> with(LinearAlgebra); 1; c_1 := h; 1; [&x, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm, BilinearForm, CARE, CharacteristicMatrix, CharacteristicPolynomial, Column, ColumnDimension, ColumnOperation, ColumnSpace, CompanionMatrix, CompressedSparseForm, ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation, CrossProduct, DARE, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix, Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors, Equal, ForwardSubstitute, FrobeniusForm, FromCompressedSparseForm, FromSplitForm, GaussianElimination, GenerateEquations, GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm, HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct, LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2, MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply, MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize, NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, ProjectionMatrix, QRDecomposition, RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm, Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector, SchurForm, SingularValues, SmithForm, SplitForm, StronglyConnectedBlocks, SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace, Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip] > c_2 := (1/2)*h^2; 1; c_3 := (1/6)*h^3+(1/12)*b*h-(1/6)*g; 1; c_4 := (1/24)*h^4+(1/12)*b*h^2-(1/6)*g*h; 1; > c_5 := (3/10)*b*c_3-(1/80)*b^2*c_1+(1/5)*h*c_4-(1/5)*((1/4)*b*h+(1/2)*g)*c_2; 1; c_5 := simplify(c_5); 1; > c_6 := (1/3)*b*c_4-(1/48)*b^2*c_2+(1/6)*h*c_5-(1/6)*((1/4)*b*h+(1/2)*g)*c_3; 1; c_6 := simplify(c_6); 1; > c_7 := (5/14)*b*c_5-(3/112)*b^2*c_3+(1/7)*h*c_6-(1/7)*((1/4)*b*h+(1/2)*g)*c_4; 1; c_7 := simplify(c_7); 1; > c_8 := (3/8)*b*c_6-(1/32)*b^2*c_4+(1/8)*h*c_7-(1/8)*((1/4)*b*h+(1/2)*g)*c_5; 1; c_8 := simplify(c_8); 1; > c_9 := (7/18)*b*c_7-(5/144)*b^2*c_5+(1/9)*h*c_8-(1/9)*((1/4)*b*h+(1/2)*g)*c_6; 1; c_9 := simplify(c_9); 1; > c_10 := (2/5)*b*c_8-(3/80)*b^2*c_6+(1/10)*h*c_9-(1/10)*((1/4)*b*h+(1/2)*g)*c_7; 1; c_10 := simplify(c_10); 1; > c_11 := (9/22)*b*c_9-(7/176)*b^2*c_7+(1/11)*h*c_10-(1/11)*((1/4)*b*h+(1/2)*g)*c_8; 1; c_11 := simplify(c_11); 1; > c_12 := (5/12)*b*c_10-(1/24)*b^2*c_8+(1/12)*h*c_11-(1/12)*((1/4)*b*h+(1/2)*g)*c_9; 1; c_12 := simplify(c_12); 1; > c_13 := (11/26)*b*c_11-(9/208)*b^2*c_9+(1/13)*h*c_12-(1/13)*((1/4)*b*h+(1/2)*g)*c_10; 1; c_13 := simplify(c_13); 1; > c_14 := (3/7)*b*c_12-(5/112)*b^2*c_10+(1/14)*h*c_13-(1/14)*((1/4)*b*h+(1/2)*g)*c_11; 1; c_14 := simplify(c_14); 1; > c_15 := (13/30)*b*c_13-(11/240)*b^2*c_11+(1/15)*h*c_14-(1/15)*((1/4)*b*h+(1/2)*g)*c_12; 1; c_15 := simplify(c_15); 1; > A := Matrix([[c_8, c_9, c_10, c_11, c_12, c_13, c_14, c_15], [c_6, c_7, c_8, c_9, c_10, c_11, c_12, c_13], [c_4, c_5, c_6, c_7, c_8, c_9, c_10, c_11], [c_2, c_3, c_4, c_5, c_6, c_7, c_8, c_9], [c_0, c_1, c_2, c_3, c_4, c_5, c_6, c_7], [0, 0, 2, c_1, c_2, c_3, c_4, c_5], [0, 0, 0, 0, 2, c_1, c_2, c_3], [0, 0, 0, 0, 0, 0, 2, c_1]]); 1; > Z := Determinant(A); 1; > Z := subs(c_0 = 2, Z); 1; > h_n := h*(((2*a-2*h)*sqrt(b)+a^2-2*h*a+b)*((1/2)*a-(1/2)*sqrt(b))^n-((-2*a+2*h)*sqrt(b)+a^2-2*h*a+b)*((1/2)*a+(1/2)*sqrt(b))^n)/(sqrt(b)*(a^2-b)); 1; > Z2 := subs(h^3 = subs(n = 3, h_n), Z); 1; > Z2 := subs(h^4 = subs(n = 4, h_n), Z2); 1; > Z2 := subs(h^5 = subs(n = 5, h_n), Z2); 1; > Z2 := subs(h^6 = subs(n = 6, h_n), Z2); 1; > Z2 := subs(h^7 = subs(n = 7, h_n), Z2); 1; > Z2 := subs(h^8 = subs(n = 8, h_n), Z2); 1; > Z2 := subs(h^9 = subs(n = 9, h_n), Z2); 1; > Z2 := subs(h^10 = subs(n = 10, h_n), Z2); 1; > Z2 := subs(h^11 = subs(n = 11, h_n), Z2); 1; > Z2 := subs(h^12 = subs(n = 12, h_n), Z2); 1; > Z2 := subs(h^13 = subs(n = 13, h_n), Z2); 1; > Z2 := subs(h^14 = subs(n = 14, h_n), Z2); 1; > Z2 := subs(h^15 = subs(n = 15, h_n), Z2); 1; > Z2 := subs(h^16 = subs(n = 16, h_n), Z2); 1; > Z2 := subs(h^17 = subs(n = 17, h_n), Z2); 1; > Z2 := subs(h^18 = subs(n = 18, h_n), Z2); 1; > Z2 := subs(h^19 = subs(n = 19, h_n), Z2); 1; > Z2 := subs(h^20 = subs(n = 20, h_n), Z2); 1; > Z2 := subs(h^21 = subs(n = 21, h_n), Z2); 1; > Z2 := subs(h^22 = subs(n = 22, h_n), Z2); 1; > Z2 := subs(h^23 = subs(n = 23, h_n), Z2); 1; > Z2 := subs(h^24 = subs(n = 24, h_n), Z2); 1; > Z2 := subs(h^25 = subs(n = 25, h_n), Z2); 1; > Z2 := subs(h^26 = subs(n = 26, h_n), Z2); > Z2 := subs(h^27 = subs(n = 27, h_n), Z2); 1; > Z2 := subs(h^28 = subs(n = 28, h_n), Z2); 1; > Z2 := subs(h^29 = subs(n = 29, h_n), Z2); 1; > Z2 := subs(h^30 = subs(n = 30, h_n), Z2); 1; > Z2 := subs(h^31 = subs(n = 31, h_n), Z2); 1; > Z2 := subs(h^32 = subs(n = 32, h_n), Z2); 1; > Z2 := subs(h^33 = subs(n = 33, h_n), Z2); 1; > Z2 := subs(h^34 = subs(n = 34, h_n), Z2); 1; > Z2 := subs(h^36 = subs(n = 36, h_n), Z2); 1; > Z2 := subs(h^2 = a*h-(1/4)*a^2+(1/4)*b, Z2); 1; > Z2 := factor(Z2); 1; > Z2 := subs(h^2 = a*h-(1/4)*a^2+(1/4)*b, Z2); 1; > Z2 := simplify(Z2); 1; > Z2 := expand(Z2); 1; > Z4 := subs(h = 0, Z2); 1; > Z44 := subs(a^2*b^14*g^2 = 0, Z4); 1; "Z44:=subs(a^2*b^14*g^2=0,a^2*b^11*g^4=0,a^2*b^8*g^6=0,a^(2)*b^5*g^8=0,a^7*b^10* g^3=0,a^6*b^12*g^2=0,a^5*b^14*g=0,a*b^(16)*g=0,a^8*b^11*g^2=0,a^7*b^13*g=0,a^4*b ^10*g^4=0,a^3*b^9*g^5=0,a^5*b^8*g^5=0, a^7*b^13*g=0,b^3*g^10=0,b^6*g^8=0,b^9*g^6=0,b^12*g^4=0,b^15*g^2=0,b^18=0,a*b^(10 )*g^(5)=0, Z4);" > Z444 := subs(b^13 = 0, b^15 = 0, b^16 = 0, a^3*b^12*g^3 = 0, a^3*b^6*g^7 = 0, a*b^10*g^5 = 