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MaplePrimes Questions

How to get periodic solution of a simply Sine func...

Asked by: Aixleft math 120
solve trig periodic
March 05 2025
0  6

Hi! An basic and interesting issue.

First, why I run worksheet again and again, I will get different output (even seems understandable)? I guess maybe the memory is not renewed?

Second, how to obtain the periodic solution without adding ```k*Pi``` manually?

> 

`assuming`([solve(sqrt(2)*sin(2*x-(1/6)*Pi) = 1)], [`in`(x, real)])

5/24

 (1)
> 

x := solve(sqrt(2)*sin(2*x-(1/6)*Pi) = 1)+k*Pi

5/24+k*Pi

 (2)
 

NULL

Download periodic_solution_of_a_simply_Sine_function.mw

There is any way for see the outcome of result? fo...

Asked by: salim-barzani 1560
explore substitution plotting
March 05 2025
3  0

i need the result for (eqt33) but i can reach the result there is any  other way for finding? i need to plot 3D of that function but without have the function how i can do explore on it

w1.mw

another mint problem. :- name vs. [name] for Mapl...

Asked by: nm 11353
mint
March 05 2025
0  1

Is this a bug in mint?

Given this foo.mpl

foo:=proc()
    local x:=2,y:=3;       
        
    if MmaTranslator[Mma][LeafCount](x)<MmaTranslator[Mma][LeafCount](y)  then        
        0;
    else
       1;
    fi;  

end proc;

It says

Procedure foo() on lines 2 to 11
  These names were used as global names but were not declared:  LeafCount, Mma

But if I rewrite the above using :- instead:

foo:=proc()
    local x:=2,y:=3;       
        
    if MmaTranslator:-Mma:-LeafCount(x)<MmaTranslator:-Mma:-LeafCount(y)  then        
        0;
    else
       1;
    fi;  

end proc;

Now mint is happy and no message are given.

Is not  MmaTranslator:-Mma:-LeafCount(x)  the same as MmaTranslator[Mma][LeafCount](x) ?

Maple itself is happy with both. So why is mint complaining?

I am finding many problems with mint. Will post more problems found when I have more time.

Is mint still actively  maintained by Maplesoft? 

Unexpected behavior of "read"...

Asked by: DG2025 15
assumptions dotm
March 05 2025
2  4

Hi Guys,

I encountered this rather unexpected behavior of Maple 18 when using the "read" function as shown below, where Maple fails to reduce the answer to 0, especially for (5). I'm curious if there's any deeper reason for this, and if there's a better or more standard solution than mine, that is, to use "parse( convert( expr, string ) )" as in (6)?

Thanks a lot!

``

> 

restart;
> 

 

> 

assume(x>0);
> 

 

> 

f := x^2;

x^2

 (1)
> 

 

> 

save f, "read_test.m";
> 

 

> 

restart;
> 

 

> 

f;

f

 (2)
> 

 

> 

read "read_test.m";
> 

 

> 

f;

x^2

 (3)
> 

 

> 

f - x^2;

-x^2+x^2

 (4)
> 

 

> 

assume(x>0);
> 

 

> 

f - x^2;

x^2-x^2

 (5)
> 

 

> 

f1 := parse( convert( f, string ) );

x^2

 (6)
> 

 

> 

f1;

x^2

 (7)
> 

 

> 

f1 - x^2;

0

 (8)
> 

 

NULL

Download test1.mw

keep the logarithms displayed in base a without co...

Asked by: jalal 435
March 05 2025
2  3

Hi,

I am creating a multiple-choice questionnaire (MCQ) on functions, but the display of logarithmic functions is automatically converted to natural logarithms. How can I keep the logarithms displayed in base a without conversion? Thank you for your help.

S5_QCM_Expo_Log.mw

What exactly are system remember tables...

Asked by: C_R 3412
procedure remember
March 04 2025
2  3

I found system remember tables mentioned under Details in ?CacheOption.

What exactly are they? Anything special about them?

The ProgrammingGuide does not given more details. It only mentions that there are "procedures that cannot use option system remember tables". For what reason a procedure cannot use them?

Question about LerchPhi...

Asked by: Alfred_F 330
summation
March 04 2025
1  4

For the following limit determination, I do not get the known result 2, but only a term with LerchPhi. Please give me some advice.
lim(n-->oo)[(n/(2^n))*sum(k=1 to n) (2^k/k)]

Plot misbehaves in Maple 2024...

