lift(NCMatrix) -- Lifts an NCMatrix

Synopsis

Function: lift
Usage:

L = lift M
Inputs:
- M, an instance of the type NCMatrix,
Optional inputs:
- Verify => ..., default value true,
Outputs:
- L, an instance of the type 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.
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    |
     | 2*x  2*y  2*z  2*w  |
     | 2*y  2*z  2*w  2*x  |
     | -3*x -3*y -3*z -3*w |
     | -3*y -3*z -3*w -3*x |

o4 : NCMatrix

i5 : ring N

o5 = B

o5 : NCQuotientRing

i6 : ring lift N

o6 = A

o6 : NCPolynomialRing

Ways to use this method: