Maple Questions and Posts

These are Posts and Questions associated with the product, Maple
ds := DerivedSeries(PermutationGroup({[[2, 3, 5, 4]], [[1, 2, 3, 4, 5]]}))

will get a series group like:

How to get the group by the red line point out? Then I can use GroupOrder to get the order of it. I note GroupOrder[ds[2]] don't work

Hello, i want to do convert numbers to binary code 8 bytes and I want to sum the digits of each number 

For example first number is 0 i want to write 0 0 0 0 0 0 0 0 , sum=0, for 1= 0 0 0 0 0 0 0 1,  sum =1 for 7= 0 0 0 0 0 1 1 1 sum=3 etc.....
my code is this;

for i from 0 to 10 do;
> S(i):=convert(i,binary);
> end do;

and output is 

                              S(0) := 0
                              S(1) := 1
                              S(2) := 10
                            S(3) := 11
                            S(4):=100
                             S(5) := 101
                             S(6) := 110
                            S(7) := 111
                           S(8) := 1000
                             S(9) := 1001
                            S(10) := 1010
                and  Histogram(S(i));  doesnt work.                

I want to reverse a catenated expression (eg. xxtt ->x,x,t,t). I don't know the command to achieve this. Anyone with an idea please help

Thanks

Hey I’m trying to define a variable as the solution to a second order nonhomogeneous differential equation with an initial value problem.

I have tried the method below, but it doesn’t work.

N__1 := dsolve([diff(y(x), x, x) + 3*diff(y(x), x) + 2*y(x) = x^2 + 5, eval(y(x), x = 0) = 1, eval(diff(y(x), x), x = 0) = 1], y(x))

It kind of works it gives me the expression below

N__1 = y(x) = (3*exp(-2*x))/4 + 17/4 - (3*x)/2 + x^2/2 - 4*exp(-x)

But I need the expression for N__1 to define some initial values for N__2 and so on, what I have tried that doesn’t work is.

C := eval(N__1, x = 200)

N__2 := C   - Just because nothing much is happing on this interval

And it gives me the following expression for N2

N__2 := y(200) = (3*exp(-400))/4 + 78817/4 - 4*exp(-200)

I then make a piecewise function to make a function which I can plot, which use to work.                         

N := piecewise(0 <= x and x <= 200, N__1, 200 <= x and x <= 1000, eval(N__2, x = x - 200))

But when I’m trying to plot N maple gives me a warning message.

plot(N, x = 0 .. 1000)

Warning, expecting only range or variable x in expression piecewise ………………..  to be plotted but found name y.

If I define N__1 as the solution to the differential equation, then it works just fine.

N__1 := (3*exp(-2*x))/4 + 17/4 - (3*x)/2 + x^2/2 - 4*exp(-x)

But that I’m not interested in, because that will require a lot of copy paste all the time.

Thank you in advance.

how I can convert this maple code to Matlab ones?

1.mw
 

restart; t1 := time(); with(LinearAlgebra); J := readstat("Please enter integer number J: "); N1 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, 1) end proc; N2 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, x, 1 < x and x <= 2, 2-x) end proc; N := proc (J, k) options operator, arrow; unapply(N2(2^J*x-k), x) end proc; Phi := proc (J, k) options operator, arrow; evalf((N(J, k))(x))*N1(x) end proc; PhiJ := Vector[column](2^J+1); for k from -1 to 2^J-1 do PhiJ[k+2] := Phi(J, k) end do; P := Matrix(2^J+1, 2^J+1); Map2[proc (i, j) options operator, arrow; evalb(i-j = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/6, P, inplace); Map2[proc (i, j) options operator, arrow; evalb(j-i = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/6, P, inplace); Map2[proc (i, j) options operator, arrow; evalb(i = j) end proc](proc (x, a) options operator, arrow; x end proc, 2/3, P, inplace); P[1, 1] := 1/3; P[2^J+1, 2^J+1] := 1/3; P := 2^(-J)*P; E := Matrix(2^J+1, 2^J+1); Map2[proc (i, j) options operator, arrow; evalb(i-j = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/2, E, inplace); Map2[proc (i, j) options operator, arrow; evalb(j-i = 1) end proc](proc (x, a) options operator, arrow; x end proc, -1/2, E, inplace); E[1, 1] := -1/2; E[2^J+1, 2^J+1] := 1/2; DPhi := E.(1/P); X1 := Vector[column](2^J+1, symbol = x1); X2 := Vector[column](2^J+1, symbol = x2); U := Vector[column](2^J+1, symbol = u); JJ := (1/2)*U^%T.P.U; x1t := X1^%T.PhiJ; x2t := X2^%T.PhiJ; ut := U^%T.PhiJ; for i from 0 to 2^J do PhiJxJ[i+1] := apply(unapply(PhiJ, x), i/2^J) end do; for i to 2^J+1 do eq1[i] := (X1^%T.DPhi-X2^%T).PhiJxJ[i] = 0; eq2[i] := (X2^%T.DPhi-U^%T).PhiJxJ[i] = 0 end do; for i to 2^J+1 do eq3[i] := X1^%T.PhiJxJ[i]-.1, 0 end do; eq1[0] := eval(x1t, x = 0) = 0; eq2[0] := eval(x2t, x = 0)-1 = 0; eq1[2^J+2] := eval(x1t, x = 1) = 0; eq2[2^J+2] := eval(x2t, x = 1) = -1; eqq1 := {seq(eq1[i], i = 0*.2^J+2)}; eqq2 := {seq(eq2[i], i = 0.2^J+2)}; eqq3 := {seq(eq3[i], i = 1.2^J+1)}; eq := `union`(`union`(eqq1, eqq2), eqq3); with(Optimization); S := NLPSolve(JJ, eq); assign(S[2]); uexact := piecewise(0 <= x and x <= .3, (200/9)*x-20/3, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(200/9)*x+140/9); x2exact := piecewise(0 <= x and x <= .3, (100/9)*x^2-(20/3)*x+1, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(100/9)*x^2+(140/9)*x-49/9); x1exact := piecewise(0 <= x and x <= .3, (100/27)*x^3-(10/3)*x^2+x, .3 <= x and x <= .7, 1/10, .7 <= x and x <= 1, -(100/27)*x^3+(70/9)*x^2-(49/9)*x+37/27); plot([x1exact, x1t], x = 0 .. 1, style = [line, point], legend = ["Exact", "Approximate"], axis = [gridlines = [colour = green, majorlines = 2]], labels = ["t", x[1](t)], labeldirections = ["horizontal", "vertical"])

t1 := 38.500

 

[`&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]

 

J := 4

 

N1 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, 1) end proc

 

N2 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, x, 1 < x and x <= 2, 2-x) end proc

 

N := proc (J, k) options operator, arrow; unapply(N2(2^J*x-k), x) end proc

 

Phi := proc (J, k) options operator, arrow; evalf((N(J, k))(x))*N1(x) end proc

 

_rtable[36893490566539206892]

 

