Sophie

Sophie

distrib > Fedora > 15 > i386 > by-pkgid > 7ebd25ac536d248d499a3ce2acda963a > files > 6274

Macaulay2-1.3.1-8.fc15.i686.rpm

-- -*- M2-comint -*- {* hash: -1005542008 *}

i1 : M=QQ^3;

i2 : scan(4, i-> << i+1 << "-th symmetric power of M = " << schurModule({i+1},M) << endl)
                              3
1-th symmetric power of M = QQ
                              6
2-th symmetric power of M = QQ
                              10
3-th symmetric power of M = QQ
                              15
4-th symmetric power of M = QQ

i3 : S = schurModule({3,2,1}, M);

i4 : v = sum(numgens S, i-> (i+1)*S_i) -- an element of S represented by a vector

o4 = | 1 |
     | 2 |
     | 3 |
     | 4 |
     | 5 |
     | 6 |
     | 7 |
     | 8 |

       8
o4 : QQ

i5 : printSchurModuleElement(v, S);
  +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+
1*|0|0|0| 2*|0|0|1| 3*|0|0|2| 4*|0|0|0| 5*|0|0|1| 6*|0|0|2| 7*|0|1|1| 8*|0|1|2| 
  |1|1| |   |1|1| |   |1|1| |   |1|2| |   |1|2| |   |1|2| |   |1|2| |   |1|2| |
  |2| | |   |2| | |   |2| | |   |2| | |   |2| | |   |2| | |   |2| | |   |2| | |
  +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+   +-+-+-+

i6 :