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Tensor

Category Documents

Page 1 of 1

DifferentialGeometry/Tensor/Christoffel
find the Christoffel symbols of the first or second kind for a metric tensor

DifferentialGeometry/Tensor/CovariantDerivative
calculate the covariant derivative of a tensor field with respect to a connection

DifferentialGeometry/Tensor/EinsteinTensor
calculate the Einstein tensor for a metric

DifferentialGeometry/Tensor/KroneckerDelta
find the Kronecker delta tensor of rank r

DifferentialGeometry/Tensor/RicciScalar
calculate the Ricci scalar for a metric

DifferentialGeometry/Tensor/PushPullTensor
transform a tensor from one manifold or coordinate system to another

DifferentialGeometry/Tensor/WeylTensor
calculate the Weyl curvature tensor of a metric

DifferentialGeometry/Tensor/CurvatureTensor
calculate the curvature tensor of a linear connection on the tangent bundle or on a vector bundle

DifferentialGeometry/Tensor/PetrovType
determine the Petrov type of the Weyl tensor

DifferentialGeometry/Tensor/SegreType
determine the Segre type of the trace-free Ricci tensor

DifferentialGeometry/Tensor/Laplacian
find the Laplacian of a differential form with respect to a metric.

DifferentialGeometry/Tensor/TensorBrackets
calculate the Schouten bracket and Frolicher-Nijenhuis brackets of tensor fields

DifferentialGeometry/Tensor/KillingVectors
calculate the Killing vectors for a given metric

DifferentialGeometry/Tensor/KillingYanoTensors
calculate the Killing-Yano tensors for a given connection or a given metric

DifferentialGeometry/Tensor/CanonicalTensors
create various standard tensors

DifferentialGeometry/Tensor/ContractIndices
contract the indices of a tensor

DifferentialGeometry/Tensor/GenerateSymmetricTensors
generate a list of symmetric tensors from a list of tensors

DifferentialGeometry/Tensor/GenerateTensors
generate a list of tensors from a list of lists of tensors

DifferentialGeometry/Tensor/HodgeStar
apply the Hodge star operator to a differential form

DifferentialGeometry/Tensor/InverseMetric
find the inverse of a metric tensor

DifferentialGeometry/Tensor/MetricDensity
use a metric tensor to create a scalar density of a given weight

DifferentialGeometry/Tensor/MultiVector
compute the alternating sum of the tensor product of a list of vector fields

DifferentialGeometry/Tensor/PermutationSymbol
create a permutation symbol

DifferentialGeometry/Tensor/PlebanskiTensor
calculate the Plebanski tensor from a trace-free rank 2 symmetric tensor, the Plebanski spinor from a symmetric (2, 2) spinor, the Plebanski Newman-Penrose coefficients from a table of Newman-Penrose Ricci coefficients

DifferentialGeometry/Tensor/QuadraticFormSignature
find the signature of a covariant, symmetric, rank 2 tensor

DifferentialGeometry/Tensor/RaiseLowerIndices
raise or lower a list of indices of a tensor

DifferentialGeometry/Tensor/RearrangeIndices
rearrange the argument/indices of a tensor

DifferentialGeometry/Tensor/SymmetrizeIndices
symmetrize or skew-symmetrize a list of tensor indices

DifferentialGeometry/Tensor/TensorInnerProduct
compute the inner product of two vectors, forms or tensors with respect to a given metric tensor

DifferentialGeometry/Tensor/Connection
define a linear connection on the tangent bundle or on a vector bundle

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