org mirror

2023-12-09T08:44:15Z

Replace broken link with archive.org mirror

← Previous revision		Revision as of 08:44, 9 December 2023
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	In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004.<ref name="fenwick2014" />		In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error\|single-digit errors]] and all [[Transcription error#Transposition error\|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''

	== Strengths and weaknesses ==		== Strengths and weaknesses ==
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	{{Wikibooks\|Algorithm Implementation/Checksums/Damm Algorithm}}		{{Wikibooks\|Algorithm Implementation/Checksums/Damm Algorithm}}
	*[[b:Algorithm Implementation/Checksums/Damm Algorithm\|Damm validation & generation code in several programming languages]]		*[[b:Algorithm Implementation/Checksums/Damm Algorithm\|Damm validation & generation code in several programming languages]]
	*[~~http~~://blog.cantab-ip.com~~/blog~~/2014/01/20/new-format-for-singapore-ip-application-numbers-at-ipos/ Practical application in Singapore]		*[https://web.archive.org/web/20160418222701/https://blog.cantab-ip.com/2014/01/20/new-format-for-singapore-ip-application-numbers-at-ipos/ Practical application in Singapore]
	*[http://www.md-software.de/math/DAMM_Quasigruppen.txt Quasigroups for the Damm algorithm up to order 64]		*[http://www.md-software.de/math/DAMM_Quasigruppen.txt Quasigroups for the Damm algorithm up to order 64]
	*[https://rosettacode.org/wiki/Damm_algorithm At RosettaCode.org, Implementations of the Damm algorithm in many programming languages]		*[https://rosettacode.org/wiki/Damm_algorithm At RosettaCode.org, Implementations of the Damm algorithm in many programming languages]