safe-tensor: Dependently typed tensor algebra

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Please see the README on GitHub at https://github.com/nilsalex/safe-tensor#readme

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Modules

[Last Documentation]

Math
- Math.Tensor
  - Math.Tensor.Basic
    - Math.Tensor.Basic.Area
    - Math.Tensor.Basic.Delta
    - Math.Tensor.Basic.Epsilon
    - Math.Tensor.Basic.Sym2
    - Math.Tensor.Basic.TH
  - Math.Tensor.LinearAlgebra
    - Math.Tensor.LinearAlgebra.Equations
    - Math.Tensor.LinearAlgebra.Matrix
    - Math.Tensor.LinearAlgebra.Scalar
  - Math.Tensor.Safe
    - Math.Tensor.Safe.Proofs
    - Math.Tensor.Safe.TH
    - Math.Tensor.Safe.Vector

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safe-tensor-0.1.0.0.tar.gz [browse] (Cabal source package)
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Candidates

0.1.0.0, 0.2.0.0, 0.2.1.0, 0.2.1.1

Versions [RSS]	0.1.0.0, 0.2.0.0, 0.2.1.0, 0.2.1.1
Change log	CHANGELOG.md
Dependencies	base (>=4.7 && <5), constraints (>=0.10 && <0.13), containers (>=0.6 && <0.7), hmatrix (>=0.20 && <0.21), mtl (>=2.2 && <2.3), singletons (>=2.5 && <2.8) [details]
License	MIT
Copyright	2020 Nils Alex
Author	Nils Alex
Maintainer	nils.alex@fau.de
Category	Math
Home page	https://github.com/nilsalex/safe-tensor#readme
Bug tracker	https://github.com/nilsalex/safe-tensor/issues
Source repo	head: git clone https://github.com/nilsalex/safe-tensor
Uploaded	by nalex at 2020-07-07T18:55:17Z
Distributions
Downloads	674 total (15 in the last 30 days)
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Status	Docs not available [build log] All reported builds failed as of 2020-07-07 [all 2 reports]

Readme for safe-tensor-0.1.0.0

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safe-tensor

Dependently typed tensor algebra in Haskell. Useful for applications in field theory, e.g., carrying out calculations for https://doi.org/10.1103/PhysRevD.101.084025

Rationale

Tensor calculus is reflected in the type system. Let us view a tensor as a multilinear map from a product of vector spaces and duals thereof to the common field. The type of each tensor is its generalized rank, describing the vector spaces it acts on and assigning a label to each vector space. There are a few rules for tensor operations:

Only tensors of the same type may be added. The result is a tensor of this type.
Tensors may be multiplied if the resulting generalized rank does not contain repeated labels for the same (dual) vector space.
The contraction of a tensors removes pairs of vector space and dual vector space with the same label from the generalized rank.

It is thus impossible to perform inconsistent tensor operations.

There is also an existentially typed variant of the tensor type useful for runtime computations. These computations take place in the Error monad, throwing errors if operand types are not consistent.