PhiJ[1] := piecewise(16.*x <= 0. and 0. <= 16.*x+1., 16.*x+1., 0. < 16.*x and 16.*x <= 1., 1.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[2] := piecewise(0. <= 16.*x and 16.*x <= 1., 16.*x, 1. < 16.*x and 16.*x <= 2., 2.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[3] := piecewise(`and`(0. <= 16.*x-1., 16.*x <= 2.), 16.*x-1., `and`(0. < 16.*x-2., 16.*x <= 3.), 3.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[4] := piecewise(`and`(0. <= 16.*x-2., 16.*x <= 3.), 16.*x-2., `and`(0. < 16.*x-3., 16.*x <= 4.), 4.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[5] := piecewise(`and`(0. <= 16.*x-3., 16.*x <= 4.), 16.*x-3., `and`(0. < 16.*x-4., 16.*x <= 5.), 5.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[6] := piecewise(`and`(0. <= 16.*x-4., 16.*x <= 5.), 16.*x-4., `and`(0. < 16.*x-5., 16.*x <= 6.), 6.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[7] := piecewise(`and`(0. <= 16.*x-5., 16.*x <= 6.), 16.*x-5., `and`(0. < 16.*x-6., 16.*x <= 7.), 7.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[8] := piecewise(`and`(0. <= 16.*x-6., 16.*x <= 7.), 16.*x-6., `and`(0. < 16.*x-7., 16.*x <= 8.), 8.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[9] := piecewise(`and`(0. <= 16.*x-7., 16.*x <= 8.), 16.*x-7., `and`(0. < 16.*x-8., 16.*x <= 9.), 9.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[10] := piecewise(`and`(0. <= 16.*x-8., 16.*x <= 9.), 16.*x-8., `and`(0. < 16.*x-9., 16.*x <= 10.), 10.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[11] := piecewise(`and`(0. <= 16.*x-9., 16.*x <= 10.), 16.*x-9., `and`(0. < 16.*x-10., 16.*x <= 11.), 11.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[12] := piecewise(`and`(0. <= 16.*x-10., 16.*x <= 11.), 16.*x-10., `and`(0. < 16.*x-11., 16.*x <= 12.), 12.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[13] := piecewise(`and`(0. <= 16.*x-11., 16.*x <= 12.), 16.*x-11., `and`(0. < 16.*x-12., 16.*x <= 13.), 13.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[14] := piecewise(`and`(0. <= 16.*x-12., 16.*x <= 13.), 16.*x-12., `and`(0. < 16.*x-13., 16.*x <= 14.), 14.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[15] := piecewise(`and`(0. <= 16.*x-13., 16.*x <= 14.), 16.*x-13., `and`(0. < 16.*x-14., 16.*x <= 15.), 15.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[16] := piecewise(`and`(0. <= 16.*x-14., 16.*x <= 15.), 16.*x-14., `and`(0. < 16.*x-15., 16.*x <= 16.), 16.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

PhiJ[17] := piecewise(`and`(0. <= 16.*x-15., 16.*x <= 16.), 16.*x-15., `and`(0. < 16.*x-16., 16.*x <= 17.), 17.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

_rtable[36893490566536466172]

 

_rtable[36893490566536466172]

 

_rtable[36893490566536466172]

 

_rtable[36893490566536466172]

 

P[1, 1] := 1/3

 

P[17, 17] := 1/3

 

_rtable[36893490566563670004]

 

_rtable[36893490566563682652]

 

_rtable[36893490566563682652]

 

_rtable[36893490566563682652]

 

E[1, 1] := -1/2

 

E[17, 17] := 1/2

 

_rtable[36893490566592433196]

 

_rtable[36893490566592446084]

 

_rtable[36893490566592458492]

 

_rtable[36893490566592462708]

 

JJ := ((1/96)*u[1]+(1/192)*u[2])*u[1]+((1/192)*u[1]+(1/48)*u[2]+(1/192)*u[3])*u[2]+((1/192)*u[2]+(1/48)*u[3]+(1/192)*u[4])*u[3]+((1/192)*u[3]+(1/48)*u[4]+(1/192)*u[5])*u[4]+((1/192)*u[4]+(1/48)*u[5]+(1/192)*u[6])*u[5]+((1/192)*u[5]+(1/48)*u[6]+(1/192)*u[7])*u[6]+((1/192)*u[6]+(1/48)*u[7]+(1/192)*u[8])*u[7]+((1/192)*u[7]+(1/48)*u[8]+(1/192)*u[9])*u[8]+((1/192)*u[8]+(1/48)*u[9]+(1/192)*u[10])*u[9]+((1/192)*u[9]+(1/48)*u[10]+(1/192)*u[11])*u[10]+((1/192)*u[10]+(1/48)*u[11]+(1/192)*u[12])*u[11]+((1/192)*u[11]+(1/48)*u[12]+(1/192)*u[13])*u[12]+((1/192)*u[12]+(1/48)*u[13]+(1/192)*u[14])*u[13]+((1/192)*u[13]+(1/48)*u[14]+(1/192)*u[15])*u[14]+((1/192)*u[14]+(1/48)*u[15]+(1/192)*u[16])*u[15]+((1/192)*u[15]+(1/48)*u[16]+(1/192)*u[17])*u[16]+((1/192)*u[16]+(1/96)*u[17])*u[17]

 

x1t := x1[1]*piecewise(16.*x <= 0. and 0. <= 16.*x+1., 16.*x+1., 0. < 16.*x and 16.*x <= 1., 1.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[2]*piecewise(0. <= 16.*x and 16.*x <= 1., 16.*x, 1. < 16.*x and 16.*x <= 2., 2.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[3]*piecewise(`and`(0. <= 16.*x-1., 16.*x <= 2.), 16.*x-1., `and`(0. < 16.*x-2., 16.*x <= 3.), 3.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[4]*piecewise(`and`(0. <= 16.*x-2., 16.*x <= 3.), 16.*x-2., `and`(0. < 16.*x-3., 16.*x <= 4.), 4.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[5]*piecewise(`and`(0. <= 16.*x-3., 16.*x <= 4.), 16.*x-3., `and`(0. < 16.*x-4., 16.*x <= 5.), 5.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[6]*piecewise(`and`(0. <= 16.*x-4., 16.*x <= 5.), 16.*x-4., `and`(0. < 16.*x-5., 16.*x <= 6.), 6.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[7]*piecewise(`and`(0. <= 16.*x-5., 16.*x <= 6.), 16.*x-5., `and`(0. < 16.*x-6., 16.*x <= 7.), 7.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[8]*piecewise(`and`(0. <= 16.*x-6., 16.*x <= 7.), 16.*x-6., `and`(0. < 16.*x-7., 16.*x <= 8.), 8.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[9]*piecewise(`and`(0. <= 16.*x-7., 16.*x <= 8.), 16.*x-7., `and`(0. < 16.*x-8., 16.*x <= 9.), 9.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[10]*piecewise(`and`(0. <= 16.*x-8., 16.*x <= 9.), 16.*x-8., `and`(0. < 16.*x-9., 16.*x <= 10.), 10.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[11]*piecewise(`and`(0. <= 16.*x-9., 16.*x <= 10.), 16.*x-9., `and`(0. < 16.*x-10., 16.*x <= 11.), 11.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[12]*piecewise(`and`(0. <= 16.*x-10., 16.*x <= 11.), 16.*x-10., `and`(0. < 16.*x-11., 16.*x <= 12.), 12.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[13]*piecewise(`and`(0. <= 16.*x-11., 16.*x <= 12.), 16.*x-11., `and`(0. < 16.*x-12., 16.*x <= 13.), 13.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[14]*piecewise(`and`(0. <= 16.*x-12., 16.*x <= 13.), 16.*x-12., `and`(0. < 16.*x-13., 16.*x <= 14.), 14.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[15]*piecewise(`and`(0. <= 16.*x-13., 16.*x <= 14.), 16.*x-13., `and`(0. < 16.*x-14., 16.*x <= 15.), 15.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[16]*piecewise(`and`(0. <= 16.*x-14., 16.*x <= 15.), 16.*x-14., `and`(0. < 16.*x-15., 16.*x <= 16.), 16.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x1[17]*piecewise(`and`(0. <= 16.*x-15., 16.*x <= 16.), 16.*x-15., `and`(0. < 16.*x-16., 16.*x <= 17.), 17.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

