## Working with vectors...

If I understand how to use vectors in Maple, I need to give the number of elements.  Is this correct?  I am working with vectors that I do not know the number of elements.  I can use a large number that will be greater than the required number of elements, but this does not seem to be a good solution.  The number of elements is 2000 for about 10 different vectors.  What is the best method to set up the victors for this application?

## Why are the Gauss-Bonnet figures incorrect in my w...

The worksheet below displays dual cones inside the unit sphere, but the Gauss-Bonnet formula (area of upper cone's spherical cap plus length of dual cone's intersection with unit sphere) does not equal 2*Pi.

Please find my error.

Dual_cones.mw

## How do I turn a system of parametric equations int...

In Maple 2020, I clicked on "Math Apps" and then clicked on "Algebra & Geometry", followed by "Boy's Surface".

It is a set of 3 parametric equations in terms of {u,v}. I would like to eliminate u and v and turn this into a single "error" function in terms of (x,y,z) such that anywhere this function is zero, the original set of equations are satisfied for some value of {u,v}. (Ideally, the values of u and v could be determined as well, but that would be a bonus.)

I tried this:

alpha = 1;
u in [-Pi/2, Pi/2];
v in [0, Pi];
eq1 := x(u, v) = (sqrt(2)*cos(v)^2*cos(2*u) + cos(u)*sin(2*v))/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eq2 := y(u, v) = (sqrt(2)*cos(v)^2*sin(2*u) - sin(u)*sin(2*v))/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eq3 := z(u, v) = 3*cos(v)^2/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eliminate({eq1, eq2, eq3}, {u, v});

but got no response and no error message.

Additionally, I tried explaining that I want a function f such that f(x,y,z)=0, but again got no response and no error message:

eq4 := f(x, y, z) = 0;
solve({eq1, eq2, eq3, eq4}, f);

Any ideas what I'm doing wrong?

Thank you!

-- Glenn

## Tensor problem (all Christoffel symbols are zero) ...

Hello,

I am having problems with Maple. I am new to the software and I am looking to use it for tensors. I am working with the Alcubierre metric, for more details, click the images below.

https://i.imgur.com/OvBywO6.png

https://i.imgur.com/2D9Y73x.png

These images should provide more clarity with the metric. My problem is that in Maple, I have successfully entered the metric, however whenever I use for example the Christoffel command, it states that all the Christoffel symbols are equal to zero.

https://i.imgur.com/VRDQM8d.png

I believe the reason why this is happening is because I have not defined the functions properly. I should be getting an answer like the example in the last picture below.

https://i.imgur.com/tn8HpIE.png

Would anyone be able to assist me in this? I would appreciate it greatly.

Many thanks.

## Difference between seq and \$ that explains a diffe...

Hi,

While computing a simple sequence of numbers, I remarked a small difference between the result obtained with \$ and with seq.

```Digits:=20:
u:=proc(n) evalf(((n+1)/n)^(n+1)) end proc:
a:=[u(n)\$n=1..10]:
b:=[seq(u(n),n=1..10)]:
a-b;```

The result is:

```[0., 0., -4.*10^(-19), 0., 0., 6.*10^(-19), -9.*10^(-19), 0., -3.*10^(-19), 0.]
```

I have no idea why there are nonzero values in the output. Does anyone have an explanation?

It seems I get the correct values if I quote the expression before \$:

`a:=['u(n)'\$n=1..10]:`

However, it's not clear to me why this makes a difference in evalf.

## Weird numerical evaluation...

After setting:

Digits:=20;

result of:

evalhf(9.3653976306373904636884810627704*10^(-315));

is:

-9.0813464423699167205*10^(-315)

This looks nonsesnse. What is going on?

## basic question on evaluation delay...

Why

`evalf(evalf(''Pi''))`

Produces

But

```evalf(''Pi''):
evalf(%)```

Produces

3.141592654

## why same integrand gives different output from int...

Could some Maple expert please explain this strange behavior of int? Using Maple 2020 on windows 10

Same integrand. But in one case exp(arcsin(x)) and in another exp(1)^arcsin(x). Why one worked and not the other?

Here is the code

```restart;
integrand1 := (x^3*exp(arcsin(x)))/sqrt(1 - x^2);
integrand2 := (x^3*exp(1)^arcsin(x))/sqrt(1 - x^2);
simplify(integrand1-integrand2);
int(integrand1,x);
int(integrand2,x)
```

## Simplifying bouded (link as oppose to free ) vecto...

Hi - High school teacher

I'm using the with(Physics): Setup(mathematicalnotation=true):with(Physics[Vector]): libraries which gives elegant answers to some of the questions of elementary vector algebra.

