Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I can't combine standard font and Greek symbols in a plot legend. I want to type:

"Limit of X_{i}^{\rho=0} (\alpha\mapsto+\infty)>0"

where I used LaTeX notation to emphasise that I want (1) superscript and subscript of X displayed as aligned exactly on top of each other, (2) rho, alpha, mapsto-style arrow, and infinity typed in their respective symbolic forms.

thanks!

I do not have earlier Maple version to check now. But Maple 2024.1 gives division by zero on this second order ode with missing x. This looks like new problem in Maple. Would someone who have access to earlier version of Maple be able to check if this problem shows there also? I solved this and get y=x+3 as solution which Maple verifies.

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

restart;

ode:=diff(y(x),x$2)=(diff(y(x),x))^3-(diff(y(x),x))^2;
IC:=y(0)=3,D(y)(0)=1;

diff(diff(y(x), x), x) = (diff(y(x), x))^3-(diff(y(x), x))^2

y(0) = 3, (D(y))(0) = 1

dsolve([ode,IC])

Error, (in dsolve) numeric exception: division by zero

sol:=y(x)=3+x;
odetest(sol,[ode,IC])

y(x) = 3+x

[0, 0, 0]

DEtools:-odeadvisor(ode);

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

infolevel[dsolve]:=5;

5

dsolve([ode,IC])

Methods for second order ODEs:

--- Trying classification methods ---

trying 2nd order Liouville

trying 2nd order WeierstrassP

trying 2nd order JacobiSN

differential order: 2; trying a linearization to 3rd order

--- trying a change of variables {x -> y(x), y(x) -> x}

differential order: 2; trying a linearization to 3rd order

trying 2nd order ODE linearizable_by_differentiation

trying 2nd order, 2 integrating factors of the form mu(x,y)

trying differential order: 2; missing variables

-> Computing canonical coordinates for the symmetry [0, 1]

-> Rewriting ODE in canonical coordinates by means of differential invariants

Try computing 1 more symmetries for ODE written in canonical coordinates

 -> Computing symmetries using: way = 3

 Found another symmetry:

[1, 0]

 Found another symmetry:

[-x+y, 0]

Computing a convenient ordering to use the 3 symmetries available

<- differential order: 2; canonical coordinates successful

<- differential order 2; missing variables successful

Error, (in dsolve) numeric exception: division by zero

dsolve(ode)

Methods for second order ODEs:

--- Trying classification methods ---

trying 2nd order Liouville

trying 2nd order WeierstrassP

trying 2nd order JacobiSN

differential order: 2; trying a linearization to 3rd order

--- trying a change of variables {x -> y(x), y(x) -> x}

differential order: 2; trying a linearization to 3rd order

trying 2nd order ODE linearizable_by_differentiation

trying 2nd order, 2 integrating factors of the form mu(x,y)

trying differential order: 2; missing variables

-> Computing canonical coordinates for the symmetry [0, 1]

-> Rewriting ODE in canonical coordinates by means of differential invariants

Try computing 1 more symmetries for ODE written in canonical coordinates

 -> Computing symmetries using: way = 3

 Found another symmetry:

[1, 0]

 Found another symmetry:

[-x+y, 0]

Computing a convenient ordering to use the 3 symmetries available

-> Calling odsolve with the ODE diff(_b(_a) _a) = _b(_a)^3-_b(_a)^2 _b(_a) HINT = [[1 0] [-_a+y -_b*(_b-1)]]

   *** Sublevel 2 ***

   symmetry methods on request

 1st order, trying reduction of order with given symmetries:

[1, 0], [-_a+y, -_b*(_b-1)]

   1st order, trying the canonical coordinates of the invariance group

   <- 1st order, canonical coordinates successful

<- differential order: 2; canonical coordinates successful

<- differential order 2; missing variables successful

y(x) = ln(LambertW(-c__1*exp(x-1)))+c__2

 

 

Download divide_by_zero_maple_2024_1_august_5_2024.mw

I want to substitute a variable r' =sqrt(x^2 + y^2 + z^2).

But how do I change my output so that r' is displayed instead of sqrt(x^2+y^2+z^2)?

E.g. line (5) D(g)(r')x/r' and not D(g)(sqrt(x^2 + y^2 + z^2))*/sqrt(x^2 + y^2 + z^2). 

And one more question. How can I make sure that my output in (6) is only the result on the right side and the left side of the equal sign is not displayed? 


