spechtModuleElement -- the constructor for the class SpechtModuleElement

Synopsis

Usage:

spechtModuleElement(p,v)

spechtModuleElement(y,n)

spechtModuleElement(y,m)

spechtModueElement(y)
Inputs:
- y, an instance of the type YoungTableau, the label of the polytabloid
- n, an integer, a number. If not specified then it is assumed to be a 1.
- m, a rational number, a number. If not specified then it is assumed to be a 1.
- p, an instance of the type Partition, A partition that index a module
- v, a mutable hash table, A mutable hash table from a SpechtModuleElement
Outputs:
- an instance of the type SpechtModuleElement, an element of the form n*poly_y, where poly_y is the polytabloid labeled by the tableau y.

The basic constructor builds a SpechtModuleElement from just one polytabloid and its respective coefficient.

i1 : p = new Partition from {3,2,1}

o1 = Partition{3, 2, 1}

o1 : Partition

i2 : y = youngTableau(p,{2,0,3,4,5,1})

o2 = | 2 0 3 |
     | 4 5 |
     | 1 |

o2 : YoungTableau

i3 : spechtModuleElement(y,-2)

o3 = -2 | 2 0 3 |
        | 4 5 |
        | 1 |

o3 : SpechtModuleElement

i4 : spechtModuleElement(y)

o4 = | 2 0 3 |
     | 4 5 |
     | 1 |

o4 : SpechtModuleElement