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7.5.12.0. 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
==> [2]:
==> x2
==> [3]:
==> x1*x2*d1*d2+1
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x3
==> [2]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x1*x2*d1*d2+1
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x3
==> [3]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x1*x2*d1*d2+1
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x3
==> [4]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x1*x2*d1*d2+1
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [5]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x3
==> [6]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x3
==> [7]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [8]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> d2
==> [7]:
==> x3
==> [9]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> x3
==> [7]:
==> d2
==> [10]:
==> [1]:
==> 1
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2+1
==> [7]:
==> d2
==> [11]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x3
==> [12]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x3
==> [13]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x1*x2*d1*d2+1
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [14]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> d2
==> [7]:
==> x3
==> [15]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> x3
==> [7]:
==> d2
==> [16]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2+1
==> [7]:
==> d2
==> [17]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> d2
==> [7]:
==> x3
==> [18]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x1*x2*d1*d2+1
==> [6]:
==> x3
==> [7]:
==> d2
==> [19]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2+1
==> [7]:
==> d2
==> [20]:
==> [1]:
==> 1
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> x1*x2*d1*d2+1
==> [7]:
==> d2
==> [21]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x2
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x3
==> [22]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x3
==> [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]:
==> x2
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [25]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x3
==> [26]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x3
==> [27]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [28]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> d2
==> [7]:
==> x3
==> [29]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> x3
==> [7]:
==> d2
==> [30]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x2
==> [7]:
==> d2
==> [31]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> d2
==> [4]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x3
==> [32]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> d2
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [6]:
==> x3
==> [7]:
==> x3
==> [33]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> d2
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [34]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> d2
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [35]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> d2
==> [5]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [6]:
==> x3
==> [7]:
==> x3
==> [36]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [37]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [38]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [39]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [40]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x2
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [41]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x2
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x3
==> [42]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x3
==> [43]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> d2
==> [44]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> d2
==> [7]:
==> x3
==> [45]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> x3
==> [7]:
==> d2
==> [46]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> x2
==> [7]:
==> d2
==> [47]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> d2
==> [5]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [6]:
==> x3
==> [7]:
==> x3
==> [48]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [49]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> d2
==> [5]:
==> x3
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [50]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [51]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [52]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x2
==> [4]:
==> x3
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [53]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [5]:
==> x2
==> [6]:
==> d2
==> [7]:
==> x3
==> [54]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [5]:
==> x2
==> [6]:
==> x3
==> [7]:
==> d2
==> [55]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [5]:
==> x3
==> [6]:
==> x2
==> [7]:
==> d2
==> [56]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> d2
==> [6]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [7]:
==> x3
==> [57]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> d2
==> [6]:
==> x3
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [58]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x2
==> [5]:
==> x3
==> [6]:
==> d2
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [59]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x1*x2*d1*d2-x1*d1+(q2)
==> [6]:
==> x2
==> [7]:
==> d2
==> [60]:
==> [1]:
==> 1/(q2)
==> [2]:
==> x3
==> [3]:
==> x3
==> [4]:
==> x3
==> [5]:
==> x2
==> [6]:
==> d2
==> [7]:
==> x1*x2*d1*d2-x1*d1+(q2)
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See also:
homogfacFirstQWeyl;
homogfacFirstQWeyl_all;
homogfacNthWeyl.
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