Wikidata:Property proposal/defined in terms of

other items in defining formula

Originally proposed at Wikidata:Property proposal/Natural science

   Withdrawn

Description	mathematical objects used in the defining formula, for which "calculated from (P4934)" does not apply
Data type	Item
Domain	mathematical object (Q246672)
Allowed values	mathematical object (Q246672)
Example 1	linear map (Q207643) → vector addition (Q55091432), scalar multiplication (Q126736) (c.f. linear map (Q207643)defining formula (P2534)$T(\alpha \mathbf {x} +\beta \mathbf {y} )=\alpha T(\mathbf {x} )+\beta T(\mathbf {y} ),\quad \forall \alpha ,\beta \in \mathbb {R} ,\forall \mathbf {x} ,\mathbf {y} \in \operatorname {dom} (T)$)
Example 2	Laplace's equation (Q339444) → Laplace operator (Q203484) (c.f. Laplace's equation (Q339444)defining formula (P2534)$\Delta u=0$)
Example 3	Hölder's inequality (Q731894) -> p-norm (Q98828598) (c.f. Hölder's inequality (Q731894)defining formula (P2534)$\|fg\|_{1}\leq \|f\|_{p}\|g\|_{q}$)
Example 4	Gauss's law for magnetism (Q1195250) -> divergence (Q189000), magnetic field (Q11408) (c.f. Gauss's law for magnetism (Q1195250)defining formula (P2534)$\nabla \cdot \mathbf {B} =0$)
Example 5	commutative property (Q165474) -> binary operator (Q30242895) (c.f. commutative property (Q165474)defining formula (P2534)$\forall x,y\colon x\star y=y\star x$)
Example 6	Leibniz algebra (Q844980) -> commutator bracket? (c.f. Leibniz algebra (Q844980)defining formula (P2534)$[[a,b],c]=[[a,c],b]+[a,[b,c]]$)
See also	defining formula (P2534), calculated from (P4934), in defining formula (P7235)

Motivation

In Wikidata, there is an existing paradigm to model the defining formula of a particular mathematical or scientific concept, along with ways to model quantities that are used to calculate/evaluate the formula. In many cases, however, the defining formula is not something that can be calculated. It's just a definition that gives a relation. In these cases, it doesn't make sense to use calculated from (P4934), thus we propose an analaogous property "defined in terms of."

To expand on an example given above, consider Gauss's law for magnetism (Q1195250). We have Gauss's law for magnetism (Q1195250)defining formula (P2534)$\nabla \cdot \mathbf {B} =0$. Clearly, Gauss's law isn't "calculated from" the magnetic field $\mathbf {B}$, it merely gives a relation between the magnetic and electric fields, so P4934 is not approriate. The proposed property would be thus be used as follows

defined in terms of	magnetic field (Q11408) edit in defining formula (P7235) $\mathbf {B}$ 0 references add reference
		add value

defined in terms of	divergence (Q189000) edit in defining formula (P7235) $\nabla \cdot$ 0 references add reference
		add value

The-erinaceous-one (talk) 04:21, 2 September 2020 (UTC)

Discussion

Opensofias
Tobias1984
Arthur Rubin
Cuvwb
TomT0m
Physikerwelt
Lymantria
Bigbossfarin
Infovarius
Helder
PhilMINT
Malore
Lore.mazza51
Wikisaurus
The Anome
The-erinaceous-one
Daniel Mietchen
Haansn08
Xenmorpha
John Samuel
Jeremy Dover
Toni 001
Bocardodarapti
Duckmather
HTinC23
fgnievinski

Notified participants of WikiProject Mathematics

Tobias1984
Snipre
Physikerwelt
Pamputt
Petermahlzahn
Jibe-b
Restu20
Daniel Mietchen
TomT0m
ArthurPSmith
Mu301
Sarilho1
SR5
DavRosen
Danmichaelo
Ptolusque
PhilMINT
Malore
Thibdx
Ranjithsiji
Niko.georgiev
Simon Villeneuve
Toni 001
Marc André Miron
DePiep
RShigapov
CarlFriedberg
Crocodilecoup
Mkomboti
Amorenobr (talk) 01:27, 3 August 2022 (UTC)
Valverde667 (talk) 16:07, 4 August 2022 (UTC)
fgnievinski

Notified participants of WikiProject Physics

 Comment The proposed property will be applicable to fields outside of mathematics, so I welcome suggestions particullarly with regards to the domain and allowed values. The-erinaceous-one (talk) 04:21, 2 September 2020 (UTC)

 Comment Could the scope of calculated from (P4934) be generalized to "other terms mentioned in defining formula"? That's how I have understood it so far, say for magnetic flux density (Q30204) where the to-be-defined item does not appear simply on the left-hand-side and the formula can't be solved for it. How exactly would we choose between P4934 and the property proposed here? Toni 001 (talk) 08:37, 2 September 2020 (UTC)

@Toni 001: Modifying calculated from (P4934) might be a good alternative to creating a new property, especially since, as you note, the distinction between calculated from (P4934) and the proposed property would be fuzzy. One concern with going that route is that calculated from (P4934) might currently be used in cases where the defining formula is not given. Also, changing the label and description could be confusing for a lot of editors and would require updating the labels and discriptions in all the languages. But those are all switching costs and would be outweighed by the long term benefits of better-designed properties.

If we do modify calculated from (P4934), I suggest we use "other items in defining formula." @Okkn: as the creator of proposal for calculated from (P4934), perhaps you would like to weigh in on this too. The-erinaceous-one (talk) 17:37, 2 September 2020 (UTC)

I can agree with generalizing P4934. I don't think there will be any confusion. --Okkn (talk) 06:46, 4 September 2020 (UTC)

I added a comment to the property talk page. I do  Support this generalization. Toni 001 (talk) 09:13, 4 September 2020 (UTC)

Sounds good indeed. Feel free to edit label/description of P4934 to make sure it's understood by both mathematicians and other contributors. --- Jura 09:14, 4 September 2020 (UTC)

Great, I've modified the label and description of P4934 and have withdrawn this proposal. The-erinaceous-one (talk) 22:28, 4 September 2020 (UTC)