homepage: https://github.com/nilsalex/safe-tensor#readme
changelog-type: markdown
hash: 9803b51c95bacb065c95360e387ced73d513d0e90a7ce23f7079cb8747857dea
test-bench-deps: {}
maintainer: nils.alex@fau.de
synopsis: Dependently typed tensor algebra
changelog: |
  # Changelog

  ## [0.1.0.0] - 2020-07-07
  Initial release.
basic-deps:
  base: '>=4.7 && <5'
  constraints: '>=0.10 && <0.13'
  containers: '>=0.6 && <0.7'
  singletons: '>=2.5 && <2.8'
  mtl: '>=2.2 && <2.3'
  hmatrix: '>=0.20 && <0.21'
all-versions:
- 0.1.0.0
author: Nils Alex
latest: 0.1.0.0
description-type: markdown
description: |
  # 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.
license-name: MIT

Update from Hackage at 2020-07-07T18:58:23Z
Update from Hackage at 2020-07-07T18:58:23Z
