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A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is four times faster than the duck. Assuming the fox and duck pursue optimum strategies, is it possible for the duck to reach the edge of the pond and fly away without being eaten? If so, how?

there is an animation here

wonder if the equations of motion can be derived usingg maple and an animaton...?

Hallo. I'd like to make a loop for two variables. Let say:

for i from 1..10, j from 1..10

How to do it?


Hi everyone:

I have two functions in terms of theta variable, how can I expressed function Y(X)?

X :=(theta)->cos(theta)+0.8e-1*cos(3.*theta)

Y :=(theta)->-sin(theta)+0.8e-1*sin(3.*theta)

I will earn Y(X) infact.

Thanks alot...





At the first note that in this question all polynomials have parametric coefficients. Let F be a list of polynomials and f be a polynomial. I want to convert F and f into a linear homogeneous FF and ff resp. At the first I want to sortvthe monomials appears in F and f  w.r.t. a monomial order T and then replace by the new variables A_i.

For example if


(a,b,c are parameters and x,y,z are variables) then I want to convert F and f into FF and ff resp:

please note that the variables appears in F and f are:

where sorted by T=plex(x,y,z). Please note that we consider all constants and alone parameters (4, b-4, c-1) as A9. I want to convert v into

and then F into FF and f into ff.


How to calculate the integral

(symbolically or/and numerically) with Maple?


How can I stop this text from appearing in the worksheet output?

What is the purpose of this text as it's a GIANT DISTRACTION from my perspective?



> with(plots);

> with(geom3d);

outputs lots of blue text...


[Archimedean, AreCollinear, AreConcurrent, AreConjugate,

  AreCoplanar, AreDistinct, AreParallel, ArePerpendicular,

  AreSkewLines, DefinedAs, DirectionRatios, Equation, FindAngle,

  FixedPoint, GlideReflect, GlideReflection, GreatDodecahedron,

  GreatIcosahedron, GreatRhombicuboctahedron,

  GreatRhombiicosidodecahedron, GreatStellatedDodecahedron,

  HarmonicConjugate, HexakisIcosahedron, HexakisOctahedron,

  InRadius, IsArchimedean, IsEquilateral, IsFacetted, IsOnObject,

  IsQuasi, IsRegular, IsRightTriangle, IsStellated, IsTangent,

  MidRadius, NormalVector, OnSegment, ParallelVector,

  PentagonalHexacontahedron, PentagonalIcositetrahedron,

  PentakisDodecahedron, QuasiRegularPolyhedron, RadicalCenter,

  RadicalLine, RadicalPlane, RegularPolyhedron,

  RhombicDodecahedron, RhombicTriacontahedron, RotatoryReflect,

  RotatoryReflection, ScrewDisplace, ScrewDisplacement,

  SmallRhombicuboctahedron, SmallRhombiicosidodecahedron,

  SmallStellatedDodecahedron, SnubCube, SnubDodecahedron,

  StereographicProjection, StretchRotate, TangentPlane,

  TetrakisHexahedron, TrapezoidalHexecontahedron,

  TrapezoidalIcositetrahedron, TriakisIcosahedron,

  TriakisOctahedron, TriakisTetrahedron, TruncatedCuboctahedron,

  TruncatedDodecahedron, TruncatedHexahedron,

  TruncatedIcosahedron, TruncatedIcosidodecahedron,

  TruncatedOctahedron, TruncatedTetrahedron, altitude, area,

  center, centroid, coordinates, cube, cuboctahedron, detail,

  dilate, distance, dodecahedron, draw, dsegment, duality, faces,

  facet, form, gtetrahedron, hexahedron, homology, homothety,

  icosahedron, icosidodecahedron, incident, intersection,

  inverse, inversion, line, midpoint, octahedron, parallel,

  parallelepiped, plane, point, polar, pole, powerps, projection,

  radius, randpoint, reflect, reflection, rotate, rotation,

  schlafli, segment, sides, sphere, stellate, tetrahedron, tname,

  transform, translate, translation, transprod, triangle,

  vertices, volume, xcoord, xname, ycoord, yname, zcoord, zname] [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, spacecurve,

  sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]


Hello those who are in this maple primes.

I downloaded maple2015 for Mac, the newest version of the software, and tried to use it to draw a simple figure with plot3d.

But, in the end, I used gnuplot which I had happened to install though it was my first time of using it.

The problem of using my Maple was that it was too heavy and with my macbook, I found it impossible

to have it work properly. So, I am writing my question now.


