# Property talk:P2534

## Documentation

defining formula
mathematical formula representing a theorem or law. Maximum length: 400 characters
Description formula representing a theorem or law formula (Q976981) Mathematical expression Mathematical and physics based articles (note: this should be moved to the property statements) Pythagorean theorem (Q11518) → ${\displaystyle a^{2}+b^{2}=c^{2}}$mass–energy equivalence (Q35875) → ${\displaystyle E=mc^{2}}$Ohm's law (Q41591) → ${\displaystyle R={\frac {V}{I}}}$ Category:Pages using Wikidata property P2534 (Q26250053) Property proposal/Archive/45#P2534 3,661
[create] Create a translatable help page (preferably in English) for this property to be included here
 Single value: this property generally contains a single value. (Help)Exceptions are possible as rare values may exist. List of this constraint violations: Database reports/Constraint violations/P2534#Single value, SPARQL, SPARQL (new)
 Conflicts with “instance of (P31): human (Q5), chemical compound (Q11173), concrete object (Q4406616)”: this property must not be used with the listed properties and values. (Help)Exceptions are possible as rare values may exist. List of this constraint violations: Database reports/Constraint violations/P2534#Conflicts with P31, SPARQL, SPARQL (new)
 Distinct values: this property likely contains a value that is different from all other items. (Help)Exceptions are possible as rare values may exist. List of this constraint violations: Database reports/Constraint violations/P2534#Unique value, SPARQL (every item), SPARQL (by value), SPARQL (new)
 This property is being used by: Please notify projects that use this property before big changes (renaming, deletion, merge with another property, etc.)

## limit 400 characters

Degen's eight-square identity (> 400):

${\displaystyle (a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}+a_{7}^{2}+a_{8}^{2})(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}+b_{4}^{2}+b_{5}^{2}+b_{6}^{2}+b_{7}^{2}+b_{8}^{2})=\,}$
${\displaystyle (a_{1}b_{1}-a_{2}b_{2}-a_{3}b_{3}-a_{4}b_{4}-a_{5}b_{5}-a_{6}b_{6}-a_{7}b_{7}-a_{8}b_{8})^{2}+\,}$
${\displaystyle (a_{1}b_{2}+a_{2}b_{1}+a_{3}b_{4}-a_{4}b_{3}+a_{5}b_{6}-a_{6}b_{5}-a_{7}b_{8}+a_{8}b_{7})^{2}+\,}$
${\displaystyle (a_{1}b_{3}-a_{2}b_{4}+a_{3}b_{1}+a_{4}b_{2}+a_{5}b_{7}+a_{6}b_{8}-a_{7}b_{5}-a_{8}b_{6})^{2}+\,}$
${\displaystyle (a_{1}b_{4}+a_{2}b_{3}-a_{3}b_{2}+a_{4}b_{1}+a_{5}b_{8}-a_{6}b_{7}+a_{7}b_{6}-a_{8}b_{5})^{2}+\,}$
${\displaystyle (a_{1}b_{5}-a_{2}b_{6}-a_{3}b_{7}-a_{4}b_{8}+a_{5}b_{1}+a_{6}b_{2}+a_{7}b_{3}+a_{8}b_{4})^{2}+\,}$
${\displaystyle (a_{1}b_{6}+a_{2}b_{5}-a_{3}b_{8}+a_{4}b_{7}-a_{5}b_{2}+a_{6}b_{1}-a_{7}b_{4}+a_{8}b_{3})^{2}+\,}$
${\displaystyle (a_{1}b_{7}+a_{2}b_{8}+a_{3}b_{5}-a_{4}b_{6}-a_{5}b_{3}+a_{6}b_{4}+a_{7}b_{1}-a_{8}b_{2})^{2}+\,}$
${\displaystyle (a_{1}b_{8}-a_{2}b_{7}+a_{3}b_{6}+a_{4}b_{5}-a_{5}b_{4}-a_{6}b_{3}+a_{7}b_{2}+a_{8}b_{1})^{2}\,}$