But I become stuck when I try to simplify a simple expression like

Equa[01]:=AC_ = AB_ + BC_:Equa[01];                            #AC_ = AB_ + BC_
Equa[02]:={AB_=2*DB_,BC_=2*BE_}:Equa[02];
Equa[03]:=subs(Equa[02],Equa[01]):Equa[03];
#AC_ = 2*DB_ + 2*BE_
simplify(Equa[03]);                                                              #also try combine

which gives

AC_ = 2*DB_ + 2*BE_

rather than what I was hoping for

AC_ = 2*DE_

I have define a type and build a clumsy addition procedure - with no hope of overloading '+'

###########################
# TYPE VecPos (Vecteurs liés)
#
###########################
`type/VecPos`:=proc(Exp)
local LstExp:
LstExp:=convert(Exp,string):
if length(LstExp)=3 and LstExp[-1]="_" then
true
else
false
fi:
end proc:
###########################
# TYPE AddVecSub (addition de vecteur subsécants)
#
###########################
local va,vb,a,b:
if patmatch(2*Exp,a::realcons*va::VecPos+b::realcons*vb::VecPos,'Corr') then
a:=subs(Corr,a)/2:                  b:=subs(Corr,b)/2:
va:=convert(subs(Corr,va),string):  vb:=convert(subs(Corr,vb),string):
if a < 0 then
va:=convert(cat(va[2],va[1],va[3]),string);
a:= -a;
fi;
if b < 0 then
vb:=convert(cat(vb[2],vb[1],vb[3]),string);
b:= -b;
fi;
fi;

if va[2]=vb[1] then
if a > b then
return b*convert(cat(va[1],vb[2..3]),symbol)
+ (a-b)*convert(va,symbol);
elif b > a then
return a*convert(cat(va[1],vb[2..3]),symbol)
+ (b-a)*convert(vb,symbol);
else
return a*convert(cat(va[1],vb[2..3]),symbol)
fi
elif vb[2]=va[1]  then
if a > b then
return b*convert(cat(vb[1],va[2..3]),symbol)
+ (a-b)*convert(va,symbol);
elif b > a then
return a*convert(cat(vb[1],va[2..3]),symbol)
+ (b-a)*convert(vb,symbol);
else
return a*convert(cat(vb[1],va[2..3]),symbol)
fi
else
return Exp
fi
end proc:

But I am sure that their exist a better solution - which if possible should remain within the Physics[Vector] library. It is hard enough to convince high school student to use maple. Maybe adding rule in the setep... I just don't have the required time to look around.

Any help would be appreciated.

Thank

Jean-Marc Roy

Note:

patmatch(2*AB_ + 2*BC_,a::realcons*va::VecPos+b::realcons*vb::VecPos,'Corr');Corr;Corr:='Corr':

work, but neither

patmatch(AB_ + BC_,a::realcons*va::VecPos+b::realcons*vb::VecPos,'Corr');Corr;Corr:='Corr':
patmatch(AB_ + BC_,va::VecPos+vb::VecPos,'Corr');Corr;Corr:='Corr':

return results. Which explain why I mutiply 2*Exp in the addition function.

## addtable issue-add some useful inverse Laplace tra...

Hi, I am trying to add some useful inverse Laplace transforms to Maple's integral tables. I am frustrated that these transforms will only be recognized  if they are entered in exactly the same format. For example, if I type:

restart;

with(inttrans):

addtable(invlaplace, 1/(s^y*sqrt(a + s^x)), Sum(a^n*sqrt(Pi)*t^(-1 + (1/2 + n)*x + y)/(GAMMA(1/2 - n)*GAMMA(1 + n)*GAMMA(1/2*x + n*x + y)), n = 0 .. infinity), s, t, {a, x, y}, y::Range(-infinity, infinity), x::Range(-infinity, infinity), a::Range(-infinity, infinity));

savetable(invlaplace, `InvlaplaceTable.m`):

Then:

restart;

with(inttrans):

invlaplace(1/(s^y*sqrt(a + s^x)), s, t);#Ok works for general

invlaplace(1/(s^3*sqrt(a + s^x)), s, t);# Dosen't WORK ?# For y = 3.

invlaplace(1/(s^3*sqrt(s^3 + a)), s, t);# Dosen't WORK ?# For y = 3. and x = 3

value(eval(invlaplace(1/(s^y*sqrt(a + s^x)), s, t), [y = 3, x = 3]))#Workaround !!!

Thanks.

## Export to LaTeX not working properly...

Does anyone here have experience with exporting Maple worksheets to LaTeX?  According to help page

?Export as latex

"You can change the Mathematics Formatting Width to align multi-line displayed formulas by modifying the option in the Export tab of the Options dialog."

That setting, however, seems to have no effect.  The image below shows the result, after setting the line width to (the extremely narrow!) 2 inches.  Long lines still overflow the left and right margins of the paper, rendering the result useless.

I see that this was pointed out in 2016 but there appears to have been no improvements since.  Does anyone know a workaround?  I am running Maple 2020 on Linux, if that matters.

This zip file z.zip contains a Maple worksheet, the exported *.tex file, and the compiled PDF.  Here is what that PDF looks like.

## how to integrate arccos(x)*arcsin(x)?...

This Anti-derivative of  arccos(x)*arcsin(x), Maple  2020 cannot do that? It seems not difficult.

int(arccos(x)*arcsin(x),x)

In Mathematica, we can easily to get output :

2 x - Sqrt[1 - x^2] ArcSin[x] +  ArcCos[x] (Sqrt[1 - x^2] + x ArcSin[x])

## Startup Code reexecuted when pressing "Execute ent...

When pressing !!! (Execute entire worksheet) it seems to me that startup code is executed.

Is that correct, and if - why is that so?

## Physics Updates" version "642 is  installed but i...

Today I Installed  Physics Updates" version "642 in Maple2020, why does it tell me  it has installed but is not active? How to active it?

Physics:-Version(latest)

`The "Physics Updates" version "642" is installed but is not active. The active version of Physics is within the library D:\\Program Files\\Maple 2020\\lib\\maple.mla, created 2020, March 5, 9:36 hours`