I used terminal, but as I think it  might be easy to deal with to use editor not terminal itself

though I use the editor from the terminal, I want to know how I can use maple from the editor and what things I 

can do when I do so. In my image, I want to use it like using TeX from the editor.

As for coloring the code, is the best tool one for Maple V yet? And, how can I do after I wrote the code of Maple?

What can I do with emacs and Maple? Can I use emacs like IDE of TeXshop or TeXworks in LateX?


I am glad to hear from you the general concept or procedures of using it if I use emacs and Maple.


Thanks in advance.

Dear All,

Colud you please tell me how to obtain the answer f(b)-f(a), by manipulating the following expression in maple:

int(diff(f(x), x), x = a .. b)

Thank you very much. Best regards, Jand

Hello, I have a similary issue with the following post :

In a constraint equation (in mechanics), I need to make these algebraic substitutions :

--> sqrt(xA1² + yA1²) =rF1 
--> arctan(abs(yA1)/abs(xA1)) = aF1
--> sqrt(xC1^2+yC1^2) = rBTP
--> arctan(abs(yC1)/abs(xC1))=a1

I try to do it with this code :

ListAlgsubs:={sqrt(xA1^2+yA1^2)=rF1,sqrt(xA2^2+yA2^2)=rF2,sqrt(xA3^2+yA3^2)=rF3, sqrt(xA4^2+yA4^2)=rF4,arctan(abs(yA1)/abs(xA1))=aF1,-arctan(abs(yA2)/abs(xA2))=aF2,pi+arctan(abs(yA3)/abs(xA3))=aF3,pi-arctan(abs(yA4)/abs(xA4))=aF4,sqrt(xC1^2+yC1^2)=rBTP,arctan(abs(yC1)/abs(xC1))=a1};
for i from 1 to nops(ListAlgsubs)
do Branch1Cons:=applyrule(op(i,ListAlgsubs),Branch1Cons)
end do:
Branch1Cons:= simplify(Branch1Cons);

I have tried with algsubs or applyrule but it wasn't successfull in both cases.

Do you have an idea how can I do to simplify my expressions ? and namely conduct a good use of applyrule function

I join an extract of my code in order to facilitate the troubleshooting.

Thanks a lot for your help.

How can I extract the coefficients of all monomials in a multivariate polynomial?

For example if f=ax^2+bxy^3+2 then I want




coeff(f,1/10)=20 and...

Dears, When I run calculation in Maple I found an error in matrices. See the file


Hi, I have 10 equation system and 10 unknown variables. I however, want to reduce the equations to 2 with two unknowns. I'm wondering how this could be done in maple. The variables are Y, q, yd, y*, yx, H,  pd, w, P and Pv. I intend to solve the equations for Y and w. 

Thanks in advance for your help. The maple file has also been attached.





restart; Digits := 10; F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1; Pr := 1

for k from 0 to 12 do F[k+3] := (-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))+2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))+M*(k+1)*F[k+1]-T[k])*factorial(k)/factorial(k+3); T[k+2] := (-3*Pr*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2) end do:






solve({limit(numapprox:-pade(t, x, [2, 2]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [2, 2]), x = infinity) = 1}, {A, B});

{A = -.7359903327, B = 1.324616408}, {A = -0.7307377025e-1+2.009578912*I, B = .3744177908+.5971332133*I}, {A = .6936483785+.1660915631*I, B = .1622123331+.9257041678*I}, {A = -2.182873922*I, B = .8203849935*I}, {A = .3431199285*I, B = 1.783825109*I}, {A = -.6936483785+.1660915631*I, B = -.1622123331+.9257041678*I}, {A = 0.7307377025e-1+2.009578912*I, B = -.3744177908+.5971332133*I}, {A = .7359903327, B = -1.324616408}, {A = 0.7307377025e-1-2.009578912*I, B = -.3744177908-.5971332133*I}, {A = -.6936483785-.1660915631*I, B = -.1622123331-.9257041678*I}, {A = 2.182873922*I, B = -.8203849935*I}, {A = -.3431199285*I, B = -1.783825109*I}, {A = .6936483785-.1660915631*I, B = .1622123331-.9257041678*I}, {A = -0.7307377025e-1-2.009578912*I, B = .3744177908-.5971332133*I}


solve({limit(numapprox:-pade(t, x, [3, 3]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [3, 3]), x = infinity) = 1}, {A, B});

