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Can someone help me with some Grobner ba...

Kaoru 0 Maple
groebner basis
June 27 2018
0 0


 

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x1 := 0; -1; x2 := 0; -1; J2 := J1

J1

 (1)
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NULL
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ec1 := (1/J3-1/J2)*M2*M3+m*g*(g2*x3-g3*x2) = 0;

(1/J3-1/J1)*M2*M3+m*g*x3*g2 = 0

 (2)
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ec2 := (1/J1-1/J3)*M1*M3+m*g*(-g1*x3+g3*x1) = 0;

(1/J1-1/J3)*M1*M3-m*g*x3*g1 = 0

 (3)
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ec3 := (1/J2-1/J1)*M1*M2+m*g*(g1*x2-g2*x1) = 0;

0 = 0

 (4)
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ec4 := g2*M3/J3-g3*M2/J2 = 0;

g2*M3/J3-g3*M2/J1 = 0

 (5)
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ec5 := g3*M1/J1-g1*M3/J3 = 0;

g3*M1/J1-g1*M3/J3 = 0

 (6)
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ec6 := g1*M2/J2-g2*M1/J1 = 0;

g1*M2/J1-g2*M1/J1 = 0

 (7)
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F1 := (1/J3-1/J2)*M2*M3+m*g*(g2*x3-g3*x2);

(1/J3-1/J1)*M2*M3+m*g*x3*g2

 (8)
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F2 := (1/J1-1/J3)*M1*M3+m*g*(-g1*x3+g3*x1);

(1/J1-1/J3)*M1*M3-m*g*x3*g1

 (9)
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F3 := (1/J2-1/J1)*M1*M2+m*g*(g1*x2-g2*x1);

0

 (10)
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F4 := g2*M3/J3-g3*M2/J2;

g2*M3/J3-g3*M2/J1

 (11)
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F5 := g3*M1/J1-g1*M3/J3;

g3*M1/J1-g1*M3/J3

 (12)
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F6 := g1*M2/J2-g2*M1/J1;

g1*M2/J1-g2*M1/J1

 (13)
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with(Groebner)

[Basis, FGLM, HilbertDimension, HilbertPolynomial, HilbertSeries, Homogenize, InitialForm, InterReduce, IsBasis, IsProper, IsZeroDimensional, LeadingCoefficient, LeadingMonomial, LeadingTerm, MatrixOrder, MaximalIndependentSet, MonomialOrder, MultiplicationMatrix, MultivariateCyclicVector, NormalForm, NormalSet, RationalUnivariateRepresentation, Reduce, RememberBasis, SPolynomial, Solve, SuggestVariableOrder, Support, TestOrder, ToricIdealBasis, TrailingTerm, UnivariatePolynomial, Walk, WeightedDegree]

 (14)
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G := {F1, F2, F3, F4, F5, F6};

{0, g1*M2/J1-g2*M1/J1, g2*M3/J3-g3*M2/J1, g3*M1/J1-g1*M3/J3, (1/J1-1/J3)*M1*M3-m*g*x3*g1, (1/J3-1/J1)*M2*M3+m*g*x3*g2}

 (15)
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B := Basis(G, tdeg(M1, M2, M3, g1, g2, g3))

Error, (in gcd/Freeze) arguments should be polynomials

  
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IsBasis(B, tdeg(M1, M2, M3, g1, g2, g3))

Error, invalid input: Groebner:-IsBasis expects its 1st argument, G1, to be of type {list, set}, but received B

  
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``
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NULL


 

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