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 |
|---|---|
| Fermat curve | group of permutations of coordinates and n-th roots of unity via predicate surface "hasSymmetryGroup" ⓘ |
| Fountain Court | axial symmetry via predicate surface "symmetry" ⓘ |
| OPAL | azimuthally symmetric design via predicate surface "symmetry" ⓘ |
| Kähler form | complex structure J via predicate surface "isInvariantUnder" ⓘ |
| Kähler form | holomorphic isometries via predicate surface "isInvariantUnder" ⓘ |
| LHC insertion region for CMS | approximately symmetric around interaction point via predicate surface "symmetry" ⓘ |
| Laplace operator | invariant under Euclidean isometries via predicate surface "invariance" ⓘ |
| Laplace operator | rotation invariant in Euclidean space via predicate surface "invariance" ⓘ |
| Stokes parameters | global phase change of electromagnetic field ⓘ |
| Poincaré–Hopf theorem | homotopy of vector fields avoiding creation or annihilation of zeros on the boundary ⓘ |
| Bernoulli lemniscate | symmetric with respect to the x-axis via predicate surface "symmetry" ⓘ |
| Bernoulli lemniscate | symmetric with respect to the y-axis via predicate surface "symmetry" ⓘ |
| Bernoulli lemniscate | symmetric with respect to the origin via predicate surface "symmetry" ⓘ |
| Minkowski interval |
Lorentz transformation
ⓘ
surface form:
Lorentz transformations
|
| Minkowski interval |
Poincaré group
ⓘ
surface form:
Poincaré transformations
|
| Minkowski interval | boosts ⓘ |
| Minkowski interval | spatial rotations ⓘ |
| Minkowski interval | spacetime translations ⓘ |
| spin Casimir operator |
Lorentz transformation
ⓘ
surface form:
Lorentz transformations
|
| spin Casimir operator |
Poincaré group
ⓘ
surface form:
Poincaré transformations
|
| Weingarten map | isometries of the ambient Euclidean space ⓘ |
| Moore neighborhood | rotational symmetry of order 4 in 2D via predicate surface "symmetry" ⓘ |
| Moore neighborhood | reflection symmetry across grid axes via predicate surface "symmetry" ⓘ |
| Jones polynomial | ambient isotopy of links ⓘ |
| Jones polynomial | Reidemeister moves ⓘ |
| Farey tessellation | modular group PSL(2,Z) via predicate surface "isInvariantUnder" ⓘ |
| Farey tessellation | group SL(2,Z) acting projectively via predicate surface "isInvariantUnder" ⓘ |
| Farey tessellation |
modular group PSL(2,Z)
via predicate surface "hasSymmetryGroup"
ⓘ
surface form:
PSL(2,Z)
|
| Noether field | action of G via predicate surface "isInvariantUnder" ⓘ |
| HOMFLY-PT polynomial | ambient isotopy ⓘ |
| HOMFLY-PT polynomial | Reidemeister moves ⓘ |
| Kolmogorov distance | monotone transformations of the underlying variable that preserve order ⓘ |
| Kolmogorov complexity | different universal Turing machines change complexity by at most an additive constant via predicate surface "invarianceProperty" ⓘ |
| Nambu–Goto action | worldsheet diffeomorphisms ⓘ |
| Nambu–Goto action | worldsheet reparametrizations ⓘ |
| Nambu–Goto action | target-space Lorentz transformations ⓘ |
| Menger sponge | symmetry group of the cube via predicate surface "hasSymmetryGroup" ⓘ |
| Menger curvature |
Euclidean group
ⓘ
surface form:
Euclidean isometries
|
| Menger curvature | similarity transformations up to scaling ⓘ |
| Villa Almerico Capra | perfectly symmetrical layout via predicate surface "symmetry" ⓘ |
| Charniodiscus | fractal-like branching pattern via predicate surface "symmetry" ⓘ |
| Fractofusus | fractal-like branching via predicate surface "symmetry" ⓘ |
| Tribrachidium | tri-radial symmetry via predicate surface "symmetry" ⓘ |
| Pteridinium | glide reflection symmetry via predicate surface "symmetry" ⓘ |
| Moringuidae | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Pleuronectidae | asymmetrical in adults via predicate surface "symmetry" ⓘ |
| Cynoglossidae | asymmetrical in adults via predicate surface "symmetry" ⓘ |
| Hellinger distance | measure-preserving transformations ⓘ |
| Tsallis divergence | relabeling of outcomes ⓘ |
| Bardeen potential | linearized coordinate transformations via predicate surface "isGaugeInvariantUnder" ⓘ |