SuperMatrix -- Makes a super matrix from its four blocks.

Synopsis

Usage:

G = superMatrixGenerator(M1, M2, M3, M4)
Inputs:
- M1, a matrix,
- M2, a matrix,
- M3, a matrix,
- M4, a matrix,
Outputs:
- G, an instance of the type SuperMatrix,

Description

Let $M_1, M_2, M_3, M_4$ be four matrices. The number of rows in $M_1$ and $M_2$, and those of $M_3$ and $M_4$ should be equal. Also, the number of columns of $M_1$ and $M_3$, and those of M_2 and M_4 must be equal.

The idea is to define a (super) Matrix, which can be considered as $p|q\times r|s$ matrix. This super Matrix can be a morphism between super modules $A^{p|q}$ and $A^{r|s}$ over super algebra $A$.

The function uses four matrices M_1 and M_2, and also M_3 and M_4 as four blocks of a new matrix, say $\begin{pmatrix} M1&M2\\ M3&M4\end{pmatrix}$.

The key supermatrix shows the result matrix created as above.

i1 : M1 = matrix {{1, 2}, {5, 6}, {9, 10}}

o1 = | 1 2  |
     | 5 6  |
     | 9 10 |

              3       2
o1 : Matrix ZZ  <-- ZZ

i2 : M2 = matrix {{3, 4}, {7, 8}, {11, 12}}

o2 = | 3  4  |
     | 7  8  |
     | 11 12 |

              3       2
o2 : Matrix ZZ  <-- ZZ

i3 : M3 = matrix {{13, 14}, {17, 18}}

o3 = | 13 14 |
     | 17 18 |

              2       2
o3 : Matrix ZZ  <-- ZZ

i4 : M4 = matrix {{15, 16}, {19, 20}}

o4 = | 15 16 |
     | 19 20 |

              2       2
o4 : Matrix ZZ  <-- ZZ

i5 : G = superMatrixGenerator(M1, M2, M3, M4)

o5 = SuperMatrix{...1...}

o5 : SuperMatrix

i6 : G.supermatrix

o6 = | 1  2  3  4  |
     | 5  6  7  8  |
     | 9  10 11 12 |
     | 13 14 15 16 |
     | 17 18 19 20 |

              5       4
o6 : Matrix ZZ  <-- ZZ

Caveat

Methods that use an object of class SuperMatrix :

berezinian(SuperMatrix,Ring) -- see berezinian -- Computes the berezinian of a supermatrix.
inverseSuperMatrix(SuperMatrix,Ring) -- see inverseSuperMatrix -- The inverse of a super matrix.
superMatrixParity(SuperMatrix,Ring,List) -- see superMatrixParity -- parity of a super Matrix.
superTrace(SuperMatrix,Ring,List) -- see superTrace -- Super trace of a homogeneous super matrix.

For the programmer

The object SuperMatrix is a type, with ancestor classes MutableHashTable < HashTable < Thing.