Asked by: Rouben Rostamian 8506
plot plotting
March 04 2025
3  2

I wish to plot two line segments over the intervals [0,1] and [2,3].  Maple 2024 draws a single line segment over [0,3].  Oddly enough, if I specify a color option, then it produces the expected result!

This used to work correctly in Maple 2023.  Perhaps this can be corrected in the forthcoming release?

> 

restart;
> 

kernelopts(version);

`Maple 2024.2, X86 64 LINUX, Oct 29 2024, Build ID 1872373`

> 

plots:-display(
        plot(1, x=0..1),
         plot(1, x=2..3), thickness=5);
> 

plots:-display(
        plot(1, x=0..1),
         plot(1, x=2..3),thickness=5, color=red);


Download mw.mw

Not a Maple question, forgive....

Asked by: Christian Wolinski 1650
chatgpt
March 03 2025
0  2

Does this happen to you (ChatGPT session):

How to perform simplifications to find unknown con...

Asked by: zenterix 405
substitution assumptions simplification
March 03 2025
2  5

I am taking a course in quantum mechanics and trying to do the calculations in Maple.

In the worksheet below I try to solve a system of equations to find some constants. 

It isn't very relevant that the domain is physics. 

The issues I have are with manipulations of expressions (specifically, simplifications).

restart

Levine - Ch. 2.4 - Particle in a Rectangular Well

NULL

Define

s__1 := sqrt(2*m*(V__0-E))/`&hbar;` = 2^(1/2)*(m*(V__0-E))^(1/2)/`&hbar;`NULL

s__2 := -s__1 = -2^(1/2)*(m*(V__0-E))^(1/2)/`&hbar;`NULL

NULLs := sqrt(2*m*E)/`&hbar;` 

2^(1/2)*(m*E)^(1/2)/`&hbar;`

 (1)

`&psi;__1`, `&psi;__2` and `&psi;__3` are wavefunctions.

`&psi;__1` := proc (x) options operator, arrow; C*exp('s__1'*x) end proc = proc (x) options operator, arrow; C*exp('s__1'*x) end procNULL

`&psi;__2` := proc (x) options operator, arrow; A*cos('s'*x)+B*sin('s'*x) end proc = proc (x) options operator, arrow; A*cos('s'*x)+B*sin('s'*x) end procNULL

`&psi;__3` := proc (x) options operator, arrow; G*exp('s__2'*x) end proc = proc (x) options operator, arrow; G*exp('s__2'*x) end procNULL

NULL

assume(G <> 0, C <> 0)

NULL

I would also like to assume that A and B cannot both be zero simultaneously.


As can be seen above, there are four unknown constants, "A,B,C,"and G.

 

We can obtain values for these unknowns by imposing boundary conditions.

 

Some of the boundary conditions involve the first derivatives of the wavefunctions.

`&psi;__1,d` := D(`&psi;__1`) = proc (z) options operator, arrow; C*s__1*exp(s__1*z) end procNULL

`&psi;__2,d` := D(`&psi;__2`) = proc (z) options operator, arrow; -A*s*sin(s*z)+B*s*cos(s*z) end procNULL

`&psi;__3,d` := D(`&psi;__3`) = proc (z) options operator, arrow; G*s__2*exp(s__2*z) end procNULL

NULL

The boundary conditions are

NULL

`&psi;__1`(0) = `&psi;__2`(0)*`&psi;__2`(l) and `&psi;__2`(0)*`&psi;__2`(l) = `&psi;__3`(l)*(D(`&psi;__1`))(0) and `&psi;__3`(l)*(D(`&psi;__1`))(0) = (D(`&psi;__2`))(0)*(D(`&psi;__2`))(l) and (D(`&psi;__2`))(0)*(D(`&psi;__2`))(l) = (D(`&psi;__3`))(l)

NULL

My question is how to find the constants in Maple.

NULLNULL

In this problem, E < V__0 and m > 0.

 

assume(E < V__0, m > 0)

 

Solving the first boundary condition is easy.

expr1 := solve(`&psi;__1`(0) = `&psi;__2`(0), {C}) = {C = A}

NULL

Next, I solve the third boundary condition and sub in the result from solving the first boundary condition. We get B in terms of A.

expr3 := eval(solve(`&psi;__1,d`(0) = `&psi;__2,d`(0), {B}), expr1) = {B = A*(m*(V__0-E))^(1/2)/(m*E)^(1/2)}NULL

NULL

Already here it is not clear to me why Maple does not cancel the m's.