x2t := x2[1]*piecewise(16.*x <= 0. and 0. <= 16.*x+1., 16.*x+1., 0. < 16.*x and 16.*x <= 1., 1.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[2]*piecewise(0. <= 16.*x and 16.*x <= 1., 16.*x, 1. < 16.*x and 16.*x <= 2., 2.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[3]*piecewise(`and`(0. <= 16.*x-1., 16.*x <= 2.), 16.*x-1., `and`(0. < 16.*x-2., 16.*x <= 3.), 3.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[4]*piecewise(`and`(0. <= 16.*x-2., 16.*x <= 3.), 16.*x-2., `and`(0. < 16.*x-3., 16.*x <= 4.), 4.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[5]*piecewise(`and`(0. <= 16.*x-3., 16.*x <= 4.), 16.*x-3., `and`(0. < 16.*x-4., 16.*x <= 5.), 5.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[6]*piecewise(`and`(0. <= 16.*x-4., 16.*x <= 5.), 16.*x-4., `and`(0. < 16.*x-5., 16.*x <= 6.), 6.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[7]*piecewise(`and`(0. <= 16.*x-5., 16.*x <= 6.), 16.*x-5., `and`(0. < 16.*x-6., 16.*x <= 7.), 7.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[8]*piecewise(`and`(0. <= 16.*x-6., 16.*x <= 7.), 16.*x-6., `and`(0. < 16.*x-7., 16.*x <= 8.), 8.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[9]*piecewise(`and`(0. <= 16.*x-7., 16.*x <= 8.), 16.*x-7., `and`(0. < 16.*x-8., 16.*x <= 9.), 9.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[10]*piecewise(`and`(0. <= 16.*x-8., 16.*x <= 9.), 16.*x-8., `and`(0. < 16.*x-9., 16.*x <= 10.), 10.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[11]*piecewise(`and`(0. <= 16.*x-9., 16.*x <= 10.), 16.*x-9., `and`(0. < 16.*x-10., 16.*x <= 11.), 11.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[12]*piecewise(`and`(0. <= 16.*x-10., 16.*x <= 11.), 16.*x-10., `and`(0. < 16.*x-11., 16.*x <= 12.), 12.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[13]*piecewise(`and`(0. <= 16.*x-11., 16.*x <= 12.), 16.*x-11., `and`(0. < 16.*x-12., 16.*x <= 13.), 13.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[14]*piecewise(`and`(0. <= 16.*x-12., 16.*x <= 13.), 16.*x-12., `and`(0. < 16.*x-13., 16.*x <= 14.), 14.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[15]*piecewise(`and`(0. <= 16.*x-13., 16.*x <= 14.), 16.*x-13., `and`(0. < 16.*x-14., 16.*x <= 15.), 15.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[16]*piecewise(`and`(0. <= 16.*x-14., 16.*x <= 15.), 16.*x-14., `and`(0. < 16.*x-15., 16.*x <= 16.), 16.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+x2[17]*piecewise(`and`(0. <= 16.*x-15., 16.*x <= 16.), 16.*x-15., `and`(0. < 16.*x-16., 16.*x <= 17.), 17.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

ut := u[1]*piecewise(16.*x <= 0. and 0. <= 16.*x+1., 16.*x+1., 0. < 16.*x and 16.*x <= 1., 1.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[2]*piecewise(0. <= 16.*x and 16.*x <= 1., 16.*x, 1. < 16.*x and 16.*x <= 2., 2.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[3]*piecewise(`and`(0. <= 16.*x-1., 16.*x <= 2.), 16.*x-1., `and`(0. < 16.*x-2., 16.*x <= 3.), 3.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[4]*piecewise(`and`(0. <= 16.*x-2., 16.*x <= 3.), 16.*x-2., `and`(0. < 16.*x-3., 16.*x <= 4.), 4.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[5]*piecewise(`and`(0. <= 16.*x-3., 16.*x <= 4.), 16.*x-3., `and`(0. < 16.*x-4., 16.*x <= 5.), 5.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[6]*piecewise(`and`(0. <= 16.*x-4., 16.*x <= 5.), 16.*x-4., `and`(0. < 16.*x-5., 16.*x <= 6.), 6.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[7]*piecewise(`and`(0. <= 16.*x-5., 16.*x <= 6.), 16.*x-5., `and`(0. < 16.*x-6., 16.*x <= 7.), 7.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[8]*piecewise(`and`(0. <= 16.*x-6., 16.*x <= 7.), 16.*x-6., `and`(0. < 16.*x-7., 16.*x <= 8.), 8.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[9]*piecewise(`and`(0. <= 16.*x-7., 16.*x <= 8.), 16.*x-7., `and`(0. < 16.*x-8., 16.*x <= 9.), 9.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[10]*piecewise(`and`(0. <= 16.*x-8., 16.*x <= 9.), 16.*x-8., `and`(0. < 16.*x-9., 16.*x <= 10.), 10.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[11]*piecewise(`and`(0. <= 16.*x-9., 16.*x <= 10.), 16.*x-9., `and`(0. < 16.*x-10., 16.*x <= 11.), 11.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[12]*piecewise(`and`(0. <= 16.*x-10., 16.*x <= 11.), 16.*x-10., `and`(0. < 16.*x-11., 16.*x <= 12.), 12.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[13]*piecewise(`and`(0. <= 16.*x-11., 16.*x <= 12.), 16.*x-11., `and`(0. < 16.*x-12., 16.*x <= 13.), 13.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[14]*piecewise(`and`(0. <= 16.*x-12., 16.*x <= 13.), 16.*x-12., `and`(0. < 16.*x-13., 16.*x <= 14.), 14.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[15]*piecewise(`and`(0. <= 16.*x-13., 16.*x <= 14.), 16.*x-13., `and`(0. < 16.*x-14., 16.*x <= 15.), 15.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[16]*piecewise(`and`(0. <= 16.*x-14., 16.*x <= 15.), 16.*x-14., `and`(0. < 16.*x-15., 16.*x <= 16.), 16.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)+u[17]*piecewise(`and`(0. <= 16.*x-15., 16.*x <= 16.), 16.*x-15., `and`(0. < 16.*x-16., 16.*x <= 17.), 17.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

 

_rtable[36893490566593511164]

 

_rtable[36893490566474385156]

 

_rtable[36893490566474387196]

 

_rtable[36893490566474274564]

 

_rtable[36893490566474276604]

