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Ronan

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13 years, 139 days
East Grinstead, United Kingdom
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These are answers submitted by Ronan

Windows 10 File History...

Ronan 1341
June 01 2019
0 0

If you are using Windows 10 turn File History. That keeps a running backup of all files you work on. You coud set to save  once a hour. It has gotten me out of trouble a few times.

Evaluate - Remove output...

Ronan 1341
May 17 2019
1 1

 

They moved it to Evaluate Remove Output. Ctrl+Shift+R

This is one way of doing it...

Ronan 1341
April 26 2019
1 1

This works.
 

restart

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

 (1)

c1 := x*y+x+y = 7

x*y+x+y = 7

 (2)

c2 := x^2+x*y+y^2 = 13

x^2+x*y+y^2 = 13

 (3)

implicitplot([c1, c2], x = -5 .. 5, y = -5 .. 5, colour = [blue, green])

  

sol := `assuming`([solve({c1, c2}, [x, y], useassumptions)], [0 < x and x < 4, 0 < y and y < 4])

[[x = 1, y = 3], [x = 3, y = 1]]

 (4)

``


 

Download This_works.mw

Using affine geometry...

Ronan 1341
January 19 2019
1 0


Hi,

This really is just a more expanded version of vv 5208  answer.

restart

P := [x3, y3, z3]

[x3, y3, z3]

 (1)

A := [x1, y1, z1]

[x1, y1, z1]

 (2)

B := [x2, y2, z2]

[x2, y2, z2]

 (3)

H lies on the line connecting AB, H can be defined as an affine combination of A and B. -∞ < λ < ∞. If 0 < λ < 1 then λ lies between A and B

 

H := simplify(expand((1-lambda)*A+lambda*B))

[(-x1+x2)*lambda+x1, (-y1+y2)*lambda+y1, (-z1+z2)*lambda+z1]

 (4)

``

Get distance between P and H

distPH := sqrt((H[1]-P[1])^2+(H[2]-P[2])^2+(H[3]-P[3])^2)

(((-x1+x2)*lambda+x1-x3)^2+((-y1+y2)*lambda+y1-y3)^2+((-z1+z2)*lambda+z1-z3)^2)^(1/2)

 (5)

Miniminist the distance by differentiating wrt λ. Then solve for λ

mdist := diff(distPH, lambda)

(1/2)*(2*((-x1+x2)*lambda+x1-x3)*(-x1+x2)+2*((-y1+y2)*lambda+y1-y3)*(-y1+y2)+2*((-z1+z2)*lambda+z1-z3)*(-z1+z2))/(((-x1+x2)*lambda+x1-x3)^2+((-y1+y2)*lambda+y1-y3)^2+((-z1+z2)*lambda+z1-z3)^2)^(1/2)

 (6)

lambda := solve(mdist, lambda)

(x1^2-x1*x2-x1*x3+x2*x3+y1^2-y1*y2-y1*y3+y2*y3+z1^2-z1*z2-z1*z3+z2*z3)/(x1^2-2*x1*x2+x2^2+y1^2-2*y1*y2+y2^2+z1^2-2*z1*z2+z2^2)

 (7)

Back substitute. This is the shortest possible distance  between P and H

simplify(distPH)

((x1^2*y2^2-2*x1^2*y2*y3+x1^2*y3^2+x1^2*z2^2-2*x1^2*z2*z3+x1^2*z3^2-2*x1*x2*y1*y2+2*x1*x2*y1*y3+2*x1*x2*y2*y3-2*x1*x2*y3^2-2*x1*x2*z1*z2+2*x1*x2*z1*z3+2*x1*x2*z2*z3-2*x1*x2*z3^2+2*x1*x3*y1*y2-2*x1*x3*y1*y3-2*x1*x3*y2^2+2*x1*x3*y2*y3+2*x1*x3*z1*z2-2*x1*x3*z1*z3-2*x1*x3*z2^2+2*x1*x3*z2*z3+x2^2*y1^2-2*x2^2*y1*y3+x2^2*y3^2+x2^2*z1^2-2*x2^2*z1*z3+x2^2*z3^2-2*x2*x3*y1^2+2*x2*x3*y1*y2+2*x2*x3*y1*y3-2*x2*x3*y2*y3-2*x2*x3*z1^2+2*x2*x3*z1*z2+2*x2*x3*z1*z3-2*x2*x3*z2*z3+x3^2*y1^2-2*x3^2*y1*y2+x3^2*y2^2+x3^2*z1^2-2*x3^2*z1*z2+x3^2*z2^2+y1^2*z2^2-2*y1^2*z2*z3+y1^2*z3^2-2*y1*y2*z1*z2+2*y1*y2*z1*z3+2*y1*y2*z2*z3-2*y1*y2*z3^2+2*y1*y3*z1*z2-2*y1*y3*z1*z3-2*y1*y3*z2^2+2*y1*y3*z2*z3+y2^2*z1^2-2*y2^2*z1*z3+y2^2*z3^2-2*y2*y3*z1^2+2*y2*y3*z1*z2+2*y2*y3*z1*z3-2*y2*y3*z2*z3+y3^2*z1^2-2*y3^2*z1*z2+y3^2*z2^2)/(x1^2-2*x1*x2+x2^2+y1^2-2*y1*y2+y2^2+z1^2-2*z1*z2+z2^2))^(1/2)

 (8)

``

The coordinates to H

H

[(-x1+x2)*(x1^2-x1*x2-x1*x3+x2*x3+y1^2-y1*y2-y1*y3+y2*y3+z1^2-z1*z2-z1*z3+z2*z3)/(x1^2-2*x1*x2+x2^2+y1^2-2*y1*y2+y2^2+z1^2-2*z1*z2+z2^2)+x1, (-y1+y2)*(x1^2-x1*x2-x1*x3+x2*x3+y1^2-y1*y2-y1*y3+y2*y3+z1^2-z1*z2-z1*z3+z2*z3)/(x1^2-2*x1*x2+x2^2+y1^2-2*y1*y2+y2^2+z1^2-2*z1*z2+z2^2)+y1, (-z1+z2)*(x1^2-x1*x2-x1*x3+x2*x3+y1^2-y1*y2-y1*y3+y2*y3+z1^2-z1*z2-z1*z3+z2*z3)/(x1^2-2*x1*x2+x2^2+y1^2-2*y1*y2+y2^2+z1^2-2*z1*z2+z2^2)+z1]

 (9)

``


 

Download Affine_Geometry.mw

Union...

Ronan 1341
December 29 2018
0 0

Try this, I extended your list,

L1 := [{3, 5}, {4, 5}, {4, 8, 9}, {-7, 2, 3}]:
      
L2 := {};  #empty set
                            L2 := {}
for i to nops(L1) do
L2 := L1[i] union L2
end do;
                          L2 := {3, 5}
                        L2 := {3, 4, 5}
                     L2 := {3, 4, 5, 8, 9}
                  L2 := {-7, 2, 3, 4, 5, 8, 9}
 

gridrefine...

Ronan 1341
November 29 2018
1 1

Try   implicitplot(cos(x)*cosh(y) = 1, x = -3 .. 3, y = -5 .. 5, gridrefine=2).

You can set higher values for gridrefine   3,4,5

You can download a numerical solution fr...

Ronan 1341
October 24 2018
1 0

http://www.yorku.ca/marko/ComPhys/Euler/Euler.html

 

you would need to do your own animation though.

Also here in a question, I posted at the time @Rouben Rostamian    gave a quaternion solution.

https://www.mapleprimes.com/questions/221298-I-Am-Looking-For-A-rotate-Type-Command#answer236768

This is an animation I did from following the blog I mentioned in the previous reply. It shows the momentum vectors.

Error appears to be at c:=...

Ronan 1341
August 26 2018
0 0


I changed your c:= to an "if then else end if".That stops producing the Error  But I could have intrepited your statement  incorrectly.

 

> 

restart;

NULL

> 

fdsolve := proc({gamma:=NULL, rho:=NULL, mu:=NULL, omega:=NULL, t0:=NULL,
                 t1:=NULL, x0:=NULL, y0:=NULL,
                 N:=NULL}, params)
    local t, h, c, b, x, y, L, n, l, X, Y, f, g, s1, s2, s3, s4, s5, s6, s7, s8, s9;
    eval(F(t,x,y), params);
    f := unapply(%, [t,x,y]);
    eval(G(t,x,y), params);
    g := unapply(%, [t,x,y]);
    L := floor(1/mu);
    h := (t1 - t0)/N;
s1:= sum(((omega*(h*(n-1))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s2:= sum(((omega*(h*n)^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s3:= sum(((omega*(h*n)^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s4:= sum(((omega*(h*(n-i+1))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s5:= sum(((omega*(h*(n-i-1))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s6:= sum(((omega*(h*(n-i))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s7:= sum(((omega*(h*(n-i))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s8:= sum(((omega*(h*(n-i-1))^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);
s9:=sum(((omega*h^rho)^(j)*GAMMA(gamma+j))/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100);    
    c := (i,n) ->
        if i=0 then
              (h^mu)*(  ( ((n-1)^(mu+1))*s1 )-((n^(mu+1))*s2)+((n^(mu))*s3)  )else
              (h^mu)*( (((n-i+1)^(mu+1))*s4)+(((n-i-1)^(mu+1))*s5)-(2*((n-i)^(mu+1))*s6) )
        end if;

