## 7766 Reputation

17 years, 335 days

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

Maple 2023

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?

 > 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];

 > print(A);

 >

## How to simplify this trig expression...

Maple 2023

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);

## Misbehaving plot in Maple 2023...

Maple 2023
 > 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;

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

Maple 2023 plots  with a strange artifact at :

 > 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:

## Looks like a regression bug in dsolve...

Maple 2023

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));

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

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

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

Huh?

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

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

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

## How to plot this function?...

Maple 2023

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);

 > 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: