Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Is there something I should be doing whenever I use simplify to avoid things like this, or should I stop using the "is" function all together?


interface(showassumed = 0):


sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)

(n-k+1)*binomial(n+1, k)/(k+1) = binomial(n+1, k+1)


#And we have:
is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1))



#And since:
is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))



is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)) = is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))



I was trying to learn more about the commands in this package and found it to be someone non satisfying:




I am trying to solve a simple two-equation linear system with solve, but I keep getting this weird result where the magnitude order of the numerator and denominator don't cancel out. Whenever I have a linear system with floating-point numbers, more unknowns than equations and try to solve it for a specific set of variables, this happens.

Any suggestions on how to get around this? Or do I need to solve it manually?

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Thanks a million in advance,





The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

Help create file Excel in ExcelTools, but error row 564?

Please help me? 

I have a physics question I need to program it by Maple , Can you help me to solve ? Its Problem 9.34 from Griffiths

Hey there,

I'm trying to numerically intergrate a function s(K,i,j) dK using runge kutta over a 2D grid of i,j values. Essentialy, performing the same sort of integral many different times for slightly different combinations of i and j. The function is more or less gaussian, and so the bulk of the result will come from the values of K around the peak of said gaussian. For some combinations of i and j, the function seems to have a singularity on the right edge of the gaussian peak, which causes my script to spit out an error, telling me the calculation cannot be performed further to the right past the singularity. Now, like i said before, the singularity is on the very edge of the gaussian and therefore I am perfectly happy to stop the integration before the singularity, because anything past it wont contribute very much to the result.

How can I use dsolve events to halt my integration just before hitting the singularity?

RK := (i, j) -> dsolve({diff(n(K), K) = K*s(K, a[i], b[j]), n(0) = 0}, numeric, method = rkf45)



I am fairly new to using the Maple software, so I apologize if my question is completely idiotic. Apologies, also, because I could not manage to enter my code as code. When I pressed the button it made the whole text as a code. 

I run the following code to seek -if there are any- analytic solutions for the following differential equation.

odeplus := (r^2+L^2)^(5/2)*(diff(f(r), `$`(r, 2)))+((15/4)*r*(r^2+L^2)^(1/2)+3*(r^2+L^2)^(5/2)/r)*(diff(f(r), r))+M^2*f(r)/(r^2+L^2)^(5/2)-((5/2)*((r^2+L^2)^(1/2))(l-1)+(55/64)*r^2/(r^2+L^2)^(3/2)+(r^2+L^2)^(5/2)*(l^2+3*l+3/2)/r^2)*f(r)+(((r^2+L^2)^(1/2))(5+(5/2)*l)+(5/8)*r^2/(r^2+L^2)^(3/2)-(r^2+L^2)^(5/2)*(3/2+l)/r^2)*f(r) = 0

and then I do 

dsolve(odeplus, f(r))

The solutions that Maple returns is given in terms of DESol. Could anyone try and break it down for me? What is this telling me and if I can indeed from the output obtain analytic solutions? Is this some sort of operator acting on something? 

Thank you in advance. 

A catenoid is the minimal surface between two 3D circles which are co-axial and parallel.

Is there a technique for finding the formula for the minimal surface if the circles are "stretched" into ellipses with proportional major and minor axes?

Can someone help with the simplification of the result of this code? I am sure the "qs" in the final result should not appear.

Thanking you in anticipation of your positive responses

P:=sum(a[k]*x^k, k=0..2):
assume(alpha>0,alpha <= 1):
e1:=simplify(eval(P, x=q))=y[n]:
var:=seq(a[i], i=0..2):

Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 3 do
end do:
E:=collect(Cf, [y[n], f[n], f[n+1]], recursive):
#y[n+1]=collect(simplify(simplify(expand(eval(Cf,x=q+h^alpha)),size)), [y[n],f[n],f[n+1]], factor);
y[n+1]=simplify(eval(Cf, x=q+h^alpha)):
collect(%, [y[n], f[n], f[n+1]], recursive);



I have a very simple problem. When Maple displays long outputs I can only see a part of them. Here there is an example

On my previous versions of Maple I had a slider on the bottom of the page. How can I activate it in Maple 2016?

Thanks, Nicola

Can we use this euler lagrange command for the system of pde's?

If we have a system without lagrangian then euler opertor is applied corresponding to three dependent variables.

so we have three equations but in this euler lagrange command no dependent variable is mentioned.   

I have several functional equations in equally many unknown functions of at least two variables, plus parameters.  ("collect" works just for single equations, right?)

