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Weight - Weight -- the difference of two weights

Synopsis

Description

i1 : R=rootSystemA(4)

o1 = RootSystem{...8...}

o1 : RootSystem
i2 : M=cartanMatrix R

o2 = | 2  -1 0  0  |
     | -1 2  -1 0  |
     | 0  -1 2  -1 |
     | 0  0  -1 2  |

              4       4
o2 : Matrix ZZ  <-- ZZ
i3 : p1=weight(R,M_0)

o3 = |  2 |
     | -1 |
     |  0 |
     |  0 |

       4
o3 : ZZ
i4 : p2=weight(R,M_1)

o4 = | -1 |
     |  2 |
     | -1 |
     |  0 |

       4
o4 : ZZ
i5 : p1-p2

o5 = |  3 |
     | -3 |
     |  1 |
     |  0 |

       4
o5 : ZZ

Ways to use this method: