invariantUnder
P4235
predicate
Indicates that a property, structure, or quantity remains unchanged when a specified transformation or operation is applied.
All labels observed (31)
| Label | Occurrences |
|---|---|
| symmetry | 110 |
| invariantUnder canonical | 107 |
| isInvariantUnder | 36 |
| hasSymmetryGroup | 18 |
| invarianceProperty | 8 |
| isTranslationInvariant | 3 |
| invariance | 2 |
| isGaugeInvariantUnder | 2 |
| isScalarInvariantUnder | 2 |
| metricPreserved | 2 |
| symmetryConstraint | 2 |
| LorentzInvariant | 1 |
| actsTriviallyOn | 1 |
| coordinateInvariance | 1 |
| hasInvariance | 1 |
| impliesInvarianceUnder | 1 |
| invarianceGroup | 1 |
| isAreaPreservingBecause | 1 |
| isConformalInvariant | 1 |
| isConformallyInvariant | 1 |
| isHolomorphicallyInvariant | 1 |
| isHomogeneousUnder | 1 |
| isInvariant | 1 |
| isRotationInvariant | 1 |
| isTimeReversalInvariant | 1 |
| isTranslationInvariantOn | 1 |
| preservesBoundedness | 1 |
| preservesClosedness | 1 |
| preservesConvexity | 1 |
| preservesSmoothStructure | 1 |
| shiftInvariance | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: invariantUnder
Generated description
Indicates that a property, structure, or quantity remains unchanged when a specified transformation or operation is applied.
Sample triples (312)
| Subject | Object |
|---|---|
| Shannon entropy | relabeling of outcomes ⓘ |
| Einstein field equations | general coordinate transformations ⓘ |
| Chordata | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Janet–Cartan theorem | Riemannian distance locally via predicate surface "metricPreserved" ⓘ |
| Janet–Cartan theorem | inner products of tangent vectors via predicate surface "metricPreserved" ⓘ |
| Kretschmann scalar | general coordinate transformations via predicate surface "isScalarInvariantUnder" ⓘ |
| Kretschmann scalar |
Lorentz transformations
via predicate surface "isScalarInvariantUnder"
ⓘ
linked to:
Lorentz transformation
|
| Minkowski space-time | Poincaré group via predicate surface "hasSymmetryGroup" ⓘ |
| de Sitter spacetime | SO(1,4) via predicate surface "hasSymmetryGroup" ⓘ |
| de Sitter spacetime | true via predicate surface "isTimeReversalInvariant" ⓘ |
| S-matrix | Poincaré invariance via predicate surface "symmetryConstraint" ⓘ |
| S-matrix | internal symmetries of the theory via predicate surface "symmetryConstraint" ⓘ |
| Echinodermata | radial symmetry in adults via predicate surface "symmetry" ⓘ |
| Minkowski sum | true via predicate surface "preservesConvexity" ⓘ |
| Minkowski sum | true via predicate surface "preservesClosedness" ⓘ |
| Minkowski sum | true via predicate surface "preservesBoundedness" ⓘ |
| Minkowski sum | true via predicate surface "isTranslationInvariant" ⓘ |
| Minkowski functional | scaling of the defining set by positive constants up to equivalence ⓘ |
| Annelida | bilateral via predicate surface "symmetry" ⓘ |
| Deuterostomia | bilateral symmetry in early development via predicate surface "symmetry" ⓘ |
| Euclidean space | Euclidean group via predicate surface "hasSymmetryGroup" ⓘ |
| Planck constant | Lorentz invariant via predicate surface "isInvariant" ⓘ |
| Galilean relativity | Galilean group via predicate surface "hasSymmetryGroup" ⓘ |
| Ricci flow | diffeomorphisms ⓘ |
| Ricci flow | pullback by diffeomorphisms ⓘ |
| Pacific-Antarctic Ridge | magnetic stripe anomalies on seafloor via predicate surface "symmetry" ⓘ |
| Ricci scalar | diffeomorphisms via predicate surface "isInvariantUnder" ⓘ |
| Steinmetz solid | symmetric with respect to coordinate planes containing cylinder axes via predicate surface "symmetry" ⓘ |
| Steinmetz solid | invariant under 90-degree rotations exchanging cylinder axes via predicate surface "symmetry" ⓘ |
| Thaliacea | bilateral symmetry via predicate surface "symmetry" ⓘ |
| CDF detector | approximately cylindrical via predicate surface "symmetry" ⓘ |
| DØ detector | nearly hermetic via predicate surface "symmetry" ⓘ |
| Asymmetron | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Hydrozoa | radial symmetry via predicate surface "symmetry" ⓘ |
| Anthozoa | radial symmetry via predicate surface "symmetry" ⓘ |
| Arachnida | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Myriapoda | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Kronecker delta | δ_ij = δ_ji via predicate surface "symmetry" ⓘ |
| Xenacoelomorpha | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Concepción | nearly perfect cone via predicate surface "symmetry" ⓘ |
| Dirac Lagrangian | global U(1) phase transformations of ψ via predicate surface "isInvariantUnder" ⓘ |
| Euclidean metric | Euclidean isometries ⓘ |
| Euclidean metric | translations ⓘ |
| Euclidean metric | rotations ⓘ |
| Euclidean metric | orthogonal transformations ⓘ |
| Carathéodory metric | biholomorphic maps via predicate surface "isInvariantUnder" ⓘ |
| Carathéodory metric | holomorphic automorphisms of the domain via predicate surface "isInvariantUnder" ⓘ |
| Carathéodory metric | true via predicate surface "isConformalInvariant" ⓘ |
| Fermat point | similarity transformations of the triangle ⓘ |
| Fermat point | rigid motions of the plane ⓘ |