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Ronan

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11 years, 201 days
East Grinstead, United Kingdom
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These are answers submitted by Ronan

I had problems with EllipticPi earlier t...

Ronan 827
October 30 2017
0 1

Hello,

Dont know if this will help you or not. I posted the link below in March.

There are different definitions of the elliptic integrals used by various software packages. Without doing a couple of nights restudy I can't offer much else. Hope it helps.

https://www.mapleprimes.com/questions/221540-How-Do-I-Speed-Up-The-Evaluation-Of

 

 

Use evalf...

Ronan 827
October 15 2017
0 1

180*evalf(FindAngle(p1, p2))/Pi

evalf evaluates acrcos to a decimal number in radians. 180/Pi converts radians to degrees.

Options - Precision- Limit expression le...

Ronan 827
September 20 2017
0 0

Thy increasing the number of diditas displayed to 5 million and see what is that is ok.

A related post on this...

Ronan 827
August 11 2017
1 0

Yes. Dr R Lopez posted this on the change in Maple 2017 http://www.mapleprimes.com/maplesoftblog/208309-Typesetting-And-Maple-2017

The Determinant =0, so no solution...

Ronan 827
April 14 2017
0 1

The Determinant to the Equations = 0 so the system cant be solved. Maybe you have an error.
 

restart

``

with(LinearAlgebra)

[`&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]

 (1)

``

eq1 := x[1]-x[2] = 0;

x[1]-x[2] = 0

 (2)

eq2 := -x[1]+2*x[2]-x[3] = 0;

-x[1]+2*x[2]-x[3] = 0

 (3)

eq3 := -x[2]+2*x[3]-x[4] = 0;

-x[2]+2*x[3]-x[4] = 0

 (4)

eq4 := -x[3]+x[4]-t = 0;

-x[3]+x[4]-t = 0

 (5)

M, v := GenerateMatrix({eq1, eq2, eq3, eq4}, [x[1], x[2], x[3], x[4]])

Matrix(%id = 18446744074805789630), Vector[column](%id = 18446744074805789510)

 (6)

LinearSolve(M, v)

Error, (in LinearAlgebra:-LinearSolve) inconsistent system

  

LinearAlgebra:-Rank(M)

4

 (7)

GaussianElimination(M)

Matrix(%id = 18446744074805811910)

 (8)

LinearAlgebra:-Determinant(M)

0

 (9)

``


 

Download Eqns-1.mw

Break up the Sum...

Ronan 827
January 31 2016
1 6


This Is how I would approach the issue. Could be a problem if l=1 or n.

restart

``

C := (sum(A[k]*x[i, k], k = 1 .. l-1)+sum(A[k]*x[i, k], k = l+1 .. n)+A[l]*x[i, l])^2-(2*(sum(A[k]*x[i, k], k = 1 .. l-1)+sum(A[k]*x[i, k], k = l+1 .. n)+A[l]*x[i, l]))*y[i]+y[i]^2

(sum(A[k]*x[i, k], k = 1 .. l-1)+sum(A[k]*x[i, k], k = l+1 .. n)+A[l]*x[i, l])^2-2*(sum(A[k]*x[i, k], k = 1 .. l-1)+sum(A[k]*x[i, k], k = l+1 .. n)+A[l]*x[i, l])*y[i]+y[i]^2

 (1)

diff(C, A[l])

2*(sum(A[k]*x[i, k], k = 1 .. l-1)+sum(A[k]*x[i, k], k = l+1 .. n)+A[l]*x[i, l])*x[i, l]-2*x[i, l]*y[i]

 (2)

``


Download diff_sum.mw

 

 

Incorrect Variables Listed...

Ronan 827
November 16 2015
0 2

.Replace in solve({.....................},{c__1,c__3,c__4,x}) and it works

 

Undefined variables...

Ronan 827
July 22 2014
0 0


You haven't defined "p", you have "ep" so I assumed that to be e*p. You also have defined "del" so I changed that to 1 just to see what would happen. Could be totally wrong but it solves easily then.

