|
 |
 |
 |
 |
 |
 |
 |
 |
 |
7.7.13.0. facShift
Procedure from libraryncfactor.lib (see ncfactor_lib).
- Usage:
- facShift(h); h a polynomial in the n'th shift algebra
- Return:
- list
- Purpose:
- compute all factorizations of a polynomial in the nth shift
algebra
- Theory:
- h is mapped to the $n$th Weyl algebra and then factorized
there. The factorizations are mapped back (S_n in subalgebra
of Weyl algebra).
- Assume:
- basering is the nth shift algebra
- Note:
- Every entry of the output list is a list with factors for one possible factorization.
LIB "ncfactor.lib"; ring R = 0,(x1,x2,s1,s2),dp; matrix C[4][4] = 1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1; matrix D[4][4] = 0,0,s1,0, 0,0,0,s2, -s1,0,0,0, 0,-s2,0,0; def r = nc_algebra(C,D); setring(r); poly h = x1*(x1+1)*s1^2-2*x1*(x1+100)*s1+(x1+99)*(x1+100); facShift(h); ==> [1]: ==> [1]: ==> 1 ==> [2]: ==> x1*s1-x1+s1-100 ==> [3]: ==> x1*s1-x1-s1-99 ==> [2]: ==> [1]: ==> 1 ==> [2]: ==> x1*s1-x1-100 ==> [3]: ==> x1*s1-x1-99 ==> [3]: ==> [1]: ==> 1 ==> [2]: ==> x1*s1-x1-99 ==> [3]: ==> x1*s1-x1-100 |