SuperLinearAlgebra -- Package for super algebra

Description

This Package is to do the computation in superalgebras, or super vector spaces.

The computations are taken in a superRing, which is a ring with both symmetric and antisymmetric variables.

To see the definitions and theorems, see Varadarajan, V. S. (2004). "Supersymmetry for Mathematicians: An Introduction" (Vol. 11). American Mathematical Soc.

Caveat

Authors

Version

This documentation describes version 0.1 of SuperLinearAlgebra.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SuperLinearAlgebraSource,
  title = {{SuperLinearAlgebra: computations related to supermatrices. Version~0.1}},
  author = {Fereshteh Bahadorykhalily and Fatemeh Tarashi Kashani},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Types
- SuperMatrix -- Makes a super matrix from its four blocks.
Functions and commands
- berezinian -- Computes the berezinian of a supermatrix.
- inverseSuperMatrix -- The inverse of a super matrix.
- parity -- parity of an element of a super ring.
- superMatrixGenerator -- see SuperMatrix -- Makes a super matrix from its four blocks.
- superMatrixParity -- parity of a super Matrix.
- superRing -- Makes a super ring from two polynomial rings.
- superTrace -- Super trace of a homogeneous super matrix.
Methods
- berezinian(SuperMatrix,Ring) -- see berezinian -- Computes the berezinian of a supermatrix.
- inverseSuperMatrix(SuperMatrix,Ring) -- see inverseSuperMatrix -- The inverse of a super matrix.
- parity(RingElement,Ring,List) -- see parity -- parity of an element of a super ring.
- parity(Number,Ring,List) (missing documentation)
- superMatrixGenerator(Matrix,Matrix,Matrix,Matrix) -- see SuperMatrix -- Makes a super matrix from its four blocks.
- superMatrixParity(SuperMatrix,Ring,List) -- see superMatrixParity -- parity of a super Matrix.
- superRing(PolynomialRing,PolynomialRing) -- see superRing -- Makes a super ring from two polynomial rings.
- superTrace(SuperMatrix,Ring,List) -- see superTrace -- Super trace of a homogeneous super matrix.
Symbols
- supermatrix -- see SuperMatrix -- Makes a super matrix from its four blocks.

For the programmer

The object SuperLinearAlgebra is a package, defined in SuperLinearAlgebra.m2.

The source of this document is in SuperLinearAlgebra.m2:405:0.