 

_rtable[36893490566471927556]

 

_rtable[36893490566471929596]

 

_rtable[36893490566439466756]

 

_rtable[36893490566439468796]

 

_rtable[36893490566581483268]

 

_rtable[36893490566581485308]

 

_rtable[36893490566581487364]

 

_rtable[36893490566581489404]

 

_rtable[36893490566581491460]

 

_rtable[36893490566581493500]

 

_rtable[36893490566581561092]

 

_rtable[36893490566581563132]

 

eq1[1] := -20.28718708*x1[1]+25.72312247*x1[2]-6.892489894*x1[3]+1.846837101*x1[4]-.4948585097*x1[5]+.1325969380*x1[6]-0.3552924247e-1*x1[7]+0.9520031827e-2*x1[8]-0.2550884838e-2*x1[9]+0.6835075261e-3*x1[10]-0.1831452664e-3*x1[11]+0.4907353932e-4*x1[12]-0.1314889092e-4*x1[13]+3.522024353*10^(-6)*x1[14]-9.392064942*10^(-7)*x1[15]+2.348016235*10^(-7)*x1[16]-3.913360392*10^(-8)*x1[17]-1.*x2[1] = 0

 

eq2[1] := -20.28718708*x2[1]+25.72312247*x2[2]-6.892489894*x2[3]+1.846837101*x2[4]-.4948585097*x2[5]+.1325969380*x2[6]-0.3552924247e-1*x2[7]+0.9520031827e-2*x2[8]-0.2550884838e-2*x2[9]+0.6835075261e-3*x2[10]-0.1831452664e-3*x2[11]+0.4907353932e-4*x2[12]-0.1314889092e-4*x2[13]+3.522024353*10^(-6)*x2[14]-9.392064942*10^(-7)*x2[15]+2.348016235*10^(-7)*x2[16]-3.913360392*10^(-8)*x2[17]-1.*u[1] = 0

 

eq1[2] := -7.425625842*x1[1]-3.446244947*x1[2]+13.78497979*x1[3]-3.693674202*x1[4]+.9897170194*x1[5]-.2651938761*x1[6]+0.7105848494e-1*x1[7]-0.1904006365e-1*x1[8]+0.5101769676e-2*x1[9]-0.1367015052e-2*x1[10]+0.3662905327e-3*x1[11]-0.9814707864e-4*x1[12]+0.2629778184e-4*x1[13]-7.044048706*10^(-6)*x1[14]+1.878412988*10^(-6)*x1[15]-4.696032471*10^(-7)*x1[16]+7.826720785*10^(-8)*x1[17]-1.000000000*x2[2] = 0

 

eq2[2] := -7.425625842*x2[1]-3.446244947*x2[2]+13.78497979*x2[3]-3.693674202*x2[4]+.9897170194*x2[5]-.2651938761*x2[6]+0.7105848494e-1*x2[7]-0.1904006365e-1*x2[8]+0.5101769676e-2*x2[9]-0.1367015052e-2*x2[10]+0.3662905327e-3*x2[11]-0.9814707864e-4*x2[12]+0.2629778184e-4*x2[13]-7.044048706*10^(-6)*x2[14]+1.878412988*10^(-6)*x2[15]-4.696032471*10^(-7)*x2[16]+7.826720785*10^(-8)*x2[17]-1.000000000*u[2] = 0

 

eq1[3] := 1.989690448*x1[1]-11.93814269*x1[2]-.2474292549*x1[3]+12.92785971*x1[4]-3.464009568*x1[5]+.9281785663*x1[6]-.2487046973*x1[7]+0.6664022279e-1*x1[8]-0.1785619387e-1*x1[9]+0.4784552683e-2*x1[10]-0.1282016864e-2*x1[11]+0.3435147752e-3*x1[12]-0.9204223643e-4*x1[13]+0.2465417047e-4*x1[14]-6.574445459*10^(-6)*x1[15]+1.643611365*10^(-6)*x1[16]-2.739352275*10^(-7)*x1[17]-1.000000000*x2[3] = 0

 

eq2[3] := 1.989690448*x2[1]-11.93814269*x2[2]-.2474292549*x2[3]+12.92785971*x2[4]-3.464009568*x2[5]+.9281785663*x2[6]-.2487046973*x2[7]+0.6664022279e-1*x2[8]-0.1785619387e-1*x2[9]+0.4784552683e-2*x2[10]-0.1282016864e-2*x2[11]+0.3435147752e-3*x2[12]-0.9204223643e-4*x2[13]+0.2465417047e-4*x2[14]-6.574445459*10^(-6)*x2[15]+1.643611365*10^(-6)*x2[16]-2.739352275*10^(-7)*x2[17]-1.000000000*u[3] = 0

 

eq1[4] := -.5331359486*x1[1]+3.198815692*x1[2]-12.79526277*x1[3]-0.1776462123e-1*x1[4]+12.86632125*x1[5]-3.447520389*x1[6]+.9237603042*x1[7]-.2475208275*x1[8]+0.6632300579e-1*x1[9]-0.1777119568e-1*x1[10]+0.4761776926e-2*x1[11]-0.1275912022e-2*x1[12]+0.3418711639e-3*x1[13]-0.9157263318e-4*x1[14]+0.2441936885e-4*x1[15]-6.104842212*10^(-6)*x1[16]+1.017473702*10^(-6)*x1[17]-1.000000000*x2[4] = 0

 

eq2[4] := -.5331359486*x2[1]+3.198815692*x2[2]-12.79526277*x2[3]-0.1776462123e-1*x2[4]+12.86632125*x2[5]-3.447520389*x2[6]+.9237603042*x2[7]-.2475208275*x2[8]+0.6632300579e-1*x2[9]-0.1777119568e-1*x2[10]+0.4761776926e-2*x2[11]-0.1275912022e-2*x2[12]+0.3418711639e-3*x2[13]-0.9157263318e-4*x2[14]+0.2441936885e-4*x2[15]-6.104842212*10^(-6)*x2[16]+1.017473702*10^(-6)*x2[17]-1.000000000*u[4] = 0

 

eq1[5] := .1428533469*x1[1]-.8571200814*x1[2]+3.428480326*x1[3]-12.85680122*x1[4]-0.1275442419e-2*x1[5]+12.86190299*x1[6]-3.446336519*x1[7]+.9234430872*x1[8]-.2474358293*x1[9]+0.6630023004e-1*x1[10]-0.1776509084e-1*x1[11]+0.4760133314e-2*x1[12]-0.1275442419e-2*x1[13]+0.3416363623e-3*x1[14]-0.9110302994e-4*x1[15]+0.2277575748e-4*x1[16]-3.795959581*10^(-6)*x1[17]-1.000000000*x2[5] = 0

 

eq2[5] := .1428533469*x2[1]-.8571200814*x2[2]+3.428480326*x2[3]-12.85680122*x2[4]-0.1275442419e-2*x2[5]+12.86190299*x2[6]-3.446336519*x2[7]+.9234430872*x2[8]-.2474358293*x2[9]+0.6630023004e-1*x2[10]-0.1776509084e-1*x2[11]+0.4760133314e-2*x2[12]-0.1275442419e-2*x2[13]+0.3416363623e-3*x2[14]-0.9110302994e-4*x2[15]+0.2277575748e-4*x2[16]-3.795959581*10^(-6)*x2[17]-1.000000000*u[5] = 0