0, a*b^7*g^7 = 0, a*b^4*g^9 = 0, a*b^10*g^5 = 0, a^4*b^6*g^6 = 0, a^5*b^11*g^3 = 0, a*b^4*g^9 = 0, a*b^10*g^5 = 0, a^4*b^16 = 0, b^17*a^2 = 0, a^6*b^15 = 0, a^4*b^7*g^6 = 0, b^14 = 0, Z44); 1; > Z5 := subs(a^22*b^7 = -(5/66)*factorial(22)*2^24*(2^10-2)/factorial(10), a^30*g^2 = (174611/330)*factorial(13)*factorial(30)*2^22*(2^20-2)/(factorial(11)*factorial(20)), a^15*g^7 = (5/66)*factorial(13)*factorial(15)*2^17*(2^10-2)/(factorial(6)*factorial(10)), a^3*g^11 = (1/3)*factorial(13)*factorial(3)*2^13/factorial(2)^2, a^9*g^9 = (1/42)*factorial(13)*factorial(9)*2^15*(2^6-2)/(factorial(4)*factorial(6)), a^27*g^3 = (43867/798)*factorial(13)*factorial(27)*2^21*(2^18-2)/(factorial(10)*factorial(18)), a^24*b^6 = (691/2730)*factorial(24)*2^24*(2^12-2)/factorial(12), a^9*b^6*g^5 = (1/12)*factorial(13)*factorial(9)*2^20/factorial(8), a^2*b^2*g^10 = 2*factorial(13)*2^14/factorial(3), a^29*b^2*g = (43867/798)*factorial(13)*factorial(29)*2^23*(2^18-2)/(factorial(12)*factorial(18)), b^15 = 0, b^16 = 0, b^14 = 0, a^9*b^12*g = 0, a^3*b^6*g^7 = 0, b^17*a^2 = 0, a*b^13*g^3 = 0, a^3*b^12*g^3 = 0, a*b^10*g^5 = 0, a^5*b^11*g^3 = 0, a^6*b^9*g^4 = 0, Z44); 1; > Z55 := subs(a^10*b^4*g^6 = (1/30)*factorial(13)*factorial(10)*2^18*(2^4-2)/(factorial(7)*factorial(4)), a^8*b^8*g^4 = factorial(13)*factorial(8)*2^20/factorial(9), a^9*b^3*g^7 = -(1/30)*factorial(13)*factorial(9)*2^17*(2^4-2)/(factorial(6)*factorial(4)), a^8*b^5*g^6 = -(1/12)*factorial(13)*factorial(8)*2^19/factorial(7), a^7*b^7*g^5 = -factorial(13)*factorial(7)*2^19/factorial(8), a^4*b^13*g^2 = 0, a*b^7*g^7 = 0, a*b^4*g^9 = 0, a^27*b^3*g = -(3617/510)*factorial(13)*factorial(27)*2^23*(2^16-2)/(factorial(12)*factorial(16)), a^26*b^2*g^2 = (3617/510)*factorial(13)*factorial(26)*2^22*(2^16-2)/(factorial(11)*factorial(16)), a^25*b^4*g = (7/6)*factorial(13)*factorial(25)*2^23*(2^14-2)/(factorial(12)*factorial(14)), Z5); 1; > Z555 := subs(a^10*b^10*g^2 = factorial(13)*factorial(10)*2^22/factorial(11), a^12*b^3*g^6 = -(1/42)*factorial(13)*factorial(12)*2^18*(2^6-2)/(factorial(7)*factorial(6)), a^11*b^5*g^5 = -(1/30)*factorial(13)*factorial(11)*2^19*(2^4-2)/(factorial(8)*factorial(4)), a^10*b^7*g^4 = -(1/6)*factorial(13)*factorial(10)*2^20/factorial(9), a^11*b^2*g^7 = (1/42)*factorial(13)*factorial(11)*2^17*(2^6-2)/factorial(6)^2, a^12*b^6*g^4 = (1/30)*factorial(13)*factorial(12)*2^20*(2^4-2)/(factorial(9)*factorial(4)), a^11*b^8*g^3 = (1/12)*factorial(13)*factorial(11)*2^22/factorial(10), a^8*b^2*g^8 = (1/30)*factorial(13)*factorial(8)*2^16*(2^4-2)/(factorial(4)*factorial(5)), a^6*b^3*g^8 = -(1/6)*factorial(13)*factorial(6)*2^17/(factorial(5)*factorial(2)), a^10*b^13 = 0, a^4*b^7*g^6 = 0, Z55); 1; > Z555 := subs(a^7*b^4*g^7 = (1/6)*factorial(13)*factorial(7)*2^18/(factorial(6)*factorial(2)), a^5*b^5*g^7 = -factorial(13)*factorial(5)*2^17/factorial(6), a^6*b^6*g^6 = factorial(13)*factorial(6)*2^18/factorial(7), a^5*b^2*g^9 = (1/12)*factorial(13)*factorial(5)*2^16/factorial(4), a^4*b^4*g^8 = factorial(13)*factorial(4)*2^16/factorial(5), a^3*b^3*g^9 = -factorial(13)*factorial(3)*2^15/factorial(4), a^21*b^3*g^3 = -(691/2730)*factorial(13)*factorial(21)*2^21*(2^12-2)/(factorial(10)*factorial(12)), a^20*b^5*g^2 = -(5/66)*factorial(13)*factorial(20)*2^22*(2^10-2)/(factorial(11)*factorial(10)), Z555); 1; > Z555 := subs(a^19*b^7*g = -(1/30)*factorial(13)*factorial(19)*2^23*(2^8-2)/(factorial(12)*factorial(8)), a^20*b^2*g^4 = (691/2730)*factorial(13)*factorial(20)*2^20*(2^12-2)/(factorial(9)*factorial(12)), a^19*b^4*g^3 = (5/66)*factorial(13)*factorial(19)*2^21*(2^10-2)/factorial(10)^2, a^18*b^6*g^2 = (1/30)*factorial(13)*factorial(18)*2^22*(2^8-2)/(factorial(11)*factorial(8)), a^17*b^8*g = (1/42)*factorial(13)*factorial(17)*2^23*(2^6-2)/(factorial(12)*factorial(6)), a^18*b^3*g^4 = -(5/66)*factorial(13)*factorial(18)*2^20*(2^10-2)/(factorial(9)*factorial(10)), a^17*b^5*g^3 = -(1/30)*factorial(13)*factorial(17)*2^21*(2^8-2)/(factorial(10)*factorial(8)), a^16*b^7*g^2 = -(1/42)*factorial(13)*factorial(16)*2^22*(2^6-2)/(factorial(11)*factorial(6)), a^15*b^9*g = -(1/30)*factorial(13)*factorial(15)*2^23*(2^4-2)/(factorial(12)*factorial(4)), a^17*b^2*g^5 = (5/66)*factorial(13)*factorial(17)*2^19*(2^10-2)/(factorial(8)*factorial(10)), a^16*b^4*g^4 = (1/30)*factorial(13)*factorial(16)*2^20*(2^8-2)/(factorial(9)*factorial(8)), Z555); 1; > Z555 := subs(g^12 = factorial(13)*2^12, a^36 = (236364091/2730)*factorial(36)*2^24*(2^24-2)/factorial(24), a^24*g^4 = (3617/510)*factorial(13)*factorial(24)*2^20*(2^16-2)/(factorial(9)*factorial(16)), a^26*b^5 = -(7/6)*factorial(26)*2^24*(2^14-2)/factorial(14), a^33*g = (854513/138)*factorial(13)*factorial(33)*2^23*(2^22-2)/(factorial(12)*factorial(22)), a^6*g^10 = (1/30)*factorial(13)*factorial(6)*2^14*(2^4-2)/(factorial(3)*factorial(4)), a^12*g^8 = (1/30)*factorial(13)*factorial(12)*2^16*(2^8-2)/(factorial(5)*factorial(8)), a^20*b^8 = (1/30)*factorial(20)*2^24*(2^8-2)/factorial(8), a^34*b = -(854513/138)*factorial(34)*2^24*(2^22-2)/factorial(22), a^18*g^6 = (691/2730)*factorial(13)*factorial(18)*2^18*(2^12-2)/(factorial(7)*factorial(12)), a^12*b^12 = factorial(12)*2^24, a^14*b^11 = -(1/12)*factorial(14)*2^24*(2^2-2), Z555); 1; > Z555 := subs(a^21*g^5 = (7/6)*factorial(13)*factorial(21)*2^19*(2^14-2)/(factorial(8)*factorial(14)), a^16*b^10 = (1/30)*factorial(16)*2^24*(2^4-2)/factorial(4), a^18*b^9 = -(1/42)*factorial(18)*2^24*(2^6-2)/factorial(6), a^28*b^4 = (3617/510)*factorial(28)*2^24*(2^16-2)/factorial(16), a^30*b^3 = -(43867/798)*factorial(30)*2^24*(2^18-2)/factorial(18), a^32*b^2 = (174611/330)*factorial(32)*2^24*(2^20-2)/factorial(20), a^31*g*b = -(174611/330)*factorial(13)*factorial(31)*2^23*(2^20-2)/(factorial(12)*factorial(20)), a^4*g^10*b = -(1/12)*factorial(13)*factorial(4)*2^14*(2^2-2)/factorial(3), a^10*g^8*b = -(1/42)*factorial(13)*factorial(10)*2^16*(2^6-2)/(factorial(5)*factorial(6)), a^7*g^9*b = -(1/30)*factorial(13)*factorial(7)*2^15*(2^4-2)/factorial(4)^2, a^25*g^3*b = -(3617/510)*factorial(13)*factorial(25)*2^21*(2^16-2)/(factorial(10)*factorial(16)), Z555); 1; > Z555 := subs(a^15*b^6*g^3 = (1/42)*factorial(13)*factorial(15)*2^21*(2^6-2)/(factorial(10)*factorial(6)), a^23*b^5*g = -(691/2730)*factorial(13)*factorial(23)*2^23*(2^12-2)/factorial(12)^2, a^21*b^6*g = (5/66)*factorial(13)*factorial(21)*2^23*(2^10-2)/(factorial(12)*factorial(10)), a^22*b^4*g^2 = (691/2730)*factorial(13)*factorial(22)*2^22*(2^12-2)/(factorial(11)*factorial(12)), a^24*b^3*g^2 = -(7/6)*factorial(13)*factorial(24)*2^22*(2^14-2)/(factorial(11)*factorial(14)), a^23*b^2*g^3 = (7/6)*factorial(13)*factorial(23)*2^21*(2^14-2)/(factorial(10)*factorial(14)), a^16*g^6*b = -(5/66)*factorial(13)*factorial(16)*2^18*(2^10-2)/(factorial(7)*factorial(10)), a^19*g^5*b = -(691/2730)*factorial(13)*factorial(19)*2^19*(2^12-2)/(factorial(8)*factorial(12)), a^22*g^4*b = -(7/6)*factorial(13)*factorial(22)*2^20*(2^14-2)/(factorial(9)*factorial(14)), a^13*g^7*b = -(1/30)*factorial(13)^2*2^17*(2^8-2)/(factorial(6)*factorial(8)), a^28*g^2*b = -(43867/798)*factorial(13)*factorial(28)*2^22*(2^18-2)/(factorial(11)*factorial(18)), Z555); 1; > Z555 := subs(a^14*b^8*g^2 = (1/30)*factorial(13)*factorial(14)*2^22*(2^4-2)/(factorial(11)*factorial(4)), a^13*b^10*g = (1/6)*factorial(13)^2*2^23*(2^2-2)/(factorial(12)*factorial(2)), a^15*b^3*g^5 = -(1/30)*factorial(13)*factorial(15)*2^19*(2^8-2)/factorial(8)^2, a^14*b^5*g^4 = -(1/42)*factorial(13)*factorial(14)*2^20*(2^6-2)/(factorial(9)*factorial(6)), a^13*b^7*g^3 = -(1/30)*factorial(13)^2*2^21*(2^4-2)/(factorial(10)*factorial(4)), a^12*b^9*g^2 = -(1/12)*factorial(13)*factorial(12)*2^22*(2^2-2)/factorial(11), a^11*b^11*g = -factorial(13)*factorial(11)*2^23/factorial(12), a*g^11*b = -(1/2)*factorial(13)*2^13, a^14*b^2*g^6 = (1/30)*factorial(13)*factorial(14)*2^18*(2^8-2)/(factorial(7)*factorial(8)), a^13*b^4*g^5 = (1/42)*factorial(13)^2*2^19*(2^6-2)/(factorial(8)*factorial(6)), a^9*b^9*g^3 = -factorial(13)*factorial(9)*2^21/factorial(10), Z555); 1; > Z555 := factor(Z555); 1;