 

Next, consider the second boundary condition

expr2 := solve(`&psi;__2`(l) = `&psi;__3`(l), {G}) = {G = (A*cos(s*l)+B*sin(s*l))/exp(s__2*l)}

 

We can obtain G in terms of just A by subbing in previously found relationships, as follows

expr2 := simplify(subs(expr3, expr2))

{G = exp(2^(1/2)*m^(1/2)*(V__0-E)^(1/2)*l/`&hbar;`)*A*(sin(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*(V__0-E)^(1/2)+cos(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*E^(1/2))/E^(1/2)}

 (4)

NULL

Finally, consider the fourth boundary condition.

solve(`&psi;__2,d`(l) = `&psi;__3,d`(l), {G})

{G = (m*E)^(1/2)*(A*sin(2^(1/2)*(m*E)^(1/2)*l/`&hbar;`)-B*cos(2^(1/2)*(m*E)^(1/2)*l/`&hbar;`))/((m*(V__0-E))^(1/2)*exp(-2^(1/2)*(m*(V__0-E))^(1/2)*l/`&hbar;`))}

 (5)

expr4 := simplify(subs(expr3, solve(`&psi;__2,d`(l) = `&psi;__3,d`(l), {G})))

{G = (sin(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*E^(1/2)-cos(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*(V__0-E)^(1/2))*exp(2^(1/2)*m^(1/2)*(V__0-E)^(1/2)*l/`&hbar;`)*A/(V__0-E)^(1/2)}

 (6)

result := simplify(subs(expr2, expr4))

{exp(2^(1/2)*m^(1/2)*(V__0-E)^(1/2)*l/`&hbar;`)*A*(sin(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*(V__0-E)^(1/2)+cos(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*E^(1/2))/E^(1/2) = (sin(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*E^(1/2)-cos(2^(1/2)*m^(1/2)*E^(1/2)*l/`&hbar;`)*(V__0-E)^(1/2))*exp(2^(1/2)*m^(1/2)*(V__0-E)^(1/2)*l/`&hbar;`)*A/(V__0-E)^(1/2)}

 (7)

At this point, we have this complicated expression.

 

The calculations above come from the book "Quantum Chemistry" by Levine. The variable "result" above should, after a few more steps of manipulating the expression, give us

 

(2*E-V__0)*sin(sqrt(2*mE)*l/`&hbar;`) = 2*sqrt(-E^2+E*V__0)*cos(sqrt(2*mE)*l/`&hbar;`)

(2*E-V__0)*sin(2^(1/2)*mE^(1/2)*l/`&hbar;`) = 2*(-E^2+E*V__0)^(1/2)*cos(2^(1/2)*mE^(1/2)*l/`&hbar;`)

 (8)

 

I've done the calculation by hand. It is not difficult. The exponentials and the A cancel on each side and we are left with an equation involving sin(sl) and cos(sl) which easily comes out to the desired equation above.

I would like to be able to do it here in Maple.

The first thing I would do at this point is to start eliminating some of the clutter. For example, I would like to replace sqrt(2*mE)/`&hbar;` with s.

 

This is a first task (that I have asked about in a separate question).

 

Then, I would want Maple to do the cancellations for me, but I have already used "simplify".

 

Finally, I think I would like to collect terms involving cos and sin.

 

Here is what happens when I try to get Maple to solve the equations for me in one go

 

solve({`&psi;__1`(0) = `&psi;__2`(0), `&psi;__1,d`(0) = `&psi;__2,d`(0), `&psi;__2`(l) = `&psi;__3`(l), `&psi;__2,d`(l) = `&psi;__3,d`(l)}, {A, B, C, G})

{A = 0, B = 0, C = 0, G = 0}

 (9)

Download solve_constants.mw

How to simplify factors that are square roots into...

Asked by: zenterix 405
radical simplification
March 03 2025
0  2

In a calculation, I obtained the following expression from Maple.

> 

expr1:=A*sqrt(-m*(-V__0 + E))/sqrt(m*E)

A*(-m*(-V__0+E))^(1/2)/(m*E)^(1/2)

 (1)

The first question I have is why the "m's don't cancel."

Next, consider the expression

> 

expr2:=exp(sqrt(2)*sqrt(m)*sqrt(-V__0 + E)*l*I/`&hbar;`)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (2)
> 

simplify(expr2,[E-V__0=y])

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`&hbar;`)

 (3)
> 

simplify(expr2,[2*m=y])

exp(I*y^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (4)

Why doesn't the simplification below work?

