next | previous | forward | backward | up | top | index | toc | Macaulay2 website
AssociativeAlgebras :: ncBasis

ncBasis -- Returns a basis of an noncommutative ring in specified degrees.

Synopsis

Description

This command returns a basis (or minimal generating set, if the ground ring is not a field), of a graded noncommutative ring.

i1 : A = QQ<|x,y,z|>

o1 = A

o1 : FreeAlgebra
i2 : p = y*z + z*y - x^2

        2
o2 = - x  + y*z + z*y

o2 : A
i3 : q = x*z + z*x - y^2

            2
o3 = x*z - y  + z*x

o3 : A
i4 : r = z^2 - x*y - y*x

                    2
o4 = - x*y - y*x + z

o4 : A
i5 : I = ideal{p,q,r}

               2                     2                       2
o5 = ideal (- x  + y*z + z*y, x*z - y  + z*x, - x*y - y*x + z )

o5 : Ideal of A
i6 : B = A/I

o6 = B

o6 : FreeAlgebraQuotient
i7 : bas = ncBasis(4,B)

o7 = | y3x y4 yzyx yzy2 yzyz zy2x zy3 zyzx zyzy z2yx z2y2 z2yz z3x z3y z4 |

             1       15
o7 : Matrix B  <--- B

Ways to use ncBasis :

For the programmer

The object ncBasis is a method function with options.