Rouben Rostamian

MaplePrimes Activity

These are questions asked by Rouben Rostamian

I have a table indexed as A[i][j,k],  Each entry is an expression involving diff which I want to convert to but convert(A,D) doesn't work. Any suggestions on how to do that?


for i from 1 to 2 do
  for j from 1 to 2 do
    for k from 1 to 2 do
      A[i][j,k] := diff(u[i](x[1],x[2]), x[j], x[k]);
    end do
  end do;
end do;


diff(diff(u[1](x[1], x[2]), x[1]), x[1])






In a homework assignment on differential geometry, a student used Mathematica to calculate the torsion of a trefoil curve.  His result, using identical steps as mine, was significantly simpler than what I had gotten with Maple, although as we see in the attached workseet, they are mathematically equivalent.

Is there a way to coax Maple to reduce its result to something like my student has obtained?

My calculation

T1 := (-192*cos(t)^6 + 288*cos(t)^4 - 912*cos(t)^3 - 108*cos(t)^2 + 684*cos(t) - 54)/(4608*cos(t)^9 - 10368*cos(t)^7 + 6208*cos(t)^6 + 7776*cos(t)^5 - 9312*cos(t)^4 - 2440*cos(t)^3 + 3492*cos(t)^2 + 372*cos(t) - 1169);


The student's calculation

T2 := 6*(10+38*cos(3*t)+cos(6*t))/(975+70*cos(3*t)-194*cos(6*t) -18*cos(9*t));


simplify(T1 - T2);





Here we have a pretty well-behaved trig function:

y := t -> 144*cos(t)^6 - 216*cos(t)^4 + 32*cos(t)^3 + 81*cos(t)^2 - 24*cos(t) + 17;

proc (t) options operator, arrow; 144*cos(t)^6-216*cos(t)^4+32*cos(t)^3+81*cos(t)^2-24*cos(t)+17 end proc

plot(y(t), t=0..2*Pi, view=0..35);

Maple 2023 plots y^(3/2) with a strange artifact at t = Pi:

plot(y(t)^(3/2), t=0..2*Pi, view=0..200);

Any reason for that?  Maple 2021 and earlier used to produce the correct plot:



Applying Maple 2023's dsolve to the ODE shown below yields the solution y(t)=0 which is obviously incorrect.  Maple 2021 and earlier used to give a nonzero (albeit not very useful) answer.


F := (t-1)*(t-2)/(t^2+1)^3*(Heaviside(t-2)-Heaviside(t-1));


plot(F, t=0..4);

de := diff(y(t),t,t) + diff(y(t),t) = F;

diff(diff(y(t), t), t)+diff(y(t), t) = (t-1)*(t-2)*(Heaviside(t-2)-Heaviside(t-1))/(t^2+1)^3

ic := y(0)=0, D(y)(0)=0;

y(0) = 0, (D(y))(0) = 0


dsolve({de,ic}, y(t));

y(t) = 0

Specifying method=laplace will make that work, but how is an

unsuspecting user to know that what's obtained above is incorrect?


The attached worksheet shows that Maple 2023 produces an incomplete plot of a function.  Maple 2021, however, produces the full graph.  I wonder if Maple 2023's behavior is due to a bad setting in my environment or a plotting bug in Maple.



`Maple 2023.2, X86 64 LINUX, Oct 25 2023, Build ID 1753458`

y := -cos(sqrt(x))*x^3/(-x^2 + 24*cos(sqrt(x)) + 12*x - 24);


plot(y, x=0..1);

Here is the graph of the same function plotted correctly in Maple 2021:


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