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:
###########################
#
###########################
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.

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`

partial differential equation ...

Hello,

is it possible to solve the attached partial differential equation with zero initial boundary condition?

If not by assuming diff(u(sigma, tau, phi, t), t, t)=0 is there an answer for the equation?

Thanks

lapla.mw

Expanding a derivative onto an expression using Ma...

Hello I am trying to compute the following expression;

(x^2r+y^2+z^2) gamma^{0} partial_{x} (-xy(1-r)) gamma^{2} partial_{y} \Psi

in which r = sqrt(1-K(x^2+y^2+z^2)), K is a constant, the gamma's are the Dirac gamma matrices and \Psi is the wave function. Essentially I would like to have partial_{x} operate on the expression to the right of it and apply product rule where there will be three terms with the last one being partia_{x} partial_{y} \Psi where it evaluates on everything expect the partial and the wavefunction, combining into the term partial_{x} partial_{y} \Psi, and if the partials are the same they combine into a single second order derivative with respect to the given variable. I have done this calculation by hand but seeing that there is an extensive amount of terms I would like to automate it using Maple. I have tried using the D() calling sequence but it doesn't quite give me what I am looking for. Is there anything documentation which will give me what I am looking for?

How do I extract terms from multivariate polynomia...

Hello everyone. I want to know how I can extract terms with the lowest sum of the degree of x and of y in a multivariate polynomial (in x and y)?

For instance, if I've f(x) = 100x^2y^2 + 35x^2y + 45y, I want an output of 45y.

On the other hand, if I've g(x) = 13x^2y^2 + xy^2 + 2yx^2, I want an output of xy^2 + yx^2.

Limit does not give correct answer...

Hello,friends!

I try to calculate the limit of the function,

sin(x*sin(1/x))/(x*sin(1/x))  at point x=0,maple gives answer:1

However,actually it does not have a limit at x=0,because for the limit to exist at a point,there needs to exist a neighbourhood at the point so that all x in the neighbour have definition.

It means f(x) should have have definition at point x=0's negihbourhood,however small the neighbourhood is.If I choose x=1/(n*Pi), n belongs to integers,the function doesn't have definition.As n increase,there doesn't exist such a neighbourhood.So is it something maple should correct?

Why is there seemingly inconsistent behavior with ...

Hello,

All too often I encounter an annoying issue, and when it happens it makes Maple slower than just scribbling on paper.  Unfortunately I don't understand why it happens or when it is going to happen so it creates a huge waste of time.

While most of the time expressions behave as expected, other times the exact same expression behaves as if it is something other than what is shown on screen.  I just ran into such an issue as an example:

What am I missing here? Why would phi not be interpreted as phi?

The only thing I could think of not being a Maple expert is assumptions.  I found I have an assumption earlier on phi (assume(phi>0,phi<45) so I removed it, but inexplicably(to me) that only fixes the first 2 lines, the last 2 lines still have the same issue, why I can't understand.  Why would having an assumption on phi, prevent me from evaluating the expression at some value of phi? The provided value is even within the assumed range.  And in either case, why can't I declare a value for phi and have that be understood?

Sorry for what I suspect is a dumb question, and thanks in advance.

EDITED to correct = -> :=

Why did I get an unterminated loop error again?...

` `
 >
 >
 (1)
 >

Hello everyone. I was trying to code the recurrence relation given in the image below (without taking the mth power):

But, as I run the program, I am getting an "unterminated loop" error. Can someone please point out the mistake(s)?

Why this unterminated loop error?...

```rfin := proc(m::integer)
local c, i, flg := 0;
for i from 0 to m do
local b := i;
do
c := b mod 3;
if (c <> 2) then next else flg := 1;
end if;
b := 1/3*b - 1/3*c;
until b = 0;
if evalb(flg = 0) then print(i);
end if;
end do;
end proc;```

Hello everyone. I've written a procedure that outputs all numbers <= a given user I/P whose ternary representation has no 2.

However, I get an "Error, unterminated loop" message. Can someone please out the mistake(s)?