 

restart

with(Physics)

__________________________________________________________________

(1)

with(Vectors)``

Setup(spacetimeindices = greek, spaceindices = lowercaselatin, su2indices = uppercaselatin, signature = `- - - +`, coordinates = cartesian)

[coordinatesystems = {X}, signature = `- - - +`, spaceindices = lowercaselatin, spacetimeindices = greek, su2indices = uppercaselatin]

(2)

diff(r(x), x) := sqrt(x^2+y^2+z^2)

(x^2+y^2+z^2)^(1/2)

(3)

``

g(diff(r(x), x))

g((x^2+y^2+z^2)^(1/2))

(4)

diff(g(diff(r(x), x)), x)

(D(g))((x^2+y^2+z^2)^(1/2))*x/(x^2+y^2+z^2)^(1/2)

(5)

NULL

NULL

H := (x*Psigma[1, matrix]+y*Psigma[2, matrix]+z*Psigma[3, matrix]).Vector(2, {1 = 0, 2 = U(diff(r(x), x))})

(x*Physics:-Psigma[1]+y*Physics:-Psigma[2]+z*Physics:-Psigma[3]).Vector[column](%id = 36893490180036880732) = Vector[column](%id = 36893490180036881092)

(6)

NULL


 

Download representation_of_code.mw

Something seems to have changed.  I do not now have Maple 2024.0 to check or earlier Maple's as I have to reinstall windows since my C:\ drive died. 

I installed Maple 2024.1 new on windows 10 home edition.

I noticed now when evaluating the current cell, the cursor automatically jumps to next cell, which is what I want and how Maple always worked.

But now the cursor jumps to the end of the command in the next cell. Before, I could swear that not how it worked and it used to jump to the start of the next cell.

This makes it very confusing, as I keep looking for where the cursor is now.

Why was this changed in 2024.1? I looked at option and see nothing to change this. 

Here is worksheet and small movie. 

This is my display options

 


 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

x:=1;

1

y:=3;

3

z:=4;

4

h:=4;

4

 


 

Download cursor_jump_to_end_of_line.mw

 

 

Update

I tried to change the cursor size and thickness in windows 10 itself (using settings->Ease of access->Text cursor) and made it much bigger and restarted Maple but this had no effect. Cursor inside Maple remained the same.

I was hoping if there is a way to make the cursor bigger then this will make it easier to see where it jumped to when hitting enter.

It is bad, since the Maple cursor jumps to random places in the next cell. sometimes it jumps to the middle of the code in the next cell when there are more than one line there.

Here is a movie. Notice how it jumped to the start of the second line now in next cell in one case and not to the end of the code.

I can't believe no one at Maplesoft have noticed this and is able to fix it. This is ridiculous behavior. I spend few seconds each time I hit enter looking for where the cursor has landed as I keep looking at start of the next cell and it is not there. I could have 10-20 lines of code in one cell and have too look to find where the cursor is hidden in these 20 lines.

It natural for one to look for where the cursor is when woking and this makes it annoying. Hopefully someone can find a way to tell Maple to bring the old behaviour back where cursor jumps always to the start of the next cell.

 

 

 

 

restart;

local gamma;

gamma

(1)

with(Plot)

 

params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7,theta=0,gamma=1};

{alpha = 2.5, gamma = 1, k = 3, theta = 0, w = 2, beta[3] = 3, beta[4] = 1.7}

(2)

xi := sqrt(-1/(72*alpha*beta[4]+72*gamma*beta[4]))*(2*alpha*k*t+x)

(-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)

(3)

 

sol1 := [U(xi), -k*x -(9*alpha*k^2*beta[4] + 2*beta[3]^2)/(9*beta[4])*t + theta];

[U((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

(4)

 

sol2 := eval(sol1, U(xi) = -beta[3]/(3*beta[4]) + beta[3]*sinh(xi)/(6*beta[4]*cosh(xi)) + beta[3]*cosh(xi)/(6*beta[4]*sinh(xi)));

[-(1/3)*beta[3]/beta[4]+(1/6)*beta[3]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)))+(1/6)*beta[3]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

(5)

 

solnum :=eval(sol2, params);

[-.5882352940+(.2941176471*I)*sin(.7247137946*t+0.4831425297e-1*x)/cos(.7247137946*t+0.4831425297e-1*x)-(.2941176471*I)*cos(.7247137946*t+0.4831425297e-1*x)/sin(.7247137946*t+0.4831425297e-1*x), -3*x-23.67647059*t]

(6)

plots:-complexplot3d(solnum, x = -50.. 50, t = -50..50);

Warning, unable to evaluate the function to numeric values in the region; complex values were detected

 

 

NULL


if there is any other way for graph please share with me

Download complexplot3d.mw

Why doesn't evalf work on the data structures below?
 

