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labels and tickmarks problem...

Asked by: jestrup 70
plotting tickmarks
October 26 2023
1  6

I have a small problem that I can't find a solution for. How do you draw a diagram like the one shown in Maple? I can't figure out how to rotate the column labels or define tickmarks as text.

Can anyone help?

Problem viewing data tables in maple cloud viewer...

Asked by: Jean-Baptiste Runge 5
maplecloud datatable
October 26 2023
1  1

Hi, 

Some of my maple documents contain data tables. 

When I want to view these documents with the maple cloud viewer, the data tables are invisible (the table is completely grayed out) and it is therefore impossible to change the values in this table. 

The table properties are such that it is enabled, visible and editable. 
Does anyone have an idea how to solve this problem? 
Thanks in advance. 

How do I fix error in Array?...

Asked by: Carolyn Davis 15
syntax sin user-error
October 24 2023
0  1

Can anyone please assist with these errors?

> 

#Clear memory.
restart;

#Initialise variables and arrays.
h:=Pi/10;
n:=10;
k:=0.1;  
m:=6;
t:=Array(0..m):
x:=Array(0..n):
u:=Array(0..n,0..m):

#Initialise the x array and the initial u(x,0) boundary.
for i from 0 to n do
    x[i]:=i*h;
    u[i,0]:=0;
end do:

#Initialise the t array and the u(x,t) side boundaries.
for j from 0 to m do
   t[j]:=j*k;
   u[0,j]:=0;
   u[n,j]:=3*sin*t[j];
end do:

#Use the 2D CTCS explicit wave method.
for i from 1 to n-1 do
   u[i,1]:=(u[i-1,0]/2*Pi^2+sin(x)/10*Pi^2+u[i+1,0]/2*Pi^2)-1;
end do:
 
for j from 1 to m-1 do
  for i from 1 to n-1 do
   u[i,j+1]:=(((u[i-1,j]+u[i+1,j]-u[i,j-1])/Pi^2)-2);
  end do;
end do:

#Display the u(x,t)values.
printf("2D CTCS Explicit Wave Method\n");
printf("----------------------------\n");
printf("x\t\t t\t\t u\n");
for i from 0 to n do
   printf("% f\t% f\t% f\n",x[i],t[m],u[i,m]);
end do;

(1/10)*Pi

  

10

  

.1

  

6

  

Error, invalid input: sin expects its 1st argument, x, to be of type algebraic, but received Array(0..10, [0,1/10*Pi,1/5*Pi,3/10*Pi,2/5*Pi,1/2*Pi,3/5*Pi,7/10*Pi,4/5*Pi,9/10*Pi,Pi])

  

2D CTCS Explicit Wave Method
----------------------------
x                 t                 u
 0.000000         0.600000         0.000000
 0.314159         0.600000        -2.015556
 0.628319         0.600000        -2.198509
 0.942478         0.600000        -2.215724
 1.256637         0.600000        -2.218015
 1.570796         0.600000        

  

Error, (in fprintf) number expected for floating point format

  
> 

NULL


Download Asst_4_Question_2c.mw

Has anybody had this strange error: Maple does not...

Asked by: C_R 3442
crash java windows10
October 24 2023
3  1

Both, Maple and MapleSim in Versions from 2021 to 2023 do not start. A logfile is saved which starts as

# A fatal error has been detected by the Java Runtime Environment:

#

#  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x0000000000000000, pid=17256, tid=10520

#

# JRE version: OpenJDK Runtime Environment Temurin-19.0.1+10 (19.0.1+10) (build 19.0.1+10)

# Java VM: OpenJDK 64-Bit Server VM Temurin-19.0.1+10 (19.0.1+10, mixed mode, tiered, compressed oops, compressed class ptrs, g1 gc, windows-amd64)

# Problematic frame:

# C  0x0000000000000000

#

This only occurs when the notebook (on which the error occurs) is connected to the domain network. If the notebook is not connected, Maple and MapleSim can be started and will continue to run when the network is reconnected.

Has anybody seen this before or any ideas what this could be?

Edit: This all happened under Windows 10 on a notebook that has been running Maple for 3 years and only recently displayed this error.

Edit2: Connection via an USB doc which also connects to an external monitor.

Maple Editor (maple-input instead of 2d-input )...

