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 |
|---|---|
| Betti numbers | homeomorphism ⓘ |
| Betti numbers | homotopy equivalence ⓘ |
| Hilbert polynomial | projective isomorphism ⓘ |
| Saurenchelys | bilateral via predicate surface "symmetry" ⓘ |
| Stemonidium | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Plebański's heavenly equations | holomorphic coordinate transformations ⓘ |
| Bos namadicus | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Riemann xi function | even with respect to s = 1/2 via predicate surface "symmetry" ⓘ |
| Riemann xi function | ξ(1/2 + z) = ξ(1/2 - z) via predicate surface "symmetry" ⓘ |
| Riemann xi function | s ↦ 1-s ⓘ |
| Riemann xi function | complex conjugation combined with reflection across Re(s) = 1/2 ⓘ |
| Lepidopsetta bilineata | asymmetrical adult body via predicate surface "symmetry" ⓘ |
| Glyptocephalus cynoglossus | asymmetrical adult body via predicate surface "symmetry" ⓘ |
| Chascanopsetta | asymmetrical via predicate surface "symmetry" ⓘ |
| Parabothus | asymmetrical via predicate surface "symmetry" ⓘ |
| Psettina | asymmetrical via predicate surface "symmetry" ⓘ |
| Trichopsetta | asymmetrical in adult stage via predicate surface "symmetry" ⓘ |
| Syacium | asymmetrical adult body via predicate surface "symmetry" ⓘ |
| Psetta maxima | asymmetrical adult body via predicate surface "symmetry" ⓘ |
| Paraplagusia | asymmetrical body plan via predicate surface "symmetry" ⓘ |
| Symphurus | asymmetrical adult body via predicate surface "symmetry" ⓘ |
| Cynoglossus lingua | asymmetrical via predicate surface "symmetry" ⓘ |
| Labichthys carinatus | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Gröbner fan | change of coordinates preserving the ideal ⓘ |
| Herbrand quotient | isomorphisms of G-modules ⓘ |
| Podothecus accipenserinus | bilateral via predicate surface "symmetry" ⓘ |
| Chitonotidae | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Busemann function | reparametrization of the geodesic ray by additive constants ⓘ |
|
Chern–Simons forms
surface form:
Chern–Simons form
|
bundle isomorphism up to exact forms ⓘ |
| graphene | hexagonal symmetry via predicate surface "symmetry" ⓘ |
| GRS80 | axisymmetric via predicate surface "symmetry" ⓘ |
| Tate pairing | isogenies up to isomorphism ⓘ |
| Maslov index | homotopy with fixed endpoints ⓘ |
| Melanatherina | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Euleptorhamphus | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Petalichthys | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Drinfeld associators | gauge transformations up to equivalence ⓘ |
| John ellipsoid | affine transformations of the ambient space (up to image of the transformation) ⓘ |
| Hexapoda | bilateral symmetry via predicate surface "symmetry" ⓘ |
| Tutte polynomial | graph isomorphism via predicate surface "isInvariantUnder" ⓘ |
| Tutte polynomial | matroid isomorphism via predicate surface "isInvariantUnder" ⓘ |
| Arnold cat map | its defining matrix has determinant 1 via predicate surface "isAreaPreservingBecause" ⓘ |
| Weil–Petersson metric | mapping class group via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
| Teichmüller metric | mapping class group action via predicate surface "isInvariantUnder" ⓘ |
| Teichmüller metric | biholomorphic automorphisms of Teichmüller space via predicate surface "isInvariantUnder" ⓘ |
| Poincaré metric | biholomorphic automorphisms via predicate surface "isInvariantUnder" ⓘ |
| Poincaré metric | Möbius transformations preserving the domain via predicate surface "isInvariantUnder" ⓘ |
| Poincaré metric | PSL(2,R) via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
| Poincaré metric | SU(1,1) via predicate surface "isInvariantUnder" NERFINISHED ⓘ |
|
Weierstrass points
surface form:
Weierstrass point
|
automorphisms of the curve ⓘ |