Wikidata:Property proposal/is invariant under

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‎is invariant under

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Originally proposed at Wikidata:Property proposal/Natural science

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

Motivation

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"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)[reply]

Discussion

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