``

> 

restart
> 

e := 5

5

 (1)
> 

f := 0.714e-1

0.714e-1

 (2)
> 

p := 0.815e-1

0.815e-1

 (3)
> 

q := .397

.397

 (4)
> 

Sol := solve({(-n+(p*q/((1+f*n)^2+(1+T-n)^2))^2)/(e*p) = 0, -T+p*(1+e*f*n)/((1+f*n)^2+(1+T-n)^2) = 0}, [T, n])

[[T = 0.3919624923e-1, n = 0.2421000982e-3], [T = -.9371446226-.8116256169*I, n = 0.6704759545e-1+.2196973222*I], [T = -2.934201781+3.533684884*I, n = -1.734513872+2.660302975*I], [T = -3.532762021+1.455618087*I, n = -2.704556354+2.261007132*I], [T = -3.532762021-1.455618087*I, n = -2.704556354-2.261007132*I], [T = -2.934201781-3.533684884*I, n = -1.734513872-2.660302975*I], [T = -.9371446226+.8116256169*I, n = 0.6704759545e-1-.2196973222*I]]

 (5)
> 

nops(Sol)

7

 (6)
> 

for i to nops(Sol) do Sol[i] end do

[T = 0.3919624923e-1, n = 0.2421000982e-3]

  

[T = -.9371446226-.8116256169*I, n = 0.6704759545e-1+.2196973222*I]

  

[T = -2.934201781+3.533684884*I, n = -1.734513872+2.660302975*I]

  

[T = -3.532762021+1.455618087*I, n = -2.704556354+2.261007132*I]

  

[T = -3.532762021-1.455618087*I, n = -2.704556354-2.261007132*I]

  

[T = -2.934201781-3.533684884*I, n = -1.734513872-2.660302975*I]

  

[T = -.9371446226+.8116256169*I, n = 0.6704759545e-1-.2196973222*I]

 (7)
> 

``

``


Download maple-1.mw

 

A post that may help you....

Ronan 827
June 14 2013
0 0


This might help you. It was posted as an answer to my animation question many months ago. I found it extremly helpful.

http://www.mapleprimes.com/posts/136156-Example-Of-Animation

 

 

Rank...

Ronan 827
March 26 2013
0 0

Use Rank it is in the LinearAlgebra Package.

Rank(A) returns a value of   5

Hope this helps.

 

 

Compatibly?...

Ronan 827
February 12 2013
1 0

1st. Maple 16.02 is compatible with Win8

2nd Have you tried installing it in Win7 compatibility mode? Would be interesting to know if this works but even if it does install I doubt you would get any level of support on crashes etc.

 

This Book...

Ronan 827
October 13 2012
0 0

Try this http://books.google.co.uk/books?id=PK_N9aFZ3ccC&pg=PA473&lpg=PA473&dq=sylvester+dialytic+elimination+method&source=bl&ots=abVGdGz59G&sig=t6X2FTndHDS1rr2YKyEWJc2c3Gk&hl=en&sa=X&ei=XtB5UOmfHqmL0AXYn4HwBQ&ved=0CB4Q6AEwAA#v=onepage&q=sylvester%20dialytic%20elimination%20method&f=false

its part of a google book. It is what gave me the basic understanding.

The google search I used was sylvester dialytic elimination method

and the google book is Robot Analysis: The mechanics of serial and parallel Manipulators-

Hope the helps.

I do hope others reply to the original question. would polynomial ideals , grobner basis by useful here and if how to use them.

 

Sylvester Matrix...

Ronan 827
October 13 2012
0 1

These 2 equations can be solved using the Sylvester Maxtrx technique. Have annotated the worhsheet to try and explain.

Would be interesting to see other techniques for solving them.
 

restart

with(LinearAlgebra)

 

eq1 := (1/4)*p*g*A*B+(1/2)*g^2*A*B*h-(7/12)*p*g*A*h+(5/6)*A^2*h^2+(13/12)*A^2*h-(1/3)*p*A^2+(5/12)*g*A-(3/2)*g^2*A-(1/4)*p*A^2*h*c*g^2+(1/4)*p*g*A*d*h-(1/12)*p*g^2+(3/2)*A^3*h^3+(1/4)*p*A^2*h^2*d+(1/4)*p*A^2*h^2*B+(1/4)*p*A^2*h*B+(1/4)*A^2*h*c*g^2-(1/4)*p*A*c*g^3-(1/4)*g*A*B*h+(1/4)*g*A*d*h+(1/3)*A^2-(13/12)*p*A^2*h+(1/4)*p*g*A*B*h-(5/12)*p*g*A-(1/4)*g*A*B-(1/2)*g^2*A*B+(1/4)*A*c*g^3-(5/6)*p*A^2*h^2+(7/12)*g*A*h-(1/4)*A^2*h^2*d-(1/4)*A^2*h*B+(1/2)*g^2*A*B+(1/12)*g^2+(1/2)*g*A^2*h^2-(1/2)*g^4*A*c-2*g*A^2*h+(1/2)*A*d*h-(1/4)*A^2*h^2*B

