i1 : R = ZZ/32003 <|x_4,x_1,x_2,x_3|>
o1 = R
o1 : FreeAlgebra
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i2 : I = ideal {x_3^2 - x_1*x_2, x_4^2 - x_2*x_1, x_1*x_3 - x_2*x_4,
x_3*x_1 - x_2*x_3, x_1*x_4 - x_4*x_2, x_4*x_1 - x_3*x_2}
2 2
o2 = ideal (- x x + x , x - x x , x x - x x , - x x + x x , - x x +
1 2 3 4 2 1 1 3 2 4 2 3 3 1 4 2
------------------------------------------------------------------------
x x , x x - x x )
1 4 4 1 3 2
o2 : Ideal of R
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i3 : lQ = leftQuadraticMatrix I
o3 = | 0 0 -x_1 x_3 |
| x_4 -x_2 0 0 |
| -x_2 0 0 x_1 |
| 0 x_3 0 -x_2 |
| x_1 0 -x_4 0 |
| 0 x_4 -x_3 0 |
6 4
o3 : Matrix R <--- R
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i4 : rQ = rightQuadraticMatrix I
o4 = | 0 x_4 0 0 -x_2 x_1 |
| -x_2 0 x_3 0 x_4 0 |
| 0 -x_1 -x_4 -x_3 0 0 |
| x_3 0 0 x_1 0 -x_2 |
4 6
o4 : Matrix R <--- R
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i5 : d = matrix {{x_4,x_1,x_2,x_3}}
o5 = | x_4 x_1 x_2 x_3 |
1 4
o5 : Matrix R <--- R
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i6 : e = matrix transpose {{x_4,x_1,x_2,x_3}}
o6 = | x_4 |
| x_1 |
| x_2 |
| x_3 |
4 1
o6 : Matrix R <--- R
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i7 : NCReductionTwoSided(ncMatrixMult(d,rQ),I)
o7 = 0
1 6
o7 : Matrix R <--- R
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i8 : NCReductionTwoSided(ncMatrixMult(lQ,e),I)
o8 = 0
6 1
o8 : Matrix R <--- R
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i9 : S = R/I
Using numthreads = 0
o9 = S
o9 : FreeAlgebraQuotient
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i10 : (lQS,dS) = (sub(lQ,S),sub(d,S));
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i11 : (rQS,eS) = (sub(rQ,S),sub(e,S));
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i12 : ncMatrixMult(dS,rQS)
o12 = 0
1 6
o12 : Matrix S <--- S
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i13 : ncMatrixMult(lQS,eS)
o13 = 0
6 1
o13 : Matrix S <--- S
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