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 |
|---|---|
| Fefferman metric in several complex variables | CR automorphisms ⓘ |
| Poisson equation | invariant under Euclidean rotations via predicate surface "coordinateInvariance" ⓘ |
| Sylvester’s law of inertia | real change of basis by invertible matrices via predicate surface "isInvariantUnder" ⓘ |
| Sylvester’s law of inertia | congruence transformation A ↦ SᵀAS with S invertible and real via predicate surface "isInvariantUnder" ⓘ |
| Hodge Laplacian | Riemannian isometries via predicate surface "isInvariantUnder" ⓘ |
| buckminsterfullerene | Ih via predicate surface "hasSymmetryGroup" ⓘ |
| Hirzebruch genera | diffeomorphism of manifolds ⓘ |
| Hirzebruch genera | cobordism equivalence ⓘ |
| Rindler wedge | invariant under Lorentz boosts in one spatial direction via predicate surface "symmetry" ⓘ |
| Hausdorff dimension | bi-Lipschitz maps ⓘ |
| rhombicuboctahedron | octahedral symmetry via predicate surface "hasSymmetryGroup" ⓘ |
| rhombicosidodecahedron | icosahedral symmetry via predicate surface "hasSymmetryGroup" ⓘ |
| rhombicosidodecahedron | Ih via predicate surface "hasSymmetryGroup" ⓘ |
| Pontryagin classes | bundle isomorphism ⓘ |
| Jacobson radical | ring isomorphisms ⓘ |
| CPT theorem | combined CPT transformation via predicate surface "impliesInvarianceUnder" ⓘ |
| shape operator | invariant under ambient isometries via predicate surface "invarianceProperty" ⓘ |
| Pauli–Lubanski pseudovector | Poincaré group translations NERFINISHED ⓘ |
| Arf invariant | isometries of quadratic forms ⓘ |
| Arf invariant | stable equivalence of quadratic forms in characteristic two ⓘ |
| Arf invariant | knot concordance ⓘ |
| von Neumann neighborhood | regular lattices via predicate surface "isTranslationInvariantOn" ⓘ |
| von Neumann neighborhood | dihedral group of the square (D4) in 2D via predicate surface "hasSymmetryGroup" ⓘ |
| modular j-invariant | SL(2,Z) NERFINISHED ⓘ |
| modular j-invariant | modular group NERFINISHED ⓘ |
| Kauffman polynomial | ambient isotopy via predicate surface "isInvariantUnder" ⓘ |
| Kauffman polynomial | Reidemeister moves via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
|
T:z ↦ z+1
surface form:
T : z ↦ z + 1
|
q = e^{2πiz} coordinate via predicate surface "actsTriviallyOn" ⓘ |
| Euler top | rotation group SO(3) via predicate surface "hasSymmetryGroup" NERFINISHED ⓘ |
| Alexander polynomial | ambient isotopy of knots ⓘ |
| Alexander polynomial | Reidemeister moves NERFINISHED ⓘ |
| Makira thrush | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Bayes factor | reparameterization of model parameters ⓘ |
| Julia set | forward invariant under the defining map via predicate surface "invarianceProperty" ⓘ |
| Julia set | backward invariant under the defining map via predicate surface "invarianceProperty" ⓘ |
| Julia set | completely invariant under the defining map via predicate surface "invarianceProperty" ⓘ |
| Ichthyomyzon unicuspis | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Polyakov–Nambu–Jona-Lasinio model | approximate chiral symmetry via predicate surface "symmetry" ⓘ |
| Polyakov–Nambu–Jona-Lasinio model | center symmetry via Polyakov loop via predicate surface "symmetry" ⓘ |
| Jasus frontalis | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Riesz transforms | true via predicate surface "isTranslationInvariant" ⓘ |
| Mahalanobis distance | affine transformations of data ⓘ |
| Bayes optimality | equivalent reparameterizations of the model (given transformed prior and loss) ⓘ |
| Three Pagodas of Chongsheng Temple | triangular layout via predicate surface "symmetry" ⓘ |
| Wiwaxia | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Charnia masoni | fractal-like branching pattern via predicate surface "symmetry" ⓘ |
| Muraenolepididae | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Rangeomorphs | radial symmetry via predicate surface "symmetry" ⓘ |
| Rangeomorphs | bilateral-like symmetry in some taxa via predicate surface "symmetry" ⓘ |
| Frobenius conjugacy class | inner automorphisms of the Galois group via predicate surface "isInvariantUnder" ⓘ |