Asked by: 2cUniverse 115
2dmath worksheet style
October 23 2023
1  9

Since I have updated from Maple 2021 to 2023 something is wrong with my stylesheets.

I rephrase my qeustion here:

I like to change the text-style of 2D-Input to courant 12, bold, color x, no italic.

Now it is courant 12, black, italic when opening a new worksheet.

I was going to format, style, 2D-input, modify and then the font has changed when opening a new woksheet but the color is going back to black and its also italic courant when pressing enter in that worksheet.

I When opening a new worksheet, i don't want ot looad an new style set by hand every time.

 

Thanks for support

 

 

solution of differential equations...

Asked by: emersondiaz 60
ode syntax dsolve
October 22 2023
2  5

Good day to all the members who read this question.
I ask for your help to find the right way to solve this two differential equations (is attached the file). Used the common code "dsolve" but is not working on this problem. Doesn't matter if the solution is numeric or algebraic.
I will thaks a lot your kind help.
Best regards to all of you

DIFFERENTIAL_EQUATION.mw

restart

with(PDEtools)

First Part

The differential equation to solve:

(Delta*LinearAlgebra:-Transpose(D[1/2])*D__0-I*`μ__e`*D__0/(lambda+I*`μ__e`*r)-2*(`μ__e`^2*r^2+lambda^2))*R(r)

Definitions

D__n = `∂__r`+I*omega(a^2+r^2)/Delta+I*a*m/Delta+2*n*(r-M)/Delta

LinearAlgebra:-Transpose(D[n]) = `∂__r`-I*omega(a^2+r^2)/Delta-I*a*m/Delta+2*n*(r-M)/Delta

a := 1; M := 1; omega := 1; m := 1; `μ__e` := 1; lambda := 1

Delta := -2*M*r+a^2+r^2

I divided the differential equation in 3 parts (A, B, C).

A := (-I*omega(a^2+r^2)-I*a*m+r-M)*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)+Delta*(diff(R(r), r, r))+I*omega(a^2+r^2)*(diff(R(r), r))+I*a*m*(diff(R(r), r))

B := -I*`μ__e`*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)/(lambda+I*`μ__e`*r)

C := -(2*(`μ__e`^2*r^2+lambda^2))*R(r)

DE := A+B+C

E := dsolve(DE)

R(r) = DESol({diff(diff(_Y(r), r), r)-(1-r+I/(1+I*r))*(diff(_Y(r), r))/(r^2-2*r+1)-(-(2*I)*((-1-2*I)+r)/(r^2-2*r+1)-2/((1+I*r)*(r^2-2*r+1))+2*r^2+2)*_Y(r)/(r^2-2*r+1)}, {_Y(r)})

 (1)

dsolve({DE, DE(0) = 1}, numeric, range = 0 .. 20)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

  

Second Part

The differential equation to solve:

[`#msub(mi("L",fontweight = "bold"),mfrac(mn("1",fontweight = "bold"),mn("2",fontweight = "bold"),linethickness = "1"))`*LinearAlgebra:-Transpose(L[1/2])+a*`μ__e`*sin(theta)*LinearAlgebra:-Transpose(L[1/2])/(lambda+a*`μ__e`*cos(theta))+2*(lambda^2+a^2*`μ__e`*cos(theta)^2)]*S(theta) = 0

Definitions:

L__n = a*omega*`sinθ`+m*`cosecθ`+n*`cotθ`+`∂__θ`

LinearAlgebra:-Transpose(L[n]) = -a*omega*`sinθ`-m*`cosecθ`+n*`cotθ`+`∂__θ`

Also I divided the differential equation in 3 parts (A, B, C).

F := (omega*a*sin(theta)+m/sin(theta)+1/(2*tan(theta)))(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))+diff(S(theta), theta, theta)-omega*a*sin(theta)*(diff(S(theta), theta))-m*(diff(S(theta), theta))/sin(theta)+(diff(S(theta), theta))/(2*tan(theta))

G := a*`μ__e`*sin(theta)*(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))/(lambda+a*`μ__e`*cos(theta))

H := (2*(lambda^2+a^2*`μ__e`*cos(theta)^2))*S(theta)

DF := F+G+H

dsolve(DF)

dsolve({DF, DF(0) = 1}, numeric, range = 0 .. 20)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

  

NULL

Download DIFFERENTIAL_EQUATION.mw

Why does this worksheet calculates for ever?...