or LATEX (976 symbols): $(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}+a_{7}^{2}+a_{8}^{2})(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}+b_{4}^{2}+b_{5}^{2}+b_{6}^{2}+b_{7}^{2}+b_{8}^{2})=\,$ $(a_{1}b_{1}-a_{2}b_{2}-a_{3}b_{3}-a_{4}b_{4}-a_{5}b_{5}-a_{6}b_{6}-a_{7}b_{7}-a_{8}b_{8})^{2}+\,$ $(a_{1}b_{2}+a_{2}b_{1}+a_{3}b_{4}-a_{4}b_{3}+a_{5}b_{6}-a_{6}b_{5}-a_{7}b_{8}+a_{8}b_{7})^{2}+\,$ $(a_{1}b_{3}-a_{2}b_{4}+a_{3}b_{1}+a_{4}b_{2}+a_{5}b_{7}+a_{6}b_{8}-a_{7}b_{5}-a_{8}b_{6})^{2}+\,$ $(a_{1}b_{4}+a_{2}b_{3}-a_{3}b_{2}+a_{4}b_{1}+a_{5}b_{8}-a_{6}b_{7}+a_{7}b_{6}-a_{8}b_{5})^{2}+\,$ $(a_{1}b_{5}-a_{2}b_{6}-a_{3}b_{7}-a_{4}b_{8}+a_{5}b_{1}+a_{6}b_{2}+a_{7}b_{3}+a_{8}b_{4})^{2}+\,$ $(a_{1}b_{6}+a_{2}b_{5}-a_{3}b_{8}+a_{4}b_{7}-a_{5}b_{2}+a_{6}b_{1}-a_{7}b_{4}+a_{8}b_{3})^{2}+\,$ $(a_{1}b_{7}+a_{2}b_{8}+a_{3}b_{5}-a_{4}b_{6}-a_{5}b_{3}+a_{6}b_{4}+a_{7}b_{1}-a_{8}b_{2})^{2}+\,$ $(a_{1}b_{8}-a_{2}b_{7}+a_{3}b_{6}+a_{4}b_{5}-a_{5}b_{4}-a_{6}b_{3}+a_{7}b_{2}+a_{8}b_{1})^{2}\,$ --Fractaler (talk) 13:48, 8 September 2016 (UTC)

This can be obviously compressed to 580 symbols:

$(a_1^2+a_2^2+a_3^2+a_4^2+a_5^2+a_6^2+a_7^2+a_8^2)(b_1^2+b_2^2+b_3^2+b_4^2+b_5^2+b_6^2+b_7^2+b_8^2)=(a_1b_1-a_2b_2-a_3b_3-a_4b_4-a_5b_5-a_6b_6-a_7b_7-a_8b_8)^2+(a_1b_2+a_2b_1+a_3b_4-a_4b_3+a_5b_6-a_6b_5-a_7b_8+a_8b_7)^2+(a_1b_3-a_2b_4+a_3b_1+a_4b_2+a_5b_7+a_6b_8-a_7b_5-a_8b_6)^2+(a_1b_4+a_2b_3-a_3b_2+a_4b_1+a_5b_8-a_6b_7+a_7b_6-a_8b_5)^2+(a_1b_5-a_2b_6-a_3b_7-a_4b_8+a_5b_1+a_6b_2+a_7b_3+a_8b_4)^2+(a_1b_6+a_2b_5-a_3b_8+a_4b_7-a_5b_2+a_6b_1-a_7b_4+a_8b_3)^2+(a_1b_7+a_2b_8+a_3b_5-a_4b_6-a_5b_3+a_6b_4+a_7b_1-a_8b_2)^2+(a_1b_8-a_2b_7+a_3b_6+a_4b_5-a_5b_4-a_6b_3+a_7b_2+a_8b_1)^2$ and by substituting each variable to one letter can be compressed down to 292 symbols: $(A^2+B^2+C^2+D^2+E^2+F^2+G^2+H^2)(a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2)=(Aa-Bb-Cc-Dd-Ee-Ff-Gg-Hh)^2+(Ab+Ba+Cd-Dc+Ef-Fe-Gh+Hg)^2+(Ac-Bd+Ca+Db+Eg+Fh-Ge-Hf)^2+(Ad+Bc-Cb+Da+Eh-Fg+Gf-He)^2+(Ae-Bf-Cg-Dh+Ea+Fb+Gc+Hd)^2+(Af+Be-Ch+Dg-Eb+Fa-Gd+Hc)^2+(Ag+Bh+Ce-Df-Ec+Fd+Ga-Hb)^2+(Ah-Bg+Cf+De-Ed-Fc+Gb+Ha)^2$ --Infovarius (talk) 17:46, 10 September 2016 (UTC)

