qTensorProduct -- Define the (q-)commuting tensor product

Synopsis

Usage:

C = qTensorProduct(A,B,q)
Inputs:
- A, an instance of the type NCRing,
- B, an instance of the type NCRing,
- q, a ring element,
Outputs:
- C, an instance of the type NCRing,

Description

This function returns the algebra that contains A and B as a subalgebra, with the commutation law on the images of A and B given by a*b = q*b*a for all a in A and b in B. In the case of A ** B, q = 1.

i1 : A = QQ{x,y}

o1 = A

o1 : NCPolynomialRing

i2 : B = skewPolynomialRing(QQ,(-1)_QQ, {a,b})
--Calling Bergman for NCGB calculation.
Complete!

o2 = B

o2 : NCQuotientRing

i3 : C = qTensorProduct(A,B,-1_QQ)
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!

o3 = C

o3 : NCQuotientRing

i4 : ideal C

o4 = Two-sided ideal {ba+ab, ax+xa, bx+xb, ay+ya, by+yb}

o4 : NCIdeal

i5 : D = A ** B
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!

o5 = D

o5 : NCQuotientRing

i6 : ideal D

o6 = Two-sided ideal {ba+ab, ax-xa, bx-xb, ay-ya, by-yb}

o6 : NCIdeal

Ways to use qTensorProduct :

qTensorProduct(NCRing,NCRing,QQ)
qTensorProduct(NCRing,NCRing,RingElement)
qTensorProduct(NCRing,NCRing,ZZ)

For the programmer

The object qTensorProduct is a method function.