NCRingMap _ ZZ -- Matrix of one homogeneous component of an NCRingMap

Synopsis

Operator: _
Usage:

f_n
Inputs:
- f, an instance of the type NCRingMap,
- n, an integer,
Outputs:
- a matrix,

Description

This method returns the homogeneous degree n component of the ring map f. The output is the matrix (over the coefficient ring of the target) of the component map relative to the monomial bases for the source and target.

i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{w,x,y,z})
--Calling Bergman for NCGB calculation.
Complete!

o1 = A

o1 : NCQuotientRing

i2 : setWeights(A,{1,1,2,2})

o2 = A

o2 : NCQuotientRing

i3 : f = ncMap(A,A,{x,w,z,y})

o3 = NCRingMap A <--- A

o3 : NCRingMap

i4 : basis(1,A)

o4 = | w x |

o4 : NCMatrix

i5 : f_1

o5 = | 0 1 |
     | 1 0 |

              2        2
o5 : Matrix QQ  <--- QQ

i6 : basis(2,A)

o6 = | y z w^2 w*x x^2 |

o6 : NCMatrix

i7 : f_2

o7 = | 0 1 0 0  0 |
     | 1 0 0 0  0 |
     | 0 0 0 0  1 |
     | 0 0 0 -1 0 |
     | 0 0 1 0  0 |

              5        5
o7 : Matrix QQ  <--- QQ

Ways to use this method:

NCRingMap _ ZZ -- Matrix of one homogeneous component of an NCRingMap