 

eq1[6] := -0.3827743894e-1*x1[1]+.2296646336*x1[2]-.9186585345*x1[3]+3.444969504*x1[4]-12.86121948*x1[5]-0.9157263318e-4*x1[6]+12.86158577*x1[7]-3.446251521*x1[8]+.9234203114*x1[9]-.2474297245*x1[10]+0.6629858642e-1*x1[11]-0.1776462123e-1*x1[12]+0.4759898512e-2*x1[13]-0.1274972816e-2*x1[14]+0.3399927509e-3*x1[15]-0.8499818772e-4*x1[16]+0.1416636462e-4*x1[17]-1.000000000*x2[6] = 0

 

eq2[6] := -0.3827743894e-1*x2[1]+.2296646336*x2[2]-.9186585345*x2[3]+3.444969504*x2[4]-12.86121948*x2[5]-0.9157263318e-4*x2[6]+12.86158577*x2[7]-3.446251521*x2[8]+.9234203114*x2[9]-.2474297245*x2[10]+0.6629858642e-1*x2[11]-0.1776462123e-1*x2[12]+0.4759898512e-2*x2[13]-0.1274972816e-2*x2[14]+0.3399927509e-3*x2[15]-0.8499818772e-4*x2[16]+0.1416636462e-4*x2[17]-1.000000000*u[6] = 0

 

eq1[7] := 0.1025640885e-1*x1[1]-0.6153845311e-1*x1[2]+.2461538124*x1[3]-.9230767966*x1[4]+3.446153374*x1[5]-12.86153670*x1[6]-6.574445459*10^(-6)*x1[7]+12.86156300*x1[8]-3.446245416*x1[9]+.9234186678*x1[10]-.2474292549*x1[11]+0.6629835162e-1*x1[12]-0.1776415163e-1*x1[13]+0.4758254901e-2*x1[14]-0.1268867974e-2*x1[15]+0.3172169934e-3*x1[16]-0.5286949890e-4*x1[17]-1.000000000*x2[7] = 0

 

eq2[7] := 0.1025640885e-1*x2[1]-0.6153845311e-1*x2[2]+.2461538124*x2[3]-.9230767966*x2[4]+3.446153374*x2[5]-12.86153670*x2[6]-6.574445459*10^(-6)*x2[7]+12.86156300*x2[8]-3.446245416*x2[9]+.9234186678*x2[10]-.2474292549*x2[11]+0.6629835162e-1*x2[12]-0.1776415163e-1*x2[13]+0.4758254901e-2*x2[14]-0.1268867974e-2*x2[15]+0.3172169934e-3*x2[16]-0.5286949890e-4*x2[17]-1.000000000*u[7] = 0

 

eq1[8] := -0.2748196469e-2*x1[1]+0.1648917882e-1*x1[2]-0.6595671526e-1*x1[3]+.2473376822*x1[4]-.9233940136*x1[5]+3.446238372*x1[6]-12.86155948*x1[7]-4.696032471*10^(-7)*x1[8]+12.86156135*x1[9]-3.446244947*x1[10]+.9234184330*x1[11]-.2474287852*x1[12]+0.6629670801e-1*x1[13]-0.1775804679e-1*x1[14]+0.4735479144e-2*x1[15]-0.1183869786e-2*x1[16]+0.1973116310e-3*x1[17]-1.000000000*x2[8] = 0

 

eq2[8] := -0.2748196469e-2*x2[1]+0.1648917882e-1*x2[2]-0.6595671526e-1*x2[3]+.2473376822*x2[4]-.9233940136*x2[5]+3.446238372*x2[6]-12.86155948*x2[7]-4.696032471*10^(-7)*x2[8]+12.86156135*x2[9]-3.446244947*x2[10]+.9234184330*x2[11]-.2474287852*x2[12]+0.6629670801e-1*x2[13]-0.1775804679e-1*x2[14]+0.4735479144e-2*x2[15]-0.1183869786e-2*x2[16]+0.1973116310e-3*x2[17]-1.000000000*u[8] = 0

 

eq1[9] := 0.7363770250e-3*x1[1]-0.4418262150e-2*x1[2]+0.1767304860e-1*x1[3]-0.6627393225e-1*x1[4]+.2474226804*x1[5]-.9234167894*x1[6]+3.446244477*x1[7]-12.86156112*x1[8]+12.86156112*x1[10]-3.446244477*x1[11]+.9234167894*x1[12]-.2474226804*x1[13]+0.6627393225e-1*x1[14]-0.1767304860e-1*x1[15]+0.4418262150e-2*x1[16]-0.7363770250e-3*x1[17]-1.000000000*x2[9] = 0

 

eq2[9] := 0.7363770250e-3*x2[1]-0.4418262150e-2*x2[2]+0.1767304860e-1*x2[3]-0.6627393225e-1*x2[4]+.2474226804*x2[5]-.9234167894*x2[6]+3.446244477*x2[7]-12.86156112*x2[8]+12.86156112*x2[10]-3.446244477*x2[11]+.9234167894*x2[12]-.2474226804*x2[13]+0.6627393225e-1*x2[14]-0.1767304860e-1*x2[15]+0.4418262150e-2*x2[16]-0.7363770250e-3*x2[17]-1.000000000*u[9] = 0

 

eq1[10] := -0.1973116310e-3*x1[1]+0.1183869786e-2*x1[2]-0.4735479144e-2*x1[3]+0.1775804679e-1*x1[4]-0.6629670801e-1*x1[5]+.2474287852*x1[6]-.9234184330*x1[7]+3.446244947*x1[8]-12.86156135*x1[9]+4.696032471*10^(-7)*x1[10]+12.86155948*x1[11]-3.446238372*x1[12]+.9233940136*x1[13]-.2473376822*x1[14]+0.6595671526e-1*x1[15]-0.1648917882e-1*x1[16]+0.2748196469e-2*x1[17]-1.000000000*x2[10] = 0

 

eq2[10] := -0.1973116310e-3*x2[1]+0.1183869786e-2*x2[2]-0.4735479144e-2*x2[3]+0.1775804679e-1*x2[4]-0.6629670801e-1*x2[5]+.2474287852*x2[6]-.9234184330*x2[7]+3.446244947*x2[8]-12.86156135*x2[9]+4.696032471*10^(-7)*x2[10]+12.86155948*x2[11]-3.446238372*x2[12]+.9233940136*x2[13]-.2473376822*x2[14]+0.6595671526e-1*x2[15]-0.1648917882e-1*x2[16]+0.2748196469e-2*x2[17]-1.000000000*u[10] = 0

 

eq1[11] := 0.5286949890e-4*x1[1]-0.3172169934e-3*x1[2]+0.1268867974e-2*x1[3]-0.4758254901e-2*x1[4]+0.1776415163e-1*x1[5]-0.6629835162e-1*x1[6]+.2474292549*x1[7]-.9234186678*x1[8]+3.446245416*x1[9]-12.86156300*x1[10]+6.574445459*10^(-6)*x1[11]+12.86153670*x1[12]-3.446153374*x1[13]+.9230767966*x1[14]-.2461538124*x1[15]+0.6153845311e-1*x1[16]-0.1025640885e-1*x1[17]-1.00000000*x2[11] = 0

