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Rouben Rostamian

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19 years, 110 days
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These are questions asked by Rouben Rostamian

How to plot this function?...

Rouben Rostamian 8541 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

Bug in simplify piecewise...

Rouben Rostamian 8541 Maple 2023
simplify piecewise physics
October 20 2023
0 2

This used to work in Maple 2022.  Something is broken in 2023. 

 

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restart;
> 

kernelopts(version);

`Maple 2023.1, X86 64 LINUX, Jul 07 2023, Build ID 1723669`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1561 and is the same as the version installed in this computer, created 2023, October 20, 22:58 hours Pacific Time.`

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U := Int(exp(-1/4*t - 1/4*x)*piecewise(x < -2, 1, x < -1, -x - 1, 0), x = -t .. 0);

Int(exp(-(1/4)*t-(1/4)*x)*piecewise(x < -2, 1, x < -1, -x-1, 0), x = -t .. 0)

> 

Uval := simplify(value(U));

Uval := `simplify/piecewise/unfactor`(4*piecewise(t < 1, 0, t < 2, t-5+4*exp(`&ndash;`((1/4)*t)+1/4), 2 <= t, 1+4*exp(`&ndash;`((1/4)*t)+1/4)-4*exp(`&ndash;`((1/4)*t)+1/2)))

> 

eval(Uval, {x=5, t=6});

`simplify/piecewise/unfactor`(4+16*exp(-5/4)-16*exp(-1))

> 

 
 

Download simplify-piecewise-bug.mw

 

Inverse Laplace transform on Maple 2023 ...

Rouben Rostamian 8541 Maple 2023
inverse laplace
October 19 2023
1 9

Maple thinks the inverse Laplace transform of 1/(s+a) is exp(a*t).  It should be exp(−a*t).

This used to work correctly in Maple 2022.  Something got messed up in 2023.

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restart;
> 

kernelopts(version);

`Maple 2023.1, X86 64 LINUX, Jul 07 2023, Build ID 1723669`

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with(inttrans):
> 

exp(-a*t);

exp(-a*t)

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laplace(%, t, s);

1/(s+a)

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invlaplace(%, s, t);

exp(a*t)

 

Download laplace-transform-bug.mw

setoptions3d stopped working in Maple 20...

Rouben Rostamian 8541 Maple 2023
font setoptions3d
May 13 2023
1 2

This code fails in Maple 2023.  It used to work in earlier versions.  Did I miss something in the release notes?

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restart;
> 

kernelopts(version);

`Maple 2023.0, X86 64 LINUX, Mar 06 2023, Build ID 1689885`

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with(plots):
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setoptions3d(font=[Times,roman,12]);
> 

arrow(<1,1,1>);

Error, (in plottools:-rotate) invalid arguments for 3-D transformation

 

How to find a symbolic solution for this...

Rouben Rostamian 8541 Maple 2022
ode piecewise dsolve
April 15 2023
0 0

I can derive a symbolic solution by hand for the following ODE, but cannot get Maple to do it for me.  Any tricks?

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restart;

Velocity field, -infinity < x and x < infinity,  t > 0.

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v := (x,t) -> piecewise(x <= -t, 0, x < t, 1 - 1/2*(1 - x/t));

v := proc (x, t) options operator, arrow; piecewise(x <= -t, 0, x < t, 1/2+(1/2)*x/t) end proc

Position x(t):

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de := diff(x(t),t) = v(x(t),t);

de := diff(x(t), t) = piecewise(x(t) <= -t, 0, x(t) < t, 1/2+x(t)/(2*t))

Initial condition, assuming a > 0

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ic := x(0) = -a;

x(0) = -a

Symbolic solution, calculated by hand:

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x__exact := t -> piecewise(t < a, -a, t - 2*sqrt(t)*sqrt(a));

x__exact := proc (t) options operator, arrow; piecewise(t < a, -a, t-2*sqrt(t)*sqrt(a)) end proc

Verify exact solution by comparing it against the numeric solution for some a > 0:

> 

a := 3;  # any a>0 should do
dsol := dsolve({de,ic}, numeric):
plots:-odeplot(dsol, t=0..5);   # dsolve solution
plot(x__exact(t), t=0..5);      # symbolic solution (calculated by hand)
a := 'a';

3

a

Can Maple's dsolve find the exact solution?  This one returns empty in Maple 2022:

> 

dsolve({de, ic}) assuming a > 0, t > 0;

Download ode-piecewise.mw

 

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