Asked by: FDS 220
procedure
October 22 2023
0  18

Dear Power Users, I tried to make a model in Maple but after several hours of struggling I need some help. Can someone tell me what I did wrong or explain to me what is the meaning of the maplemint comment on procedure (optimalisatie)? Thank you in advance.

DiLeoCasper.mw 

How do I program Maple to display consective numbe...

Asked by: Carolyn Davis 15
seq printf
October 21 2023
0  2

For the t output I need to show 1, 1.2, 1.4....2, my attempt is highlighted in green below

Can anyone assist please?

> 

#Clear memory and load packages.
restart;
with(plots):
with(Statistics):

#Define vectors and variables.
actual:=<2,3.5136,5.8016,9.1136,13.7376,20>:
t:=<1,1.2,1.4,1.6,1.8,2>:
n:=6:
RMSE:=0:

#Perform a simple linear regression on the data.
P:=LinearFit([1,x],t,actual,x);

#Display the model errors.
printf("t    Actual P  Model P  Error\n");
for i from 1 to n do
   model:=subs(x=t[i],P):
   err:=actual[i]-model:
   RMSE:=RMSE+err^2:
   printf("%2d %7.4f% 10.4f% 9.4f\n",(i+(1/5)),actual[i],model,err);
end do:

#Display the root mean square error.
RMSE:=sqrt(RMSE/n);

#Plot the points and the model.
p1:=plot(t,actual,style=point,view=[0..7,8..26]):
p2:=plot(P,view=[0..7,8..26]):
display(p1,p2);

-HFloat(17.540266666666668)+HFloat(17.712)*x

  

t    Actual P  Model P  Error

  

Error, (in fprintf) integer expected for integer format

  

HFloat(0.7463867411787324)

  

 
> 

NULL

Download Asst_4_Question_1f.mw

How to create orthonormal triads with "Physics:-Ve...

Asked by: olivier107 10
basis orthonormal physics
October 21 2023
2  0

Hello,
I recently discovered the "Physics" package wich provides tools for manipulating abstract vectors (non-component).
In the "Physics:-Vectors", an orthonormal basis (i,j,k) is available and my main concern is how to generate arbitrary other 3D orthonormal bases to be able to calculate results in "vectorial form" without manipulating vectors' components.

To better explain my needs I have setup a kind of minimal example in the attached file where some questions are asked.

Thanks in advance for any feedback.

orthonormal-triads.mw

NULL

restart

with(Physics)

with(Physics[Vectors])

Creation of 2 rotation matrices

dir1 := `<,>`(0, 0, 1)

dir2 := `<,>`(0, 1, 0)

seq(assign(cat(R, i), Student:-LinearAlgebra:-RotationMatrix(theta[i], eval(cat(dir, i)))), i = 1 .. 2)

print(R1, R2)

Matrix(%id = 36893490614987576012), Matrix(%id = 36893490614987577572)

 (1)

whattype(R1)

Creation of  orthogonal unit "Physics:-Vectors" from previous matrices

x1_ := _i*R1[1, 1]+_j*R1[2, 1]+_k*R1[3, 1]``

y1_ := _i*R1[1, 2]+_j*R1[2, 2]+_k*R1[3, 2]

z1_ := _i*R1[1, 3]+_j*R1[2, 3]+_k*R1[3, 3]NULL

NULL

x2_ := _i*R2[1, 1]+_j*R2[2, 1]+_k*R2[3, 1]NULL

y2_ := _i*R2[1, 2]+_j*R2[2, 2]+_k*R2[3, 2]

z2_ := _i*R2[1, 3]+_j*R2[2, 3]+_k*R2[3, 3]

Q1: Is there a more elegant way of creating "Physics:-Vectors" from matrices ?

Now, suppose that we want to compute `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) : since `#mover(mi("y2"),mo("&rarr;"))` = `#mover(mi("j"),mo("&and;"))` we have `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) = sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` and sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` = sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` and sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` = cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))`

The cross product operator  `&x`(x1_, y2_) yields

cos(theta[1])*_k

 (2)

(which is a correct answer) instead of cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))` because vector `#mover(mi("z1"),mo("&rarr;"))` has is not known as a unit basis vector.