 

eq2[11] := 0.5286949890e-4*x2[1]-0.3172169934e-3*x2[2]+0.1268867974e-2*x2[3]-0.4758254901e-2*x2[4]+0.1776415163e-1*x2[5]-0.6629835162e-1*x2[6]+.2474292549*x2[7]-.9234186678*x2[8]+3.446245416*x2[9]-12.86156300*x2[10]+6.574445459*10^(-6)*x2[11]+12.86153670*x2[12]-3.446153374*x2[13]+.9230767966*x2[14]-.2461538124*x2[15]+0.6153845311e-1*x2[16]-0.1025640885e-1*x2[17]-1.00000000*u[11] = 0

 

eq1[12] := -0.1416636462e-4*x1[1]+0.8499818772e-4*x1[2]-0.3399927509e-3*x1[3]+0.1274972816e-2*x1[4]-0.4759898512e-2*x1[5]+0.1776462123e-1*x1[6]-0.6629858642e-1*x1[7]+.2474297245*x1[8]-.9234203114*x1[9]+3.446251521*x1[10]-12.86158577*x1[11]+0.9157263318e-4*x1[12]+12.86121948*x1[13]-3.444969504*x1[14]+.9186585345*x1[15]-.2296646336*x1[16]+0.3827743894e-1*x1[17]-1.00000000*x2[12] = 0

 

eq2[12] := -0.1416636462e-4*x2[1]+0.8499818772e-4*x2[2]-0.3399927509e-3*x2[3]+0.1274972816e-2*x2[4]-0.4759898512e-2*x2[5]+0.1776462123e-1*x2[6]-0.6629858642e-1*x2[7]+.2474297245*x2[8]-.9234203114*x2[9]+3.446251521*x2[10]-12.86158577*x2[11]+0.9157263318e-4*x2[12]+12.86121948*x2[13]-3.444969504*x2[14]+.9186585345*x2[15]-.2296646336*x2[16]+0.3827743894e-1*x2[17]-1.00000000*u[12] = 0

 

eq1[13] := 3.795959581*10^(-6)*x1[1]-0.2277575748e-4*x1[2]+0.9110302994e-4*x1[3]-0.3416363623e-3*x1[4]+0.1275442419e-2*x1[5]-0.4760133314e-2*x1[6]+0.1776509084e-1*x1[7]-0.6630023004e-1*x1[8]+.2474358293*x1[9]-.9234430872*x1[10]+3.446336519*x1[11]-12.86190299*x1[12]+0.1275442419e-2*x1[13]+12.85680122*x1[14]-3.428480326*x1[15]+.8571200814*x1[16]-.1428533469*x1[17]-1.00000000*x2[13] = 0

 

eq2[13] := 3.795959581*10^(-6)*x2[1]-0.2277575748e-4*x2[2]+0.9110302994e-4*x2[3]-0.3416363623e-3*x2[4]+0.1275442419e-2*x2[5]-0.4760133314e-2*x2[6]+0.1776509084e-1*x2[7]-0.6630023004e-1*x2[8]+.2474358293*x2[9]-.9234430872*x2[10]+3.446336519*x2[11]-12.86190299*x2[12]+0.1275442419e-2*x2[13]+12.85680122*x2[14]-3.428480326*x2[15]+.8571200814*x2[16]-.1428533469*x2[17]-1.00000000*u[13] = 0

 

eq1[14] := -1.017473702*10^(-6)*x1[1]+6.104842212*10^(-6)*x1[2]-0.2441936885e-4*x1[3]+0.9157263318e-4*x1[4]-0.3418711639e-3*x1[5]+0.1275912022e-2*x1[6]-0.4761776926e-2*x1[7]+0.1777119568e-1*x1[8]-0.6632300579e-1*x1[9]+.2475208275*x1[10]-.9237603042*x1[11]+3.447520389*x1[12]-12.86632125*x1[13]+0.1776462123e-1*x1[14]+12.79526277*x1[15]-3.198815692*x1[16]+.5331359486*x1[17]-1.00000000*x2[14] = 0

 

eq2[14] := -1.017473702*10^(-6)*x2[1]+6.104842212*10^(-6)*x2[2]-0.2441936885e-4*x2[3]+0.9157263318e-4*x2[4]-0.3418711639e-3*x2[5]+0.1275912022e-2*x2[6]-0.4761776926e-2*x2[7]+0.1777119568e-1*x2[8]-0.6632300579e-1*x2[9]+.2475208275*x2[10]-.9237603042*x2[11]+3.447520389*x2[12]-12.86632125*x2[13]+0.1776462123e-1*x2[14]+12.79526277*x2[15]-3.198815692*x2[16]+.5331359486*x2[17]-1.00000000*u[14] = 0

 

eq1[15] := 2.739352275*10^(-7)*x1[1]-1.643611365*10^(-6)*x1[2]+6.574445459*10^(-6)*x1[3]-0.2465417047e-4*x1[4]+0.9204223643e-4*x1[5]-0.3435147752e-3*x1[6]+0.1282016864e-2*x1[7]-0.4784552683e-2*x1[8]+0.1785619387e-1*x1[9]-0.6664022279e-1*x1[10]+.2487046973*x1[11]-.9281785663*x1[12]+3.464009568*x1[13]-12.92785971*x1[14]+.2474292549*x1[15]+11.93814269*x1[16]-1.989690448*x1[17]-1.00000000*x2[15] = 0

 

eq2[15] := 2.739352275*10^(-7)*x2[1]-1.643611365*10^(-6)*x2[2]+6.574445459*10^(-6)*x2[3]-0.2465417047e-4*x2[4]+0.9204223643e-4*x2[5]-0.3435147752e-3*x2[6]+0.1282016864e-2*x2[7]-0.4784552683e-2*x2[8]+0.1785619387e-1*x2[9]-0.6664022279e-1*x2[10]+.2487046973*x2[11]-.9281785663*x2[12]+3.464009568*x2[13]-12.92785971*x2[14]+.2474292549*x2[15]+11.93814269*x2[16]-1.989690448*x2[17]-1.00000000*u[15] = 0

 

eq1[16] := -7.826720785*10^(-8)*x1[1]+4.696032471*10^(-7)*x1[2]-1.878412988*10^(-6)*x1[3]+7.044048706*10^(-6)*x1[4]-0.2629778184e-4*x1[5]+0.9814707864e-4*x1[6]-0.3662905327e-3*x1[7]+0.1367015052e-2*x1[8]-0.5101769676e-2*x1[9]+0.1904006365e-1*x1[10]-0.7105848494e-1*x1[11]+.2651938761*x1[12]-.9897170194*x1[13]+3.693674202*x1[14]-13.78497979*x1[15]+3.446244947*x1[16]+7.425625842*x1[17]-1.00000000*x2[16] = 0

 

eq2[16] := -7.826720785*10^(-8)*x2[1]+4.696032471*10^(-7)*x2[2]-1.878412988*10^(-6)*x2[3]+7.044048706*10^(-6)*x2[4]-0.2629778184e-4*x2[5]+0.9814707864e-4*x2[6]-0.3662905327e-3*x2[7]+0.1367015052e-2*x2[8]-0.5101769676e-2*x2[9]+0.1904006365e-1*x2[10]-0.7105848494e-1*x2[11]+.2651938761*x2[12]-.9897170194*x2[13]+3.693674202*x2[14]-13.78497979*x2[15]+3.446244947*x2[16]+7.425625842*x2[17]-1.00000000*u[16] = 0