## Symbol definitions

How to add symbol definitions? They were in the original propsal, where are they now? Ignatus (talk) 22:16, 10 December 2016 (UTC)

Well, in the mass–energy equivalence (Q35875) I see the definirtions in has part (P527). But it is VERY bad semantically use of this property. Hardly the description should leave the formula's qualifiers since the letters define the formula, not the object (the symbols often vary in different traditions but the formulae built with them are equivalent if correctly defined). And we probably can't now make qualifiers with relation <math:symbol | item:definition> (and I'm afraid not any definition will have an item defining it, or we'll sink in items used to define formulae only, like in PithagorHeron, shame on my head's formula for area of a triangle ${\displaystyle F={\sqrt {p(p-a)(p-b)(p-c)}}}$). Ignatus (talk) 22:30, 10 December 2016 (UTC) Opened a discussion on WD:Project chat/Archive/2016/12#Symbol definitions with math datatype 22:56, 10 December 2016 (UTC)
I would prefer using Datasets from Commons (mw:Help:Tabular data) as legends for formulae and images, they support structured lists, and even localization! Ignatus (talk) 20:11, 27 December 2016 (UTC)

## Supported environment

I would like to insert the Butcher tableau of Midpoint method (Q17103851) as formula but I can't:

 \begin{tabular}{c|c c} 0 & 0 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ \hline & 0 & 1 \end{tabular} 

How can I do that? --★ → Airon 90 13:29, 14 April 2018 (UTC)

## Expand the scope to every mathematical concept

Currently, the description of this property says that it can be used only for theorem and laws statements. Why not for mathematical concept definitions in general? For example, for something like this:

defining formula (P2534) < ${\displaystyle x\mathop {sgn} (x)}$ >

.--Malore (talk) 00:27, 13 June 2018 (UTC)

De facto it is already used this way in more than 50%. Maybe we need a new property for definition formulars. Bigbossfarin (talk) 10:09, 13 June 2018 (UTC)
Support broadening the definition of this property to reflect usage (which has been that way a long time!) ArthurPSmith (talk) 18:02, 15 June 2018 (UTC)
• There is a general problem with the datatype. It can't be reliably queried on query server. Maybe we should try to find another working solution.
--- Jura 09:24, 17 June 2018 (UTC)
What kind of queries are you interested in? Spqrql is quite powerful. See for example meaning of identifiers in ideal gas law  – The preceding unsigned comment was added by [[User:|]] ([[User talk:|talk]] • contribs).
The need for contributors is fairly simple: one needs to be able the retrieve the current value as entered through Wikidata query server.
--- Jura 12:06, 17 June 2018 (UTC)
The security philosphy is that the original source code is not shared, despite in its original context. Only a secure version which can be used as input is availible from the query service. I would be keen to learn for which usecase the original source code would be required. --Physikerwelt (talk) 17:33, 17 June 2018 (UTC)