Property talk:P2534

Documentation

defining formula
mathematical formula representing a theorem or law. Maximum length: 400 characters

Description

formula representing a theorem or law

Represents

formula (Q976981)

Data type

Mathematical expression

Domain

According to this template: Mathematical and physics based articles

According to statements in the property:
mathematical concept (Q24034552), concept in physics (Q33104303), scientific law (Q408891) or mathematical object (Q246672)

When possible, data should only be stored as statements

Usage notes

Maximum length: 400 characters

Example

Pythagorean theorem (Q11518) →

a^{2}+b^{2}=c^{2}

mass–energy equivalence (Q35875) →

E=mc^{2}

Ohm's law (Q41591) →

R={\frac {U}{I}}

Tracking: usage

Category:Pages using Wikidata property P2534 (Q26250053)

limit 400 characters[edit]

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

(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}\,

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)[reply]

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)[reply]

Symbol definitions[edit]

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

Well, in the mass–energy equivalence (Q35875) I see the definirtions in has part(s) (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 ~~Pithagor~~^{Heron, shame on my head}'s formula for area of a triangle

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)[reply]

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)[reply]

Supported environment[edit]

I would like to insert the Butcher tableau of midpoint methods (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? --★ → A ir on 90 13:29, 14 April 2018 (UTC)[reply]

@Airon90: I have been looking into doing the same thing. But I think it might actually be better to add a new property for Butcher's tableau. Then we can have both the numerical method as a formula and a tableau.

The-erinaceous-one (talk) 05:35, 25 July 2020 (UTC)[reply]

According to [1], you can actually create tables using the following command: \begin{array}{|c|c|c|} a & b & S \\ \hline 0 & 0 & 1\\0 & 1& 1\\1&0&1\\1&1&0 \\ \end{array}

The-erinaceous-one (talk) 05:45, 25 July 2020 (UTC)[reply]

@The-erinaceous-one: I think that it is better to insert A, b and c separately as formulas (applies to part (P518) Runge-Kutta matrix (Q97664752), Runge-Kutta weights vector (Q97664754), Runge-Kutta nodes vector (Q97664755) respectively) --★ → A ir on 90 09:27, 25 July 2020 (UTC)[reply]

@Airon90: I wouldn't be opposed to entering A, b, and c separately, but I don't see the advantage. What do you see as the upside of separating them? If we do separate them, I would want there to be some way of displaying in the standard Butcher tableau format. Also, I made a Butcher tableau property proposal yesterday [2]. Perhaps we should move this discussion there? The-erinaceous-one (talk) 21:30, 25 July 2020 (UTC)[reply]

@Airon90: Another idea, I just had, was that we could add a property <Butcher tableau> and then use has part(s) (P527): Runge-Kutta matrix (Q97664752), Runge-Kutta weights vector (Q97664754), Runge-Kutta nodes vector (Q97664755) as a qualifiers. The-erinaceous-one (talk)

We move the discussion about new property there --★ → A ir on 90 07:51, 26 July 2020 (UTC)[reply]

Expand the scope to every mathematical concept[edit]

Notified participants of WikiProject Mathematics 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:

⟨ absolute value (Q120812)  

 ⟩ defining formula (P2534) ⟨ 

x\mathop {sgn} (x)

 ⟩

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

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

Formatting of vector quantities[edit]

How should we format vector quantities? In school I used to draw arrows over vector quantities, probably because this is easiest when using a pen (compared to drawing a boldface letter). For defining formula I have seen both boldface and a vector arrow. Should we standardize on one particular format (for quantities used in mechanics, electromagnetism, ...)? I have entered all new formulas using boldface, following ISO/IEC 80000 (Q568496). I like this most (but could be convinced otherwise). Any other preference? Toni 001 (talk) 12:33, 18 December 2019 (UTC)[reply]

I prefer bold to arrows. ArthurPSmith (talk) 20:03, 18 December 2019 (UTC)[reply]

I have the same feelings as you, Toni. But I suppose arrows are more universal (also for schoolers) and more understandable. --Infovarius (talk) 08:58, 19 December 2019 (UTC)[reply]

I could imagine that in handwriting the arrow is preferred because it is easier to draw an arrow over a letter than to "write" a bold symbol. Toni 001 (talk) 10:28, 11 November 2020 (UTC)[reply]

I agree with using bold over arrows for typset vectors. I've seldom seen arrow notation used in print.— The Erinaceous One 🦔 08:55, 12 November 2020 (UTC)[reply]

Single value constraint[edit]

defining formula (P2534) has a single-value constraint (Q19474404). I think in general that this is good. However, different sources (or even different parts of the same source) might give different definitions for the same quantity, as is the case for wavenumber (Q192510): $\sigma =1/\lambda =\nu /c$ . I think it is important to find a way to store each definition, and have each sourced properly. The source requirement precludes dumping all definitions into the same line (x = definition 1 = definition 2) as one would not know which definition is stated in which source. In addition, some quantities are not simply defined as thing = definition, but appear inside a formula (that is, not simply on the left hand side), as is the case for magnetic flux density (Q30204).