 

eq1[17] := 3.913360392*10^(-8)*x1[1]-2.348016235*10^(-7)*x1[2]+9.392064942*10^(-7)*x1[3]-3.522024353*10^(-6)*x1[4]+0.1314889092e-4*x1[5]-0.4907353932e-4*x1[6]+0.1831452664e-3*x1[7]-0.6835075261e-3*x1[8]+0.2550884838e-2*x1[9]-0.9520031827e-2*x1[10]+0.3552924247e-1*x1[11]-.1325969380*x1[12]+.4948585097*x1[13]-1.846837101*x1[14]+6.892489894*x1[15]-25.72312247*x1[16]+20.28718708*x1[17]-1.*x2[17] = 0

 

eq2[17] := 3.913360392*10^(-8)*x2[1]-2.348016235*10^(-7)*x2[2]+9.392064942*10^(-7)*x2[3]-3.522024353*10^(-6)*x2[4]+0.1314889092e-4*x2[5]-0.4907353932e-4*x2[6]+0.1831452664e-3*x2[7]-0.6835075261e-3*x2[8]+0.2550884838e-2*x2[9]-0.9520031827e-2*x2[10]+0.3552924247e-1*x2[11]-.1325969380*x2[12]+.4948585097*x2[13]-1.846837101*x2[14]+6.892489894*x2[15]-25.72312247*x2[16]+20.28718708*x2[17]-1.*u[17] = 0

 

eq3[1] := 1.*x1[1]-.1, 0

 

eq3[2] := 1.000000000*x1[2]-.1, 0

 

eq3[3] := 1.000000000*x1[3]-.1, 0

 

eq3[4] := 1.000000000*x1[4]-.1, 0

 

eq3[5] := 1.000000000*x1[5]-.1, 0

 

eq3[6] := 1.000000000*x1[6]-.1, 0

 

eq3[7] := 1.000000000*x1[7]-.1, 0

 

eq3[8] := 1.000000000*x1[8]-.1, 0

 

eq3[9] := 1.000000000*x1[9]-.1, 0

 

eq3[10] := 1.000000000*x1[10]-.1, 0

 

eq3[11] := 1.00000000*x1[11]-.1, 0

 

eq3[12] := 1.00000000*x1[12]-.1, 0

 

eq3[13] := 1.00000000*x1[13]-.1, 0

 

eq3[14] := 1.00000000*x1[14]-.1, 0

 

eq3[15] := 1.00000000*x1[15]-.1, 0

 

eq3[16] := 1.00000000*x1[16]-.1, 0

 

eq3[17] := 1.*x1[17]-.1, 0

 

eq1[0] := 1.*x1[1] = 0

 

eq2[0] := 1.*x2[1]-1 = 0

 

eq1[18] := 1.*x1[17] = 0

 

eq2[18] := 1.*x2[17] = -1

 

eqq1 := {-7.425625842*x1[1]-3.446244947*x1[2]+13.78497979*x1[3]-3.693674202*x1[4]+.9897170194*x1[5]-.2651938761*x1[6]+0.7105848494e-1*x1[7]-0.1904006365e-1*x1[8]+0.5101769676e-2*x1[9]-0.1367015052e-2*x1[10]+0.3662905327e-3*x1[11]-0.9814707864e-4*x1[12]+0.2629778184e-4*x1[13]-7.044048706*10^(-6)*x1[14]+1.878412988*10^(-6)*x1[15]-4.696032471*10^(-7)*x1[16]+7.826720785*10^(-8)*x1[17]-1.000000000*x2[2] = 0}

 

eqq2 := {-7.425625842*x2[1]-3.446244947*x2[2]+13.78497979*x2[3]-3.693674202*x2[4]+.9897170194*x2[5]-.2651938761*x2[6]+0.7105848494e-1*x2[7]-0.1904006365e-1*x2[8]+0.5101769676e-2*x2[9]-0.1367015052e-2*x2[10]+0.3662905327e-3*x2[11]-0.9814707864e-4*x2[12]+0.2629778184e-4*x2[13]-7.044048706*10^(-6)*x2[14]+1.878412988*10^(-6)*x2[15]-4.696032471*10^(-7)*x2[16]+7.826720785*10^(-8)*x2[17]-1.000000000*u[2] = 0}

 

eqq3 := {0, 1.*x1[17]-.1}

 

eq := {0, 1.*x1[17]-.1, -7.425625842*x1[1]-3.446244947*x1[2]+13.78497979*x1[3]-3.693674202*x1[4]+.9897170194*x1[5]-.2651938761*x1[6]+0.7105848494e-1*x1[7]-0.1904006365e-1*x1[8]+0.5101769676e-2*x1[9]-0.1367015052e-2*x1[10]+0.3662905327e-3*x1[11]-0.9814707864e-4*x1[12]+0.2629778184e-4*x1[13]-7.044048706*10^(-6)*x1[14]+1.878412988*10^(-6)*x1[15]-4.696032471*10^(-7)*x1[16]+7.826720785*10^(-8)*x1[17]-1.000000000*x2[2] = 0, -7.425625842*x2[1]-3.446244947*x2[2]+13.78497979*x2[3]-3.693674202*x2[4]+.9897170194*x2[5]-.2651938761*x2[6]+0.7105848494e-1*x2[7]-0.1904006365e-1*x2[8]+0.5101769676e-2*x2[9]-0.1367015052e-2*x2[10]+0.3662905327e-3*x2[11]-0.9814707864e-4*x2[12]+0.2629778184e-4*x2[13]-7.044048706*10^(-6)*x2[14]+1.878412988*10^(-6)*x2[15]-4.696032471*10^(-7)*x2[16]+7.826720785*10^(-8)*x2[17]-1.000000000*u[2] = 0}

 

[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve]

 

Error, (in Optimization:-NLPSolve) constraints must be specified as a set or list of equalities and inequalities

 

uexact := piecewise(0 <= x and x <= .3, 200*x*(1/9)-20/3, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -200*x*(1/9)+140/9)

 

x2exact := piecewise(0 <= x and x <= .3, (100/9)*x^2-(20/3)*x+1, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(100/9)*x^2+(140/9)*x-49/9)

 

piecewise(0 <= x and x <= .3, (100/27)*x^3-(10/3)*x^2+x, .3 <= x and x <= .7, 1/10, .7 <= x and x <= 1, -(100/27)*x^3+(70/9)*x^2-(49/9)*x+37/27)

 