I know that for certain parameter ranges, all the functions involved will be quadratic, and I know some coefficients are zero.  That gives me some  coefficients to determine.  I want to

  1. specify the functional equations [done in a very primitive low-tech way in the attachment, using atomic variables rather than indices ... have I done correctly?!?] 
  2. get Maple to collect coefficients (the K's and the L's in the attachment; the variables are (y,z))
  3. get Maple to state an equation system these coefficients have to satisfy (these will unfortunately be coupled quadratics)
  4. get Maple to solve that equation system if possible, and if not: to tell me when (= for what parameter values, parameters being the "remaining letters" in the attachment) I have specified enough coefficients
  5. in case of a solution, get Maple to tell me which coefficients are real and positive (for those that are solution of quadratic eq's: whether a positive solution exists)

Phew. I am still a complete newbie. Edit: Attachment link: where the equations themselves are EQ0, EQ1 and EQ2 at the bottom. Copying and pasting them, they look like this (download

0 = -r__0*(K__011*y^2+K__022*z^2-K__012*(y-L__1)*(z-L__2)-K__01*(y-L__1)+K__02*(z-L__2))+(-2*K__011*y+m__1+K__012*(z-L__2)+K__01)*((2/3)*c__1*y-(4/3)*K__11*y+(2/3)*`K__12 `*(z-L__2)+(20/9)*K__011*y-(10/9)*K__012*(z-L__2)-(10/9)*K__01-(10/9)*m__1-(1/3)*c__2*z+(2/3)*K__22*z-(1/3)*`K__21 `*(y-L__1)-(16/9)*K__022*z+(8/9)*K__012*(y-L__1)-(8/9)*K__02+(8/9)*m__2)+(-2*K__022*z+m__2+K__012*(y-L__1)-K__02)*((2/3)*c__2*z-(4/3)*K__22*z+(2/3)*`K__21 `*(y-L__1)+(20/9)*K__022*z-(10/9)*K__012*(y-L__1)+(10/9)*K__02-(10/9)*m__2-(1/3)*c__1*y+(2/3)*K__11*y-(1/3)*`K__12 `*(z-L__2)-(16/9)*K__011*y+(8/9)*K__012*(z-L__2)+(8/9)*K__01+(8/9)*m__1)+(-(4/3)*K__011*y+(2/3)*K__022*z+(2/3)*K__012*(z-L__2)-(1/3)*K__012*(y-L__1)-(1/3)*m__2+(2/3)*m__1+(1/3)*K__02+(2/3)*K__01)^2+((2/3)*K__011*y-(4/3)*K__022*z-(1/3)*K__012*(z-L__2)+(2/3)*K__012*(y-L__1)+(2/3)*m__2-(1/3)*m__1-(2/3)*K__02-(1/3)*K__01)^2:


0 = -r__1*(K__11*y^2-`K__12 `*y*(z-L__2))+`K__12 `*y*((2/3)*c__2*z-(4/3)*K__22*z+(2/3)*`K__21 `*(y-L__1)+(20/9)*K__022*z-(10/9)*K__012*(y-L__1)+(10/9)*K__02-(10/9)*m__2-(1/3)*c__1*y+(2/3)*K__11*y-(1/3)*`K__12 `*(z-L__2)-(16/9)*K__011*y+(8/9)*K__012*(z-L__2)+(8/9)*K__01+(8/9)*m__1)+((2/3)*c__1*y-(4/3)*K__11*y+(2/3)*`K__12 `*(z-L__2)-(1/3)*c__2*z+(2/3)*K__22*z-(1/3)*`K__21 `*(y-L__1)-(10/9)*K__022*z+(5/9)*K__012*(y-L__1)-(5/9)*K__02+(5/9)*m__2+(8/9)*K__011*y-(4/9)*K__012*(z-L__2)-(4/9)*K__01-(4/9)*m__1)^2:


0 = -r__2*(K__22*z^2-`K__21 `*(y-L__1)*z)+`K__21 `*z*((2/3)*c__1*y-(4/3)*K__11*y+(2/3)*`K__12 `*(z-L__2)+(20/9)*K__011*y-(10/9)*K__012*(z-L__2)-(10/9)*K__01-(10/9)*m__1-(1/3)*c__2*z+(2/3)*K__22*z-(1/3)*`K__21 `*(y-L__1)-(16/9)*K__022*z+(8/9)*K__012*(y-L__1)-(8/9)*K__02+(8/9)*m__2)+((2/3)*c__2*z-(4/3)*K__22*z+(2/3)*`K__21 `*(y-L__1)-(1/3)*c__1*y+(2/3)*K__11*y-(1/3)*`K__12 `*(z-L__2)-(10/9)*K__011*y+(5/9)*K__012*(z-L__2)+(5/9)*K__01+(5/9)*m__1+(8/9)*K__022*z-(4/9)*K__012*(y-L__1)+(4/9)*K__02-(4/9)*m__2)^2:




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