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 |
|---|---|
| Trichinellidae | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Wirtinger presentation of knot groups | Reidemeister moves NERFINISHED ⓘ |
| Brugia timori | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Trichinellida | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Placozoa | asymmetrical via predicate surface "symmetry" ⓘ |
| Gaussian orthogonal ensemble | invariant under orthogonal conjugation via predicate surface "invarianceProperty" ⓘ |
| Gaussian orthogonal ensemble | orthogonal group O(n) via predicate surface "hasSymmetryGroup" NERFINISHED ⓘ |
| Ctenophora | biradial symmetry via predicate surface "symmetry" ⓘ |
| Gaussian unitary ensemble | invariant under conjugation by unitary matrices via predicate surface "invarianceProperty" ⓘ |
| Gaussian symplectic ensemble | invariant under conjugation by compact symplectic group via predicate surface "hasInvariance" ⓘ |
| Gaussian symplectic ensemble | compact symplectic group Sp(N) via predicate surface "hasSymmetryGroup" ⓘ |
| Enteropneusta | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Dirichlet kernel | D_n(-x) = D_n(x) via predicate surface "symmetry" ⓘ |
| Ammotragus | bilateral symmetry via predicate surface "symmetry" ⓘ |
| distance covariance | orthogonal transformations of the data ⓘ |
| distance covariance | translations of the data ⓘ |
|
Hermitian forms (work on quadratic forms)
surface form:
Hermitian form
|
unitary change of basis ⓘ |
| Weyl denominator | Weyl group up to sign ⓘ |
| Weyl vector | Weyl group of the root system up to sign change under simple reflections ⓘ |
| Moyal product | linear symplectic transformations of phase space ⓘ |
| Dirac current | global U(1) transformations via predicate surface "isGaugeInvariantUnder" ⓘ |
| dAlembert operator | yes via predicate surface "LorentzInvariant" ⓘ |
| Donaldson–Witten theory | smooth deformations of the metric ⓘ |
| Witten–Reshetikhin–Turaev invariant | orientation-preserving homeomorphisms of 3-manifolds ⓘ |
| Witten–Reshetikhin–Turaev invariant | Kirby moves NERFINISHED ⓘ |
| Zone of Avoidance of the Milky Way | roughly symmetric about the Galactic plane via predicate surface "symmetry" ⓘ |
| Thurston norm | homeomorphisms of the 3-manifold ⓘ |
| Pythagorean identity in trigonometry | invariant under θ → −θ via predicate surface "symmetry" ⓘ |
| CEBAF Large Acceptance Spectrometer | azimuthally symmetric design via predicate surface "symmetry" ⓘ |
| Kobayashi metric | true via predicate surface "isHolomorphicallyInvariant" ⓘ |
| Kobayashi metric | biholomorphic maps via predicate surface "isInvariantUnder" ⓘ |
| Bergman metric | biholomorphic maps ⓘ |
| Bergman metric | automorphism group of the domain ⓘ |
| Lempert function on convex domains | biholomorphic mappings ⓘ |
| Lempert function on convex domains | holomorphic automorphisms of the domain ⓘ |
| Fermat surface | (μ_n)^4 / μ_n via predicate surface "hasSymmetryGroup" ⓘ |
| Fermat surface | S_4 via predicate surface "hasSymmetryGroup" ⓘ |
| Yoldiidae | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Yoldia | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Cartan–Killing form | inner automorphisms of Lie algebra via predicate surface "isInvariantUnder" ⓘ |
| Cartan–Killing form | adjoint action of Lie group via predicate surface "isInvariantUnder" ⓘ |
| Omni-Purpose Apparatus for LEP | approximately cylindrical geometry via predicate surface "symmetry" ⓘ |
| Senneh knot | asymmetrical via predicate surface "symmetry" ⓘ |
| Fubini–Study form | unitary group U(n+1) via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
| Fubini–Study form | projective unitary group PU(n+1) via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
| Fubini–Study form | holomorphic isometries of CP^n via predicate surface "isInvariantUnder" ⓘ |
| Fubini–Study form | action of U(n+1) on CP^n via predicate surface "isHomogeneousUnder" ⓘ |
| Kähler cone | biholomorphisms ⓘ |
|
Dolbeault cohomology classes
surface form:
Dolbeault cohomology class
|
biholomorphic maps ⓘ |
| de Rham cohomology | diffeomorphisms of manifolds ⓘ |