> 

simplify(expr2,[2*m*(E-V__0)=y])

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (5)

I also tried with other commands

> 

eval(expr2,2*m=y)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (6)
> 

eval(expr2,E-V__0=y)

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`&hbar;`)

 (7)
> 

eval(expr2,2*m*(E-V__0)=y)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (8)
> 

algsubs(2*m=y,expr2)

exp(I*y^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (9)
> 

algsubs(E-V__0=y,expr2)

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`&hbar;`)

 (10)
> 

algsubs(2*m*(E-V__0)=y,expr2)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`&hbar;`)

 (11)
 

NULL

In reality, I would like to the entirety of sqrt(2m(E-V__0)/hbar) a variable by the name of s.

Download simplify_roots.mw

Why does this procedure definition work when I nam...

Asked by: zenterix 405
procedure 2dmath differentiation
March 03 2025
0  2

Below is a simple demonstration of something that I am very confused about in another worksheet I am working on.

Basically, I have a function of x called psi_I and I want to define another function of x called psi_I,d which is just the derivative of psi_I.

In, the snippet below, this works if I use the variable names psi_1 and psi_1,d, but not if I replace the "1" with a "I" as I want to do.

In addition, I don't know why the output (6) is different from (7) or (8). All three are from the same command in Maple.

restart

`&psi;__1` := proc (x) options operator, arrow; C*exp(a*x) end proc

proc (x) options operator, arrow; C*exp(a*x) end proc

 (1)

`&psi;__1,d` := unapply(diff(`&psi;__1`(x), x), x)

proc (x) options operator, arrow; C*a*exp(a*x) end proc

 (2)

`&psi;__1,d`(x)

C*a*exp(a*x)

 (3)

NULL

restart

`&psi;__I` := proc (x) options operator, arrow; C*exp(a*x) end proc

proc (x) options operator, arrow; C*exp(a*x) end proc

 (4)

`&psi;__I,d` := unapply(diff(`#msub(mi("psi",fontstyle = "normal"),mi("1"))`(x), x), x)

D(psi__1)

 (5)

`#msub(mi("psi",fontstyle = "normal"),mi("1,d"))`(x)

`psi__1,d`(x)

 (6)

`#msub(mi("psi",fontstyle = "normal"),mi("I,d"))`(x)

(D(psi__1))(x)

 (7)

`&psi;__I,d`(x)

(D(psi__1))(x)

 (8)

NULL

Download psi_subscript.mw

How do replacing some special character to get ano...

Asked by: SSMB 100
substitution duplicate-question duplicate-account
March 03 2025
4  3

i want to to get the eq(14) but i need to do some Hard replacing which i am unfamiliar with it any one can help ?

> 

restart;
> 

 

> 

f :=  1 + exp(eta[1]) + b[1, 2]*exp(eta[1] + eta[2]) + exp(eta[2]) + b[2, 3]*exp(eta[2] + eta[3]) + b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1] + eta[2] + eta[3]) + b[1, 3]*exp(eta[1] + eta[3]) + exp(eta[3])

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])+b[2, 3]*exp(eta[2]+eta[3])+b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1]+eta[2]+eta[3])+b[1, 3]*exp(eta[1]+eta[3])+exp(eta[3])

 (1)
> 

NULL
> 

C :=(i,j)->6*l[j]*l[i]*(l[i] + l[j])/((l[i] - l[j])^2*beta)

proc (i, j) options operator, arrow; 6*l[j]*l[i]*(l[i]+l[j])/((l[i]-l[j])^2*beta) end proc

 (2)
> 

NULL
> 

etai := k[i]*(t*w[i]+y*l[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+x)+eta[i]

 (3)
> 

theta[i] := t*w[i]+y*l[i]+x

t*w[i]+y*l[i]+x

 (4)
> 

eqw := w[i] = -(alpha*l[i]+beta)/l[i]

w[i] = -(alpha*l[i]+beta)/l[i]

 (5)
> 

theta[1] := normal(eval(eval(theta[i], eqw), i = 1)); theta[2] := normal(eval(eval(theta[i], eqw), i = 2))

-(alpha*t*l[1]-y*l[1]^2+beta*t-x*l[1])/l[1]

  

-(alpha*t*l[2]-y*l[2]^2+beta*t-x*l[2])/l[2]

