Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Let say, 

A= A1+A2+.....................+An

B=B1+B2+.....................+Bn,

C=C1+C2+.....................+Cn

And all the values of A1 to Cn may be both positive or Negative.

Then, how to program to find the Maximum Value of  (A^2+B^2+C^2+A.B+B.C+C.A)^(1/2).

The long form of ScientificConstants[GetValue] is not working in at least Maple 2021 and Maple 2022

ScientificConstants[GetValue](Constant(g))

 

This is causing issues for MapleFlow, not being able to call on a constant. 

**edit some of the long forms work - specifically the GetValue does not.  I modified the title to reflect that.**

i have this sequence :f:=n->n/n+1
       

> f1:=seq(f(n), n = 0 .. 10);
                       f1:= 0,1/2,3/4,4/5,5/6,6/7,7/8,8/9,10/11

i want to create these sequences by using f :

1) 0,2/3,4/5,6/7,8/9,...

2)2/3,9/10,16/17,..

3) 1/2^2,3^2/4^2,5^2/6^2,7^2/8^2

4)0,3/4,8/9,24/25,35/36
        can anyone help me ?              

Suppose 

$P(x,y)=\sum_{i+j=0}^N \alpha_{i}x^{i}y^{j}$

is a multivariable polynomial of Nth degree. How may I express the first and second derivatives of $P(x,y)$ through Maplesoft?

Hello Everyone;

Hope you are fine. Solve comand is solving Equation saperately but samultanously. Kindly guide me about this. I have uploaded and pasted the code as well. The last comand (in red color) is not working. I am waiting for the kind response.

Thanks

QuestionNo1.mw

 

 

 

with(GroupTheory);
G := GaloisGroup(x^5 + 20*x + 32, x);

I just can get a result like:

GroupTheory:-GaloisGroup(x^5 + 20*x + 32, x)

But how do I know exactly what group it is? Actually I know the galois group is D5, But can we use maple to get this information?

Hi! I'm having doubts about the "automatic spacing" in maple. I would like to know two things:

1-can incorrect spacing ruin my code? (Ex by typing "spacebar" too many times )

2- i know that to type spacebar is obligatory after: proc()" "...end proc;    Is there any other situation in wich to use spacebar isn't optional? Thanks for your answers

In the positive range Maple confirms that this is true.
In the real range Maple fails to provide an answer (see attachments).

Is this identity correct?

restart

kernelopts(version)

`Maple 2022.0, X86 64 WINDOWS, Mar 8 2022, Build ID 1599809`

(1)

NULL

is(arctan(-x) = -arctan(x))

true

(2)

`assuming`([is(arctan(x, y) = -arctan(-x, y))], [x::real, y::real])

FAIL

(3)

`assuming`([is(arctan(x, y) = -arctan(-x, y))], [x::positive, y::positive])

true

(4)

`assuming`([simplify(arctan(-x, y)+arctan(x, y), trig)], [x::real, y::real])

arctan(-x, y)+arctan(x, y)

(5)

But

plot3d([arctan(-x, y)+arctan(x, y)], x = -1000000 .. 1000000, y = -1000000 .. 1000000, title = arctan(-x, y)+arctan(x, y))

 

On a unit circle

x = cos(alpha), y = sin(alpha)

x = cos(alpha), y = sin(alpha)

(6)

subs(x = cos(alpha), y = sin(alpha), arctan(-x, y)+arctan(x, y))

arctan(-cos(alpha), sin(alpha))+arctan(cos(alpha), sin(alpha))

(7)

`assuming`([simplify(%)], [alpha::real])

arctan(-cos(alpha), sin(alpha))+arctan(cos(alpha), sin(alpha))

(8)

`assuming`([simplify(%)], [alpha::positive])

arctan(-cos(alpha), sin(alpha))+arctan(cos(alpha), sin(alpha))

(9)

`assuming`([simplify(%)], [-Pi < alpha and alpha < Pi])

arctan(-cos(alpha), sin(alpha))+arctan(cos(alpha), sin(alpha))

(10)

plot(arctan(-cos(alpha), sin(alpha))+arctan(cos(alpha), sin(alpha)), alpha = -2*Pi .. 2*Pi, axes = boxed, color = red)

 

NULL


Download arctan_xy_simplify.mw

and another maybe related case where simplification does not work

arctan_xy_simplify_2.mw

Hello everyone,

I am trying to solve an equation using the "solve(...)" function but the coefficients of the equation are changing.

I am using the coefficients as list but the "solve(...)" function gives error: "Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'badly formed input to solve: not fully algebraic'"

I am attaching the Maple document.

 

However, what I want to achieve, is the solution for each value in the list.

Here is an easy example of what I am saying:

a=3*x+k where k=[list of values], a=[another list of values].

I want to find "x" for each pair of values (a,k) in the list.

 

Thank you !
 

``

``

LCC Resonant Converter - Frequency Finder

 

 

restart``

with(Student[Calculus1])

V__out := 50.0

`&omega;__line` := 2.0*Pi*50

t := [seq(0 .. 10*10^(-3), .1*10^(-3))]

theta := `&omega;__line`*t

v__line := 85*sqrt(2.0)*`~`[sin](theta)

m := 1

Q__s := 3.2*`~`[`^`](`~`[sin](theta), 2)

``

f__n := `assuming`([solve((1/120)*V__out = 1/sqrt((-m*x^2+m+1)^2+(Q__s*(x-1/x))^2), x, useassumptions)], [x::positive])

Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'badly formed input to solve: not fully algebraic'

 

``


 

Download LCC_gain_freqFinder.mwLCC_gain_freqFinder.mw

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

 

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