View source for Testwiki:Property proposal/algebraic properties

=== {{TranslateThis | anchor = en
| en = identity element
<!-- |xx = property names in some other languages -->
}} ===
{{Property proposal
|status			= 8864
|description		= {{TranslateThis
 | en = value of the identity element of the mathematical operation
<!-- | xx = descriptions in other languages -->
 }}
|subject item           = identity element <!-- item corresponding to the concept represented by the property, if applicable; example: item child (Q7569) for property child (P40) -->
|infobox parameter	= <!-- Wikipedia infobox parameters, if any; ex: "population" in [[:en:template:infobox settlement]] -->
|datatype		= item <!-- put datatype here (one of: item, external-id, string, media, coordinates, monolingual text, multilingual text, time, URL, number, geo-shape, tabular, lexeme, form, sense, mathematical expression, or a possibly new one) -->
|domain			= {{Q|164307}} <!-- entity type (item, property, lexeme, form, sense) and types of items that may bear this property; give QIDs if possible -->
|allowed values		= {{Q|246672}} <!-- type of linked items (Q template or text), string pattern (regex if possible), list or range of allowed values, etc. -->
|allowed units          = <!-- units that are allowed for values of this property -->
|source			= <!-- external reference URL, Wikipedia list article, etc. -->
<!-- you should provide 3 examples at least-->
|example 1		= {{Q|32043}} → {{Q|204}} <!-- {{Q|1}} → value -->
|example 2		= {{Q|40276}} → {{Q|199}}
|example 3		= {{Q|244761}} → {{Q|254474}}
|example 4		= {{Q|2264115}} → {{Q|338028}}
|example 5		= {{Q|Q1049914}} → {{Q|193794}}
|planned use            = <!-- what use do you plan to make of the property within the next month -->
|see also               = <!-- other, related properties -->
|robot and gadget jobs	= <!-- Should or are bots or gadgets doing any task with this? (Checking other properties for consistency, collecting data, etc.) -->
|subpage		= algebraic properties
|topic			= natural science
}}

More examples: [https://en.wikipedia.org/wiki/Identity_element#Examples].

=== {{TranslateThis | anchor = en
| en = mathematical inverse
<!-- |xx = property names in some other languages -->
}} ===
{{Property proposal
|status			= 8865
|description		= {{TranslateThis
 | en = the inverse element with respect to binary operation given as a qualifier  <!-- DESCRIPTION IN ENGLISH -->
<!-- | xx = descriptions in other languages --> 
 }}
|subject item           = {{Q|246672}} <!-- item corresponding to the concept represented by the property, if applicable; example: item child (Q7569) for property child (P40) -->
|datatype		= item <!-- put datatype here (one of: item, external-id, string, media, coordinates, monolingual text, multilingual text, time, URL, number, geo-shape, tabular, lexeme, form, sense, mathematical expression, or a possibly new one) -->
|domain			= {{Q|246672}} <!-- entity type (item, property, lexeme, form, sense) and types of items that may bear this property; give QIDs if possible -->
|allowed values		= {{Q|246672}} <!-- type of linked items (Q template or text), string pattern (regex if possible), list or range of allowed values, etc. -->
|allowed units          = <!-- units that are allowed for values of this property -->
|source			= <!-- external reference URL, Wikipedia list article, etc. -->
<!-- you should provide 3 examples at least-->
|example 1		= {{Statement|Q200|mathematical inverse|Q2114394|P2210|Q40276}} 
|example 2		= {{Statement|Q310395|mathematical inverse|Q199|P2210|Q32043}}
|example 3		= {{Statement|Q199691|mathematical inverse|Q2162701|P2210|Q244761}}
|example 4		= {{Statement|Q152415|mathematical inverse|Q674517|P2210|Q244761}}
|example 5		= {{Statement|Q32043|mathematical inverse|Q40754}}
<!--  if convenient, include more examples by following the same pattern: 
|example ...		=  {{Q|1}} → value
-->
|planned use            = <!-- what use do you plan to make of the property within the next month -->
|external links         = <!-- for identifiers, search string to pass to sister projects' Special:LinkSearch pages, e.g. example.com  -->
|see also               = <!-- other, related properties -->
|robot and gadget jobs	= <!-- Should or are bots or gadgets doing any task with this? (Checking other properties for consistency, collecting data, etc.) -->
|subpage		= algebraic properties
|topic			= natural science
}}

==== Other examples ====
* {{Q|98967608}} <=> {{Q|30587593}}
* {{Q|210857}} <=> {{Q|1183700}}
* {{Q|6520159}} <=> {{Q|98968150}}

=== {{TranslateThis | anchor = en
| en = has operator
<!-- |xx = property names in some other languages -->
}} ===
{{Property proposal
|status			= 8866
|description		= {{TranslateThis
 | en = mathematical operator associated with this algebraic structure  <!-- DESCRIPTION IN ENGLISH -->
<!-- | xx = descriptions in other languages --> 
 }}
|subject item           =  <!-- item corresponding to the concept represented by the property, if applicable; example: item child (Q7569) for property child (P40) -->
|datatype		= item <!-- put datatype here (one of: item, external-id, string, media, coordinates, monolingual text, multilingual text, time, URL, number, geo-shape, tabular, lexeme, form, sense, mathematical expression, or a possibly new one) -->
|domain			= {{Q|205464}} <!-- entity type (item, property, lexeme, form, sense) and types of items that may bear this property; give QIDs if possible -->
|allowed values		= {{Q|131030}} <!-- type of linked items (Q template or text), string pattern (regex if possible), list or range of allowed values, etc. -->
|allowed units          = <!-- units that are allowed for values of this property -->
|source			= <!-- external reference URL, Wikipedia list article, etc. -->
<!-- you should provide 3 examples at least-->
|example 1		= {{Q|4681347}} → {{Q|32043}}
|example 2		= {{Q|849512}} → {{Q|244761}}
|example 3		= {{Q|Q2915729}} → {{Q|2264115}}, {{Q|1049914}}
|example 4		= {{Q|186247}} → {{Q|55091432}}, {{Q|126736}}
<!--  if convenient, include more examples by following the same pattern: 
|example ...		=  {{Q|1}} → value
-->
|planned use            = <!-- what use do you plan to make of the property within the next month -->
|external links         = <!-- for identifiers, search string to pass to sister projects' Special:LinkSearch pages, e.g. example.com  -->
|see also               = <!-- other, related properties -->
|robot and gadget jobs	= <!-- Should or are bots or gadgets doing any task with this? (Checking other properties for consistency, collecting data, etc.) -->
|subpage		= algebraic properties
|topic			= natural science
}}

