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.

Source code

The source code from which this documentation is derived is in the file SuperLinearAlgebra.m2.

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.
- 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.