NULL

NULL

eq2 := -(5/6)*A*c*g*h^3*B*d-4*h^3*c*g*A-(11/3)*c^2*g^4*h-9*A*c*g*h^2+7*h*B*c*g^2-6*A*c*g*h+(10/3)*c^2*g^4*h*B+(1/6)*h^2*B^4-(10/3)*c^2*g^3*h^2*A+(7/6)*B^2*h^3*d+3*B*c*g^2-A*c*g-2*h^2*c*g^2-(7/6)*d^2*h+(7/3)*B^2*h^3*d+(29/12)*d^2*h^3*B-h^4*c*A^2-c*A^2*h^2-B*h^3*d+(3/2)*c*d*g^2-B^2*c*g^2-3*d*h*B-3*d*h^2*B+(1/6)*B^3*h^2*d+(7/6)*d*B^2*h+(29/12)*d^2*h^2*B-4*h*c*g^2-(5/6)*B^2*h^3*A*c*g-(1/6)*B^2*c*g^2*d*h^2-(5/6)*B^2*h^2*A*c*g+(5/6)*B*c^2*g^3*A*h^2-(23/4)*d*h^2*B*c*g^2+(14/3)*d*h^3*A*c*g-(59/12)*d*h*B*c*g^2+(19/6)*d*h^2*A*c*g+(7/2)*B*A*c*g*h+(17/2)*B*A*c*g*h^2+5*B*h^3*A*c*g+(1/12)*B^4*h+(5/4)*d^3*h^3-(3/2)*c^3*g^6+(1/12)*h^3*B^4-(7/6)*h^3*d^2-(7/3)*d^2*h^2-B*d-2*c*g^2-4*c^2*g^4+(1/2)*d*h^4*c*A^2+(1/2)*B*h^4*c*A^2+(1/2)*B*h^3*c*A^2+(5/6)*A^2*c^2*g^2*h^3-(1/6)*B^3*c*g^2*h^2+(1/12)*h*c^2*g^4*B^2-(1/6)*B^3*c*g^2*h+(17/4)*d*h*c^2*g^4-4*d^2*h^2*c*g^2+(31/6)*d*h^2*c*g^2-(9/2)*c^2*g^3*A*h+(17/3)*d*h*c*g^2+4*B*h^2*c*g^2-(17/6)*h*B^2*c*g^2-(11/6)*B^2*h^2*c*g^2+(5/2)*c^2*g^4*B+(1/12)*d^2*h^3*B^2+(1/6)*B^3*h^3*d-2*c*A^2*h^3

NULL

NULL

Sylvesterg := SylvesterMatrix(eq1, eq2, h);

PolySylg := sort(LinearAlgebra:-Determinant(Sylvesterg), g);

``

Alternatively a Polynomial in h can be made

 

NULL

You need Numerical values for A,B,c,d,p to solve the polynomial

Then back substitute the roots into one of the equations to get the corresponding values of g or h.

 

Test Values

A := 3/2; 1; B := 6/5; 1; c := 9/7; 1; d := 4/3; -1; p := 1/2

Digits := 20;

sort(PolySylg, g)

G := [fsolve(PolySylg, g)];

NULL

Back Substitution

NULL

for i to nops(G) do g := G[i]; H1[i] := fsolve(eq1, h) end do

 

for i to nops(G) do g := G[i]; H2[i] := fsolve(eq2, h) end do

NULL


Download 2_non-linear_equatio.mw

I would suggest you contact your supplie...

Ronan 827
October 08 2012
0 0

I would suggest you contact your supplier. I purchased a home use license of maple 15 early march and got a free upgrade to maple 16 when it was released. I just purchesed the home user license for maple 16 last week. I suppose by the time maple 17 and sim 7 are released I will need to pay something to get an upgrade.

assign works now...

Ronan 827
May 22 2012
0 0

Thank you all for replys and comments. I did get assign to work. there was a duplicate entry ie 2 rows the same which caused the problem. To clarify a some of the ponts raised. The rows are dependant on the previous rows. I choose a matrix because in a previous post Iwas told lists can be inefficant. Also athe matrix is visually easy to read I find. What I posed was just a short made up example. Thr algsubs on the equations is to shorten them as the can go on for screenful after screenfull. At the end of the assembling the equations I end uo with a 4x4 matrix whose determinant multiplies out to a 20th order polynomial. It is at this point I am using the assign to the valuse saved in the store matrix. I shall experiment with the

"#If you prefer assignment then you can use the two elementwise operations assign~ and  =~  : assign~(store[..,1]=~store[..,2]): a1,CX3,S1; "

At present I am using a for i to 100 do loop.

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