# Wikidata:Property proposal/defined in terms of

### other items in defining formula

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

defined in terms of
divergence (Q189000)
 in defining formula (P7235) ${\displaystyle \nabla \cdot }$
0 references

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

#### Discussion

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)