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.

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 .