lift(NCMatrix) -- Lifts an NCMatrix

Synopsis

Usage:
L = lift M
Function: lift
Inputs:
- M, an object of class NCMatrix
Optional inputs:
- Verify => ...,
Outputs:
- L, an object of class NCMatrix

Description

This command lifts an NCMatrix to a matrix over its ambient NCRing.

i1 : A = QQ{x,y,z,w}

o1 = A

o1 : NCPolynomialRing

i2 : B = A/ncIdeal{y*z + z*y - x^2, x*z + z*x - y^2, z^2 - x*y - y*x}
--Calling Bergman for NCGB calculation.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12252-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12252-0/3.ter ... Complete!

o2 = B

o2 : NCQuotientRing

i3 : M = ncMatrix {{x,y,z,w},{y,z,w,x}}

o3 = | x  y  z  w |
     |            |
     | y  z  w  x |

o3 : NCMatrix

i4 : N = M || 2*M || -3*M

o4 = |  x    y    z    w  |
     |                    |
     |  y    z    w    x  |
     |                    |
     |  2x   2y   2z   2w |
     |                    |
     |  2y   2z   2w   2x |
     |                    |
     | -3x  -3y  -3z  -3w |
     |                    |
     | -3y  -3z  -3w  -3x |

o4 : NCMatrix

i5 : ring N

o5 = B

o5 : NCQuotientRing

i6 : ring lift N

o6 = A

o6 : NCPolynomialRing