Wikidata:Property proposal/is invariant under

‎is invariant under

Originally proposed at Wikidata:Property proposal/Natural science

   Done: is invariant under (P12457) (Talk and documentation)

Description	subject is preserved by this process / function / group of transformation
Represents	invariant (Q188211)
Data type	Item
Template parameter	For polyhedron, "symmetry" in en:Template:Infobox polyhedron.
Domain	item, invariant (Q188211), invariant (Q2370229), and more generally mathematical object (Q246672).
Allowed values	process (Q3249551), function (Q11348), group (Q83478), symmetry (Q12485)
Example 1	Gaussian curvature (Q945953)is invariant underisometry (Q740207)statement is subject of (P805)Theorema Egregium (Q1048874)
Example 2	mass (Q11423)is invariant underchemical reaction (Q36534)excluding (P1011)open system (Q898312)statement is subject of (P805)conservation of mass (Q483948)
Example 3	entropy (Q45003)is invariant underisentropic process (Q907271)
Example 4	graph property (Q722659)is invariant undergraph isomorphism (Q303100)
Example 5	knot invariant (Q1862434)is invariant underambient isotopy (Q2037595)
Example 6	dimension of a vector space (Q929302)is invariant underlinear isomorphism (Q77873528)
Example 7	n-sphere (Q306610)is invariant underorthogonal group (Q1783179)
Example 8	regular icosahedron (Q18015071)is invariant undericosahedral symmetry (Q5986738)
Example 9	variance (Q175199)is invariant undertranslation (Q211459)
Example 10	normal subgroup (Q743179)is invariant underconjugation (Q77980581)
Source	en:Invariant (mathematics) and en:Invariant (physics)
See also	point group (P589), space group (P690) for crystals.
Wikidata project	WikiProject Mathematics (Q8487137), WikiProject Physics (Q8487193)

Motivation

"A is invariant / constant under, or preserved / kept unchanged by B" is usually an important property of A, but currently the way to model this seems to be Ainstance of (P31)invariant (Q188211)of (P642)B involving the infamous of (P642). Another way I can think of is to say Bdoes not have effect (P7167)change (Q1150070)of (P642)A.

Some other notes:

1. When object is a symmetry, it might be possible to say regular icosahedron (Q18015071)has characteristic (P1552)icosahedral symmetry (Q5986738), but "symmetry" besides being a property can also mean the transformation itself (or the whole symmetry group (Q902019) of transformations), so I believe the "unchanged by" relation is more suitable than has characteristic (P1552), the latter also encouraging to use a "more specific property".
2. One might also consider the inverse property “is symmetry of / keeps constant / preserves”. It works well for the defining properties e.g. Equiareal map (Q5384436)preservesarea (Q11500) and isothermal process (Q486921)preservestemperature (Q11466), but this is in general one to many e.g. determinant (Q178546), trace (Q321102), and rank (Q656784) are invariant under change of basis (Q810255), and also many notable polyhedrons share the same symmetry type.
3. One might also consider separating the "symmetry group / has symmetry" property for geometric objects from this "is invariant under" property. I think there is no need because symmetry properties are defined as being invariant under certain transformations.

Would this be a useful property to have?

–HTinC23 (talk) 01:43, 6 February 2024 (UTC)

Discussion

•  Support, an important property for science.--Arbnos (talk) 09:03, 12 February 2024 (UTC)
•  Support Definitely an important mathematical property --YjM | _d^c 23:28, 12 February 2024 (UTC)
• @HTinC23, Arbnos, YjM:  Done as is invariant under (P12457). Regards, ZI Jony ^(Talk) 17:36, 16 February 2024 (UTC)