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Rouben Rostamian

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18 years, 170 days
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These are questions asked by Rouben Rostamian

How to convert a table of diffs to D...

Rouben Rostamian 8018 Maple 2023
convert table diff
April 20 2024
1 1

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

> 

restart;
> 

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;
> 

A[1][1,1];

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

> 

print(A);

A

> 

 
 

Download convert-table.mw

 

How to simplify this trig expression...

Rouben Rostamian 8018 Maple 2023
simplification trig
March 13 2024
1 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);

(-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));

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);

0

 

Download torsion2.mw

Misbehaving plot in Maple 2023...

Rouben Rostamian 8018 Maple 2023
plot
February 25 2024
1 1
> 

restart;

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:

  

Download bug-in-plot.mw

Looks like a regression bug in dsolve...

Rouben Rostamian 8018 Maple 2023
ode dsolve differential-equations
February 20 2024
0 0

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.

> 

restart;
> 

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

(t-1)*(t-2)*(Heaviside(t-2)-Heaviside(t-1))/(t^2+1)^3

> 

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

Huh?

> 

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?

Download dsolve-bug.mw

How to plot this function?...

Rouben Rostamian 8018 Maple 2023
plot
December 08 2023
1 1

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.

> 

restart;
> 

kernelopts(version);

`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);

-cos(x^(1/2))*x^3/(-x^2+24*cos(x^(1/2))+12*x-24)

> 

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

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

Download cannot-plot.mw

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