b := (i,n) -> (h^mu)*( ((n-i)^(mu)*s7)-((n-i-1)^(mu)*s8) );

    t := Array(0..N, i-> (1-i/N)*t0 + i/N*t1, datatype=float[8]);
    x[0], y[0] := x0, y0;                                           
    for n from 0 to N-1 do
        X[0], Y[0] :=
            x[0] + add(b(i,n+1)*f(t[i],x[i],y[i]), i=0..n),
            y[0] + add(b(i,n+1)*g(t[i],x[i],y[i]), i=0..n);
        for l from 1 to L do
            X[l], Y[l] :=
                x[0] + add(c(i,n+1)*f(t[i],x[i],y[i]), i=0..n)
                     + (h^mu)*s9*f(t[n+1], X[l-1], Y[l-1]),
                y[0] + add(c(i,n+1)*g(t[i],x[i],y[i]), i=0..n)
                     + (h^mu)*s9*g(t[n+1], X[l-1], Y[l-1]);
        end do;
        x[n+1], y[n+1] := X[L], Y[L];
        #printf("y[%d]=%a\n", n+1, y[n+1]);
    end do;
    return Array(0..N, i -> [t[i], x[i], y[i]]);
end proc

proc (params, { N := NULL, gamma := NULL, mu := NULL, omega := NULL, rho := NULL, t0 := NULL, t1 := NULL, x0 := NULL, y0 := NULL }) local t, h, c, b, x, y, L, n, l, X, Y, f, g, s1, s2, s3, s4, s5, s6, s7, s8, s9; eval(F(t, x, y), params); f := unapply(%, [t, x, y]); eval(G(t, x, y), params); g := unapply(%, [t, x, y]); L := floor(1/mu); h := (t1-t0)/N; s1 := sum((omega*(h*(n-1))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s2 := sum((omega*(h*n)^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s3 := sum((omega*(h*n)^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s4 := sum((omega*(h*(n-i+1))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s5 := sum((omega*(h*(n-i-1))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s6 := sum((omega*(h*(n-i))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s7 := sum((omega*(h*(n-i))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s8 := sum((omega*(h*(n-i-1))^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+1)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); s9 := sum((omega*h^rho)^j*GAMMA(gamma+j)/(GAMMA(j*rho+mu+2)*factorial(j)*GAMMA(gamma)), j = 0 .. 100); c := proc (i, n) options operator, arrow; if i = 0 then h^mu*((n-1)^(mu+1)*s1-n^(mu+1)*s2+n^mu*s3) else h^mu*((n-i+1)^(mu+1)*s4+(n-i-1)^(mu+1)*s5-2*(n-i)^(mu+1)*s6) end if end proc; b := proc (i, n) options operator, arrow; h^mu*((n-i)^mu*s7-(n-i-1)^mu*s8) end proc; t := Array(0 .. N, proc (i) options operator, arrow; (1-i/N)*t0+i*t1/N end proc, datatype = float[8]); x[0], y[0] := x0, y0; for n from 0 to N-1 do X[0], Y[0] := x[0]+add(b(i, n+1)*f(t[i], x[i], y[i]), i = 0 .. n), y[0]+add(b(i, n+1)*g(t[i], x[i], y[i]), i = 0 .. n); for l to L do X[l], Y[l] := x[0]+add(c(i, n+1)*f(t[i], x[i], y[i]), i = 0 .. n)+h^mu*s9*f(t[n+1], X[l-1], Y[l-1]), y[0]+add(c(i, n+1)*g(t[i], x[i], y[i]), i = 0 .. n)+h^mu*s9*g(t[n+1], X[l-1], Y[l-1]) end do; x[n+1], y[n+1] := X[L], Y[L] end do; return Array(0 .. N, proc (i) options operator, arrow; [t[i], x[i], y[i]] end proc) end proc

 (1)
> 

 

> 

 


 

Download _Prab-1.mw

Another Suggestion too...

Ronan 1341
January 10 2018
0 0
If you want to some home study by yourself this is very good. Called Maths Foundation series.
 
https://www.youtube.com/user/njwildberger/playlists?view=50&shelf_id=10&sort=dd
 

I had problems with EllipticPi earlier t...

Ronan 1341
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 1341
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 1341
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 1341
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 1341
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 1341
January 31 2016
2 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

 

 

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