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7.7.13.0. homogfacNthQWeyl_all
Procedure from library ncfactor.lib (see ncfactor_lib).

Usage:
homogfacNthQWeyl_all(h); h is a homogeneous polynomial in the n'th q-Weyl algebra with respect to the weight vector
[-1,...,-1,1,...,1].
\__ __/ \__ __/ \/ \/ n/2 n/2

Return:
list

Purpose:
Computes all factorizations of a homogeneous polynomial h in the n'th q-Weyl algebra

Theory:
homogfacNthQWeyl returns a list with lists representing each a factorization of the given,
[-1,...,-1,1,...,1]-homogeneous polynomial.

General assumptions:
- The basering is the nth Weyl algebra and has the form, that the first n variables represent x1, ..., xn, and the second n variables do represent the d1, ..., dn. - We have n parameters q_1,..., q_n given.

Example:
 
LIB "ncfactor.lib";
ring R = (0,q1,q2,q3),(x1,x2,x3,d1,d2,d3),dp;
matrix C[6][6] = 1,1,1,q1,1,1,
1,1,1,1,q2,1,
1,1,1,1,1,q3,
1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1;
matrix D[6][6] = 0,0,0,1,0,0,
0,0,0,0,1,0,
0,0,0,0,0,1,
-1,0,0,0,0,0,
0,-1,0,0,0,0,
0,0,-1,0,0,0;
def r = nc_algebra(C,D);
setring(r);
poly h =x1*x2^2*x3^3*d1*d2^2+x2*x3^3*d2;
homogfacNthQWeyl_all(h);
==> [1]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x2
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [2]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [3]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [4]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x2
==>    [7]:
==>       d2
==> [5]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       d2
==>    [4]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [6]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       d2
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [7]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       d2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [8]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       d2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [9]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x2
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [10]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [11]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x2
==>    [7]:
==>       d2
==> [12]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       d2
==>    [5]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [13]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [14]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [15]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [5]:
==>       x2
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [16]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [5]:
==>       x3
==>    [6]:
==>       x2
==>    [7]:
==>       d2
==> [17]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       d2
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [18]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [19]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [6]:
==>       x2
==>    [7]:
==>       d2
==> [20]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       d2
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [21]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [22]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [23]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [24]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [25]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [26]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [27]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x1*x2*d1*d2+1
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [28]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x1*x2*d1*d2+1
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [29]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x1*x2*d1*d2+1
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [30]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x1*x2*d1*d2+1
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [31]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [32]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [33]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [34]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [35]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [36]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [37]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       d2
==>    [5]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [38]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x3
==> [39]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [40]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2+1
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [41]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [42]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       d2
==>    [5]:
==>       x3
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [43]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [5]:
==>       x2
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [44]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [45]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [46]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [47]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [48]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [49]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==>    [7]:
==>       x3
==> [50]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       d2
==>    [7]:
==>       x3
==> [51]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x1*x2*d1*d2+1
==>    [6]:
==>       x3
==>    [7]:
==>       d2
==> [52]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [53]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       d2
==>    [6]:
==>       x3
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [54]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x2
==>    [6]:
==>       x1*x2*d1*d2+1
==>    [7]:
==>       d2
==> [55]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [56]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x3
==>    [4]:
==>       x2
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2+1
==>    [7]:
==>       d2
==> [57]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [58]:
==>    [1]:
==>       1
==>    [2]:
==>       x3
==>    [3]:
==>       x2
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2+1
==>    [7]:
==>       d2
==> [59]:
==>    [1]:
==>       1/(q2)
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       d2
==>    [7]:
==>       x1*x2*d1*d2-x1*d1+(q2)
==> [60]:
==>    [1]:
==>       1
==>    [2]:
==>       x2
==>    [3]:
==>       x3
==>    [4]:
==>       x3
==>    [5]:
==>       x3
==>    [6]:
==>       x1*x2*d1*d2+1
==>    [7]:
==>       d2
See also: homogfacFirstQWeyl; homogfacFirstQWeyl_all.