{A = 4.154051132, B = 17.13248053}, {A = .5466914672+.2697341397*I, B = .1291930705+.9494499975*I}, {A = .4506017673+.3824137679*I, B = -.2437153257+1.192091322*I}, {A = .5458260296+.5776530367*I, B = .3085138074+1.260130057*I}, {A = .3007754662+.5799020019*I, B = 0.8347381159e-1+1.033103936*I}, {A = .3916946210+1.036293227*I, B = .9202208108+1.239552889*I}, {A = .1349186305+.5994923360*I, B = 1.926737919+1.099451808*I}, {A = .5141206762+2.582294380*I, B = -.7917198503+.5287783790*I}, {A = 1.669898274*I, B = 1.659206265*I}, {A = 3.170666197*I, B = -.6372670837*I}, {A = -.5141206762+2.582294380*I, B = .7917198503+.5287783790*I}, {A = -.1349186305+.5994923360*I, B = -1.926737919+1.099451808*I}, {A = -.3916946210+1.036293227*I, B = -.9202208108+1.239552889*I}, {A = -.3007754662+.5799020019*I, B = -0.8347381159e-1+1.033103936*I}, {A = -.5458260296+.5776530367*I, B = -.3085138074+1.260130057*I}, {A = -.4506017673+.3824137679*I, B = .2437153257+1.192091322*I}, {A = -.5466914672+.2697341397*I, B = -.1291930705+.9494499975*I}, {A = -4.154051132, B = -17.13248053}, {A = -.5466914672-.2697341397*I, B = -.1291930705-.9494499975*I}, {A = -.4506017673-.3824137679*I, B = .2437153257-1.192091322*I}, {A = -.5458260296-.5776530367*I, B = -.3085138074-1.260130057*I}, {A = -.3007754662-.5799020019*I, B = -0.8347381159e-1-1.033103936*I}, {A = -.3916946210-1.036293227*I, B = -.9202208108-1.239552889*I}, {A = -.1349186305-.5994923360*I, B = -1.926737919-1.099451808*I}, {A = -.5141206762-2.582294380*I, B = .7917198503-.5287783790*I}, {A = -1.669898274*I, B = -1.659206265*I}, {A = -3.170666197*I, B = .6372670837*I}, {A = .5141206762-2.582294380*I, B = -.7917198503-.5287783790*I}, {A = .1349186305-.5994923360*I, B = 1.926737919-1.099451808*I}, {A = .3916946210-1.036293227*I, B = .9202208108-1.239552889*I}, {A = .3007754662-.5799020019*I, B = 0.8347381159e-1-1.033103936*I}, {A = .5458260296-.5776530367*I, B = .3085138074-1.260130057*I}, {A = .4506017673-.3824137679*I, B = -.2437153257-1.192091322*I}, {A = .5466914672-.2697341397*I, B = .1291930705-.9494499975*I}








Digits := 19:

inf := 28.5:

equ1 := diff(f(eta), eta, eta, eta)+3*(diff(f(eta), eta, eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+3*(diff(diff(f(eta), eta), eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0


equ2 := diff(theta(eta), eta, eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0;

diff(diff(theta(eta), eta), eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0


FNS := f(eta), theta(eta);

f(eta), theta(eta)


s := 0:

BC := f(0) = s, (D(f))(0) = 0, (D(f))(inf) = 1, theta(0) = 1, theta(inf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(f))(28.5) = 1, theta(0) = 1, theta(28.5) = 0


CODE := [M = 2, Pr = 1, S = 1]:

S1 := dsolve({BC, subs(CODE, equ1), subs(CODE, equ2)}, {f(eta), theta(eta)}, type = numeric):


[eta = 0., f(eta) = 0., diff(f(eta), eta) = 0., diff(diff(f(eta), eta), eta) = .7424080874401649594, theta(eta) = 1.000000000000000000, diff(theta(eta), eta) = .9438662130843066161]






Thank you so much for your time. Here's the real problem

f'''(η) + 3f(η)f''(η) - 2[f'(η)] 2 + θ(η) - m*f'(η) = 0

θ''(η) + 3*Pr*f(η)θ'(η) + s*θ(η) = 0

Boundary conditions are:

at η=0: f(η)=f'(η)=0; θ(η)=1;

as η→∞ f'(η)=1; θ(η)=0;

Where m = magnetic parameter (in this case taken as 2)

S = shrinking parameter (in this case taken as 1)

Pr = taken as 1 too

I haven't been able to solve this using differential transforms method (i.e getting the values of f''(0) and θ'(0) denoted by A and B respectively) but shooting method works just fine. :( I seriously need help with this. Thanks you in advance.
I've attached my codes above and i'm hoping someone helps me out real soon. thanks very one.

I am planning on getting Maple 18 Student Editon and I am wondering if the calculus palette is in Maple 18 student edition.



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