This seems to suggest that in some cases we might want to violate the single value constraint.

However, there is an additional problem: To really explain the formula, we should first have a statement my itemin defining formula (P7235)my symbol to state which symbol is used in the formula to define my item. Then we should have further statements involving calculated from (P4934) with in defining formula (P7235) as qualifier to explain which other quantities appear in the formula and which symbols are used for those quantities. This gets somewhat messy when there is more than one defining formula; one might be forced to use non-standard symbol names in some defining formula to avoid conflicts with another formula.

The latter might seem to suggest that we should have one item for each formula. But this is probably not what we should do if the definitions are equivalent, because then they describe the same concept and deserve only one item. But we should definitely have all definitions - even if equivalent - so that someone coming from one area of science can work with what they are familiar with.

This is a though problem that I've been wondering about for the last few month. If you have any suggestions, then let's discuss. Toni 001 (talk) 11:57, 29 December 2019 (UTC)[reply]

I'm finding more and more cases where even the same source gives different formulas, none of which is preferred. Therefore I removed the single (best) value constraint. (The way to explain variables has since been updated, see below.) Toni 001 (talk) 08:32, 4 September 2021 (UTC)[reply]

How to explain variables[edit]

A formula has no meaning without an explanation of its variables. With the recent creation of symbol represents (P9758) we now have an easy way to explain each variable (or operator) in a formula:

For each variable in the formula declare in defining formula (P7235) as main value,
then link that variable to an item using symbol represents (P9758) as qualifier.

That's it.

It has been a long way to get here, with two competing systems being used (one using calculated from (P4934) with in defining formula (P7235) qualifiers and the other using has part(s) (P527) with a larger mix of qualifiers), and with many good ideas for improvement being discussed at length.

I now started migrating formulas, first starting with the ones which previously used calculated from (P4934). For now I'm going manually, one item at a time, to fix issues I find along the way.

Best wishes. Toni 001 (talk) 08:43, 20 August 2021 (UTC)[reply]

Somehow this loses the main link from one item to another item. in defining formula (P7235) is better used as designed: as qualifier for calculated from. I suppose there is room for P9758 for whatever it was designed. --- Jura 08:20, 7 November 2021 (UTC)[reply]

Formulas as qualifiers[edit]

It has been proposed to use defining formula (P2534) as qualifier. There are two issues with this:

A formula is useless unless its symbols are explained. In the current data model this is possible only when the formula appears as main value.
Using it as qualifier to has characteristic (P1552), instance of (P31) etc. bypasses the requirement to propose and discuss a new property.

Toni 001 (talk) 06:40, 25 April 2023 (UTC)[reply]

1) If the formula doesn't contain any variable (i.e. consists of numbers) it doesn't requre "symbol explaining".

2) There's no need to separate illustrating formula from corresponding class (P31). Infovarius (talk) 07:17, 27 April 2023 (UTC)[reply]

To 1: For the data model it is irrelevant whether the number of variables to be explained happens to be zero.

To 2: Could you please elaborate? Toni 001 (talk) 05:33, 28 April 2023 (UTC)[reply]

1) Relevant. You simply can't explain zero variables. 2) Formula in

⟨ M127 (Q2808991)  

 ⟩ instance of (P31) ⟨ double Mersenne number (Q1318413)  

 ⟩

doesn't make sense separately from the property. --Infovarius (talk) 20:36, 29 April 2023 (UTC)[reply]

To 2: One could imagine a property or collection of properties to model different representations of prime numbers. Toni 001 (talk) 05:59, 3 May 2023 (UTC)[reply]

KISS. Why to overcomplicate? --Infovarius (talk) 19:21, 4 May 2023 (UTC)[reply]

This is not the place to discuss the property proposal process. Please try the project chat if you think that there's an issue. Toni 001 (talk) 04:51, 5 May 2023 (UTC)[reply]

Pardon? It's you who think that there's an issue. I don't want a new property and am happy with current model (with qualifiers). --Infovarius (talk) 11:10, 7 May 2023 (UTC)[reply]

Property talk:P2534

Contents

Documentation

limit 400 characters[edit]

Symbol definitions[edit]

Supported environment[edit]

Expand the scope to every mathematical concept[edit]

Formatting of vector quantities[edit]

Single value constraint[edit]

How to explain variables[edit]

Formulas as qualifiers[edit]

Navigation menu

Property talk:P2534

Documentation

limit 400 characters[edit]

Symbol definitions[edit]

Supported environment[edit]

Expand the scope to every mathematical concept[edit]

Formatting of vector quantities[edit]

Single value constraint[edit]

How to explain variables[edit]

Formulas as qualifiers[edit]

Navigation menu

Search