 (6)
> 

fix:=proc(F)
   local i,j;
   i:=op(1,F); j:=op(2,F);
   if i<j then
      C(i,j);
   else
      F;
   fi;
end proc:
> 

evalindets(f,b[anything,anything],F->fix(F));

1+exp(eta[1])+6*l[2]*l[1]*(l[1]+l[2])*exp(eta[1]+eta[2])/((l[1]-l[2])^2*beta)+exp(eta[2])+6*l[3]*l[2]*(l[2]+l[3])*exp(eta[2]+eta[3])/((l[2]-l[3])^2*beta)+216*l[2]^2*l[1]^2*(l[1]+l[2])*l[3]^2*(l[1]+l[3])*(l[2]+l[3])*exp(eta[1]+eta[2]+eta[3])/((l[1]-l[2])^2*beta^3*(l[1]-l[3])^2*(l[2]-l[3])^2)+6*l[3]*l[1]*(l[1]+l[3])*exp(eta[1]+eta[3])/((l[1]-l[3])^2*beta)+exp(eta[3])

 (7)
> 

simplify(%);

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])+b[2, 3]*exp(eta[2]+eta[3])+b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1]+eta[2]+eta[3])+b[1, 3]*exp(eta[1]+eta[3])+exp(eta[3])

 (8)
 

 

Download get_result.mw

How to `Describe` “Iterator:-Product”? ...

Asked by: sursumCorda 1244
March 03 2025
2  2

I would like to generate a brief description of the object Iterator:-Product but I get the following error:  

Describe(Iterator:-Product);

object Product :: Class<<36893490916968945900>>:

    ModuleApply( )

    ModuleCopy( self::_Product, proto::_Product, 
Error, (in Describe) `proto` does not evaluate to a module

How do I get rid of this message? 

ssystem("dir C:") result is in Spanish...

Asked by: minhhieuh2003 140
ssystem internationalization
March 03 2025
0  1

i used: 
Y := ssystem("dir C:"); print(Y)
result is

[0,"\" El volumen de la unidad C es OS\n El n£mero de serie del volumen es: 54A9-09DA\n\n Directorio de C:\\Program Files\\Maple 2016"

Windows operating system English version but Maple shows Spanish result
I want result is English. Please help me

Y := ssystem("dir C:"):

[0, " El volumen de la unidad C es OS El n£mero de serie del volumen es: 54A9-09DA Directorio de C:\Program Files\Maple 2016 21/02/2025 07:53 AM <DIR> . 22/02/2025 08:34 AM <DIR> .. 21/02/2025 07:50 AM <DIR> afm 21/02/2025 07:55 AM <DIR> bin.X86_64_WINDOWS 21/02/2025 07:52 AM <DIR> data 13/02/2025 07:46 AM <DIR> eBookTools 21/02/2025 07:50 AM <DIR> etc 02/02/2016 05:05 AM 73,861 EULA.html 21/02/2025 07:52 AM <DIR> examples 21/02/2025 07:52 AM <DIR> examplesclassic 21/02/2025 07:52 AM <DIR> Excel 21/02/2025 07:50 AM <DIR> extern 21/02/2025 07:52 AM <DIR> Fonts 13/01/2016 06:39 AM 223,499 Install.html 21/02/2025 07:52 AM <DIR> java 21/02/2025 07:52 AM <DIR> jre 21/02/2025 07:52 AM <DIR> lib 21/02/2025 07:55 AM <DIR> license 27/01/2011 11:13 PM 6,296 Maple Cloud Terms of Service.html 17/02/2016 02:54 PM 5,490,560 MapleToolbox2016.0WindowsX64Installer.exe 13/02/2025 07:48 AM 317,257 Maple_2016_Install_2025_02_13_08_46_07.log 21/02/2025 07:52 AM 317,834 Maple_2016_Install_2025_02_21_08_47_47.log 21/02/2025 07:50 AM <DIR> profiles 21/02/2025 07:52 AM 5,396 readme.txt 21/02/2025 07:52 AM <DIR> redist 21/02/2025 07:52 AM <DIR> samples 21/02/2025 07:52 AM <DIR> uninstall 21/02/2025 07:52 AM <DIR> update 13/02/2025 07:46 AM <DIR> Users 7 archivos 6,434,703 bytes 22 dirs 148,583,636,992 bytes libres"]

 (1)

``

Download language_maple.mw

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