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___N__C__Matrix.out
-- -*- M2-comint -*- hash: 14385727256224654643 i1 : A = QQ{a,b,c,d} o1 = A o1 : NCPolynomialRing i2 : M = ncMatrix {{a,b,c,d}} o2 = | a b c d | o2 : NCMatrix i3 : N = ncMatrix {{M,2*M,3*M},{4*M,5*M,6*M}} o3 = | a b c d 2*a 2*b 2*c 2*d 3*a 3*b 3*c 3*d | | 4*a 4*b 4*c 4*d 5*a 5*b 5*c 5*d 6*a 6*b 6*c 6*d | o3 : NCMatrix i4 : B = QQ{x,y,z} o4 = B o4 : NCPolynomialRing i5 : f = y*z + z*y - x^2 2 o5 = zy+yz-x o5 : B i6 : g = x*z + z*x - y^2 2 o6 = zx-y +xz o6 : B i7 : h = z^2 - x*y - y*x 2 o7 = z -yx-xy o7 : B i8 : I = ncIdeal {f,g,h} 2 2 2 o8 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy} o8 : NCIdeal i9 : Igb = ncGroebnerBasis I --Calling Bergman for NCGB calculation. Complete! 2 2 2 o9 = y x-xy ; Lead Term = (y x, 1) 2 2 2 yx -x y; Lead Term = (yx , 1) 2 zx-y +xz; Lead Term = (zx, 1) 2 zy+yz-x ; Lead Term = (zy, 1) 2 2 z -yx-xy; Lead Term = (z , 1) o9 : NCGroebnerBasis i10 : M = ncMatrix {{x, y, z}} o10 = | x y z | o10 : NCMatrix i11 : sigma = ncMap(B,B,{y,z,x}) o11 = NCRingMap B <--- B o11 : NCRingMap i12 : N = ncMatrix {{M},{sigma M}, {sigma sigma M}} o12 = | x y z | | y z x | | z x y | o12 : NCMatrix i13 : Nred = N^3 % Igb o13 = | -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 | | y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y | | 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 | o13 : NCMatrix i14 : C = B/I o14 = C o14 : NCQuotientRing i15 : phi = ncMap(C,B,gens C) o15 = NCRingMap C <--- B o15 : NCRingMap i16 : NC = phi N o16 = | x y z | | y z x | | z x y | o16 : NCMatrix i17 : N3C = NC^3 o17 = | -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 | | y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y | | 2*y^2*z+y^3+y*x*y+x*y*x+2*x^2*z+x^3 -y^2*z+y^3+y*x*z-y*x*y+x*y*z+x*y^2+2*x*y*x+x^2*z+3*x^2*y y^2*z+y*x*z+2*y*x*y+x*y*z+3*x*y^2-x*y*x-x^2*z+x^2*y+x^3 | o17 : NCMatrix i18 : X = NC + 3*NC o18 = | 4*x 4*y 4*z | | 4*y 4*z 4*x | | 4*z 4*x 4*y | o18 : NCMatrix i19 : Y = NC | 2*NC o19 = | x y z 2*x 2*y 2*z | | y z x 2*y 2*z 2*x | | z x y 2*z 2*x 2*y | o19 : NCMatrix i20 : Z = X || NC o20 = | 4*x 4*y 4*z | | 4*y 4*z 4*x | | 4*z 4*x 4*y | | x y z | | y z x | | z x y | o20 : NCMatrix i21 :