====Motivation====

Algebriac {{Q-|83478}}s are an important class of mathematical object. In Wikidata, there are 184 instances [https://w.wiki/ejf] and 585 subclasses [https://w.wiki/ejh] of algebraic groups, but they are lacking the most basic information to describe them. A group consists of a mathematical {{Q|36161}} and an invertible {{Q|164307}}, which has a unique {{Q|185813}}. 
In order to model this information, I propose creating three new properties: identity element, mathematical inverse, and has operator. (These properties are applicable beyond just groups, however. Multiple examples are listed above.)

Existing properties are inadequate or cumbersome for modeling these relationships. We could model "identity element" and "has operator" with existing properties by using {{P|527}}, but it results in {{Statement|Q26851380|P527|Q204|P2868|Q185813|P2210|Q32043}} and {{Statement|Q26851380|P527|Q32043|P2868|Q99839939}} but that is super convoluted and querying it would be difficult. 
Similarly, we can model "mathematical inverse" as {{Statement|Q310395|opposite of|Q199|P2210|Q32043|P1013|mathematical inverse}} but, again, this is awkward and also prevents us from enforcing expected relationships, such as the symmetry of inverses. 

I considered three ways of modeling identity element:
# {{Statement|set of real numbers|identity element|zero|with respect to|addition}}
# {{Statement|set of real numbers|has operation|addition|identity element|zero}}
# {{Statement|set of real numbers|has operation|addition}} {{Statement|addition|identity element|zero}}
Option 1 was dismissed because an "identity" is an identity of an of the ''operator'' rather than the set, so the modeling should reflec that. Option 2 is an improvement over option 1---and we might want to use "identity element" as a qualifier sometimes (please discuss)---but I think option 3 is best choice because it is simple and will prevent duplication if the same operator is used on multiple structures. (Option 3 might be problematic, however, if some algebraic structure, let's call it <math>S</math>, uses an operator that has an identity element <math>I</math>, but <math>I\not\in S</math>. I don't know if this is possible or not.)

—'''[[User:The-erinaceous-one|<span style="color: SaddleBrown ;"> The Erinaceous One 🦔</span>]]''' 10:53, 2 October 2020 (UTC)

===={{int:Talk}}====
{{ping project|Mathematics}}
: {{s}} for all of these; however I have a question about the "mathematical inverse" proposal - two of your examples have the qualifier and two don't - does that suggest these are two distinct properties, or is there a better way to describe this? [[User:ArthurPSmith|ArthurPSmith]] ([[User talk:ArthurPSmith|<span class="signature-talk">{{int:Talkpagelinktext}}</span>]]) 20:51, 2 October 2020 (UTC)
:: {{ping|ArthurPSmith}} No, it should only be one property. I've added a qualifier for the sine/arccosine example and qualfier would work on the Laplace transform example, but I'm not sure what the right qualifier value is. We could use {{Statement|Q199691|mathematical inverse|Q2162701|P2210|Q244761}}, but I'm not sure if it's accuracte to talk about the function composition of integral transforms. (I.e. is an integral transformation a function on functions?) —'''[[User:The-erinaceous-one|<span style="color: SaddleBrown ;"> The Erinaceous One 🦔</span>]]''' 22:14, 2 October 2020 (UTC)
::: I've thought about it more and {{Statement|Q199691|mathematical inverse|Q2162701|P2210|Q244761}} is correct, so now all the "mathematical inverse" examples have qualifiers. —'''[[User:The-erinaceous-one|<span style="color: SaddleBrown ;"> The Erinaceous One 🦔</span>]]''' 21:45, 3 October 2020 (UTC)

{{ping|Jura1|Ederporto|}} would one of you be able to create these properties? —'''[[User:The-erinaceous-one|<span style="color: SaddleBrown ;"> The Erinaceous One 🦔</span>]]''' 09:06, 11 November 2020 (UTC)
* {{s}} --<span style="text-shadow: 1px 1px 4px purple">[[User:Tinker Bell|Tinker Bell]] [[User_talk:Tinker Bell|<span style="color:#ed428d;font-size:1.4em">★</span>]] [[Special:Contributions/Tinker Bell|<span style="color:#ed428d;font-size:1.1em">♥</span>]]</span> 02:40, 17 November 2020 (UTC)
: {{ping|The-erinaceous-one|ArthurPSmith|Tinker Bell}} {{done}} {{p|8864}}, {{p|8865}}, {{p|8866}} [[User:Pamputt|Pamputt]] ([[User talk:Pamputt|<span class="signature-talk">{{int:Talkpagelinktext}}</span>]]) 17:07, 26 November 2020 (UTC)