M1 := Matrix([[m__1, m__2]])

Matrix(%id = 36893488151929448556)

(1)

M := [M1, M1]

[Matrix(%id = 36893488151929448556), Matrix(%id = 36893488151929448556)]

(2)

m__1 := 1; m__2 := 2

M

[Matrix(%id = 36893488151929448556), Matrix(%id = 36893488151929448556)]

(3)

evalf(M)

[Matrix(%id = 36893488151929440844), Matrix(%id = 36893488151929440964)]

(4)

evalf(M[1])

Matrix(%id = 36893488151929437108)

(5)

evalf(op(M))

Matrix(%id = 36893488151929432292), Matrix(%id = 36893488151929432412)

(6)

evalf(op(M[1]))

1., 2., {(1., 1.) = m__1, (1., 2.) = m__2}, datatype = anything, storage = rectangular, order = Fortran_order, shape = []

(7)

NULL


 

Download evalf.mw

i am trying to solve definite integral but i want result in A,B form i dont want to assign numerical values to them can i get that  in maple? i have tried evalf, eval and simplify command but it is not working kindly help me out

restart

NULL

integrand := p*exp(-A/sqrt(p)-B/p)

p*exp(-A/p^(1/2)-B/p)

(1)

integral := int(integrand, p = 0 .. infinity)

int(p*exp(-A/p^(1/2)-B/p), p = 0 .. infinity)

(2)

simplify(integral)

int(p*exp(-(A*p+B*p^(1/2))/p^(3/2)), p = 0 .. infinity)

(3)

evalf(integral)

int(p*exp(-1.*A/p^(1/2)-1.*B/p), p = 0. .. Float(infinity))

(4)

eval(integral)

int(p*exp(-A/p^(1/2)-B/p), p = 0 .. infinity)

(5)
 

NULL

Download integral.mwintegral.mw

I was wondering if this has ever been discussed?

File preview would make life easier when searching an older document.

Since it seems to be a non trivial programming task, I was wondering whether generating a pdf document in parallel to a worksheet could be an option (in a subfolder). However, doing this by hand for all existing documents is not pratical.
 

Could this (generating pdf files) be done by a batchjob?

 

Why does sqrt(-2) give as a result only i*sqrt(2)?

Why does the result not also include -i*sqrt(2)?

How to Call a maple code from inside a python code in jupyter say or sypder.

I tried to solve a equation f(x). Finally I got a polynomial with coefficients.  (see Solve_for_coefficients.mw)

I want to find the values of unknown coeffients in the last polynomial equation as procedure to equating each cofficients to zero.

For example, the coefficients of x^2 is 1/48*(-24*p[2]+48*q[1]+24*q[2]+24) = 0.

Likewise, collect all the coefficients from x^0 to x^4 and solve them. Finally we get the coefficients value.

My question is How to collect the coefficients in this polynomial and solve this coefficients?

Hi,

How do we get from equation 11 to equation 13 with Maple by converting equations 12?

Hello

I would like to calculate the number of partitions of a number s with length n, where the maximum value in the partitions is also n.

For example: s=10, n=4

The result should be 5, because there are 5 partions with length 4 and maximum value 4:

4411, 4321, 4222, 3331, 3322

If I use "PartitionFixedSize(10,'parts'=4)", it makes also partitions with values > 4, for example 5311. How to limit this?

Thank you for an answer!

Kind regards

 

 

Suppose we have the following simple Matrix

T := <1,2;3,4>;

How do we replace an entry with another expression?

I know that for a list L := [1,2,3] we can do, for example subsop(2=500,L) to replace the entry at index 2.

This creates a new list since lists are immutable.

As far as I can tell, a Matrix is mutable.

However, I wish to change an entry in a Matrix without mutating it.

My actual use case is the following.

I use LinearAlgebra:-Eigenvectors to obtain a Matrix of eigenvectors. Some of the entries are huge expressions with many variables. I would like to sub in placeholders where these huge expressions are so I can visualize the Matrix better, but without modifying the original Matrix.

Is it possible to  convert an existing document in worksheet mode to document mode in Maple22 ?

It seems you can only select either at creation of document but not convert documents already existing.

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