This method constructs a skew polynomial ring with coefficient ring R and generators elements of L. The relations all have the form a*b - f*b*a where a and b are in L. If R is a Bergman coefficient ring, an NCGroebnerBasis is computed for B.
i1 : R = QQ[q]/ideal{q^4+q^3+q^2+q+1}
o1 = R
o1 : QuotientRing
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i2 : A = skewPolynomialRing(R,promote(2,R),{x,y,z,w})
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o2 = A
o2 : FreeAlgebraQuotient
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i3 : x*y == 2*y*x
o3 = true
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i4 : B = skewPolynomialRing(R,q,{x,y,z,w})
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o4 = B
o4 : FreeAlgebraQuotient
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i5 : x*y == q*y*x
o5 = true
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i6 : Bop = oppositeRing B
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o6 = Bop
o6 : FreeAlgebraQuotient
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i7 : y*x == q*x*y
o7 = true
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i8 : C = skewPolynomialRing(QQ,2_QQ, {x,y,z,w})
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o8 = C
o8 : FreeAlgebraQuotient
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i9 : x*y == 2*y*x
o9 = true
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i10 : D = skewPolynomialRing(QQ,1_QQ, {x,y,z,w})
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o10 = D
o10 : FreeAlgebraQuotient
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i11 : isCommutative C
o11 = false
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i12 : isCommutative D
o12 = false
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i13 : Cop = oppositeRing C
Warning: F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
o13 = Cop
o13 : FreeAlgebraQuotient
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i14 : y*x == 2*x*y
o14 = true
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