Warning, expecting only range variable x in expression x1[1]*piecewise(0. <= 16.*x+1. and 16.*x <= 0.,16.*x+1.,0. < 16.*x and 16.*x <= 1.,1.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[2]*piecewise(0. <= 16.*x and 16.*x <= 1.,16.*x,1. < 16.*x and 16.*x <= 2.,2.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[3]*piecewise(0. <= 16.*x-1. and 16.*x <= 2.,16.*x-1.,0. < 16.*x-2. and 16.*x <= 3.,3.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[4]*piecewise(0. <= 16.*x-2. and 16.*x <= 3.,16.*x-2.,0. < 16.*x-3. and 16.*x <= 4.,4.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[5]*piecewise(0. <= 16.*x-3. and 16.*x <= 4.,16.*x-3.,0. < 16.*x-4. and 16.*x <= 5.,5.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[6]*piecewise(0. <= 16.*x-4. and 16.*x <= 5.,16.*x-4.,0. < 16.*x-5. and 16.*x <= 6.,6.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[7]*piecewise(0. <= 16.*x-5. and 16.*x <= 6.,16.*x-5.,0. < 16.*x-6. and 16.*x <= 7.,7.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[8]*piecewise(0. <= 16.*x-6. and 16.*x <= 7.,16.*x-6.,0. < 16.*x-7. and 16.*x <= 8.,8.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[9]*piecewise(0. <= 16.*x-7. and 16.*x <= 8.,16.*x-7.,0. < 16.*x-8. and 16.*x <= 9.,9.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[10]*piecewise(0. <= 16.*x-8. and 16.*x <= 9.,16.*x-8.,0. < 16.*x-9. and 16.*x <= 10.,10.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[11]*piecewise(0. <= 16.*x-9. and 16.*x <= 10.,16.*x-9.,0. < 16.*x-10. and 16.*x <= 11.,11.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[12]*piecewise(0. <= 16.*x-10. and 16.*x <= 11.,16.*x-10.,0. < 16.*x-11. and 16.*x <= 12.,12.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[13]*piecewise(0. <= 16.*x-11. and 16.*x <= 12.,16.*x-11.,0. < 16.*x-12. and 16.*x <= 13.,13.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[14]*piecewise(0. <= 16.*x-12. and 16.*x <= 13.,16.*x-12.,0. < 16.*x-13. and 16.*x <= 14.,14.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[15]*piecewise(0. <= 16.*x-13. and 16.*x <= 14.,16.*x-13.,0. < 16.*x-14. and 16.*x <= 15.,15.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[16]*piecewise(0. <= 16.*x-14. and 16.*x <= 15.,16.*x-14.,0. < 16.*x-15. and 16.*x <= 16.,16.-16.*x)*piecewise(0 <= x and x <= 1,1)+x1[17]*piecewise(0. <= 16.*x-15. and 16.*x <= 16.,16.*x-15.,0. < 16.*x-16. and 16.*x <= 17.,17.-16.*x)*piecewise(0 <= x and x <= 1,1) to be plotted but found names [x1[1], x1[2], x1[3], x1[4], x1[5], x1[6], x1[7], x1[8], x1[9], x1[10], x1[11], x1[12], x1[13], x1[14], x1[15], x1[16], x1[17]]

 

 

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Hello Everyone;

Hope you are fine. I am applying rk-4 and Runge-Kutta-Fehlberg method for system of odes but there is no difference in the result of these method. Can anybody guide about that for my problem. I have uploaded the code. Thanks in advance.

Question#3.mw

 

Hello!

How do I solve this system? could someone help me please.

restart;
eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t),

y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

with:
x(0) = 1
y(0) =
y(0) = 857.1428571

restart

eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t), y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

{x(t+1) = .9999800000*x(t)+0.7000000000e-7*y(t), y(t+1) = 0.6000000000e-4*x(t)+.9999999300*y(t)}

(1)

x(0) = 1

x(0) = 1

(2)

y(0) = 0.6e-2/(0.1e-3*0.7e-1)

y(0) = 857.1428571

(3)

``

Download SystemRecursive.mw

Good day all.

My particular question concerns a Traveling Salesman-type problem.

Suppose I wish to move along the x-y plane and visit specific nodes (see the attached worksheet).

Starting at the origin, A, I intend to visit four locations, B to E, and finally return to the origin point. These nodes may be visited in any order - but, my total distance travelled must be a minimum.
However, my direction of travel is restricted; namely:

1. Movement is limited to the x and y-directions only (up and down as well as left and right)
2. Horizontal (left or right) movement is permitten only at y=1 and y=10

This second rule restricts me from turning left or right in between y= 1 and 10.
The Traveling Salesman routine (attached) is constructed to select a tour that is confined to orthogonal movement but it does not observe the second restriction (i.e. move left or right when you reach y=1 or y=10).

Is there any way in which I can build this condition into the routine so that the movement along the circuit observes the restrictions? 

If so - is it possible to graphically illustrate the order of travel (using arrows from point-to-point) on a point plot?

I appreciate you taking the time to read this.

MaplePrimes_May_6.mw

I tried to graph the function f(x)=x^(1/3) but it only gives me a graph for non-negative x's, when the function f has all real numbers as its domain.

Maybe I'm doing it wrong.

Thank you.

Hey I’m trying to shift a function horizontally to the right.

I have the following 3 functions:

V1 := -x

V2:= -2*x + 4.95

V3:= -x + 1.665

Function V2 I want to shift l_1 to the right, and V3 I want to shift l_1 + l_2 to the right.

I know I can do this manually by define the functions:

V2:= -2*(x-l_1) + 4.95

V3:= -(x-l_1-l_2) + 1.665

Where l_1:=1.665 and l_2:=4.95

Is there a way to do this without typing it manually?

By the way it’s only for plotting, so it’s not necessary for me to actually define them, if there is a way to do it within a plot some how.

Thank you in advance.

I am trying to solve these equation using fsolve, but it returns the same valve. Please provide a solution.\

Please see the attachment. 

Hi, with Units[Simple] package loaded, I tried to differentiate a few functions using D[n] but it does not work. problem.mw

a := proc (x, y) options operator, arrow; exp(x*y) end proc

proc (x, y) options operator, arrow; exp(y*x) end proc

(1)

D[1](a)

proc (x, y) options operator, arrow; y*exp(y*x) end proc

(2)

D[2](a)

proc (x, y) options operator, arrow; x*exp(y*x) end proc

(3)

retart

retart

(4)

"with(Units[Simple]):"

a := proc (x, y) options operator, arrow; exp(x*y) end proc

proc (x, y) options operator, arrow; Units:-Simple:-exp(Units:-Simple:-`*`(x, y)) end proc

(5)

D[1](a)

Error, (in tools/gensym) too many levels of recursion

 

D[2](a)

Error, (in tools/gensym) too many levels of recursion

 

NULL

Download problem.mw

Hi! I've got a set of subsets S with Abeing the i-subset. I need to sum up all the x's in all the Ai's. How can this be achieved?

(ex):

sum( { {a, b, c}, {a, b, d} } )= 2a+2b+c+d

Hey I’m trying to define the antiderivative for a function:

g(x) = 1

G(x) = int(g(x),x)

When I then type:

G(x) and press enter Maple gives me G(x) = x which of course is correct

But I can’t type:

G(5)

Then it gives me the error message:

Error, (in int) integration range or variable must be specified in the second argument, got 5

How to fix this?

I know I can type G(x) = x manually but I’m not interested in doing so, because in my document I’m going to have a lot of antiderivatives.

Thanks in advance.

I have a student who then she uses tools/assistent/import data and then the file then Maple claims the Excel file is empty? She uses Maple 2021.2. File works on other my and other student computers. 

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