Similarly, `&x`(z1_, x1_) yields -sin(theta[1])*`#mover(mi("i"),mo("&and;"))`+cos(theta[1])*`#mover(mi("j"),mo("&and;"))` instead of  `#mover(mi("y1"),mo("&rarr;"))` as it would be the case when computing `&x`(_k, _i) ?

Q2: Is there a way to declare new triads of "Physics:-Vectors" with properties similar to the provided triad _i, _j, _k ?

Q3: Is the code defining the canonical basis i, _j, _kavailable for inspection and inspiration to setup orthonormal triads ?

Q4: Is it possible to get a (column) matrix of the vector components ? The function Physics:-Vectors:-Component(y1_, n) can only get 1 component at a time and only in the canonical basis i, _j, _k.

NULL

restart

with(Physics)

with(Physics[Vectors])NULL

After a proper definition of 2 new vector bases `#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y1"),mo("&rarr;"))`, `#mover(mi("z1"),mo("&rarr;"))` and `#mover(mi("x2"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`, `#mover(mi("z2"),mo("&rarr;"))`, the position vector OM_ := l__1*x1_+l__2*x2_NULLNULL

l__1*x1_+l__2*x2_

 (3)

NULL

projected on `#mover(mi("x2"),mo("&rarr;"))` would yield directly Typesetting[delayDotProduct](l__1, `#mover(mi("x2"),mo("&rarr;"))`.`#mover(mi("x1"),mo("&rarr;"))`, true)+l__2 instead of expand(OM_.x2_)

l__1*Physics:-Vectors:-`.`(x1_, x2_)+l__2*Physics:-Vectors:-Norm(x2_)^2

 (4)

because of the unit vectors.

Download orthonormal-triads.mw

Bug in simplify piecewise...

Asked by: Rouben Rostamian 8531
simplify piecewise physics
October 20 2023
1  2

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

 

> 

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.`

> 

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 broken...

Asked by: Rouben Rostamian 8531
inverse laplace
October 19 2023
2  10

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.

> 

restart;
> 

kernelopts(version);

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

> 

with(inttrans):
> 

exp(-a*t);

exp(-a*t)

> 

laplace(%, t, s);

1/(s+a)

> 

invlaplace(%, s, t);

exp(a*t)

 

Download laplace-transform-bug.mw

Plotting a function with factorials. Why does this...

Asked by: Scot Gould 1039
plot plotting factorial
October 18 2023
2  10

This is not a critical situation. A solution was developed. However, I am interested in trying to understand and explain to a colleague why their function failed to plot. The colleague often works on problems involving large factorial values.

failed_plot.mw

How can I resolve this numeric integral containing...

Asked by: Hullzie16 343
integration numeric overflow
October 11 2023
3  12

Hi Everyone, 

I have a numeric integral which I hope to evaluate (ideally over a infinite domain) that for some reason is giving me difficulty and I cannot seem to find a work around. I want to use method = _d01amc in the integral as a means to speed up the process - I am motivating this by the answer i recieved from @acer in https://www.mapleprimes.com/questions/236772-Any-Ideas-On-How-To-Speed-Upimprove - however I keep recieving an error indicating overflow. 

This seems rather strange to me due to the fact that if I omit a method and just let Maple do its own thing it will eventually spit out an answer albeit slower then I would prefer for the procedure I am going to eventually impliment. 

My integrand and attempts/confusion can be seen in the attached worksheet. 

Any thoughts appreciated. 

OverflowError.mw

What is a more efficient way to generate OEIS' "A1...

Asked by: sursumCorda 1254
performance sequence prime
October 11 2023
2  18

The sequence A161786 consists of “primes with at least one digit appearing exactly four times in the decimal expansion”. Below is the Maple program given in that OEIS page:

The code above picks out primes having exactly four identical digits (determined by ) from the first 10,000 prime numbers. However, it's easy to check that this program is rather slow (It takes about 2.6s to execute it!). 
Actually, I would like to select such primes from pn, pn+1, pn+2, …, pn+m-1 (typically, n＝1,000,000 and m＝1,000,000), where pk denotes the k-th prime number, yet the original program failes to do so in twenty minutes. Part of the reason is that for long sequences, the efficiency can be critical. Therefore I make a slight modification to the original code: 

A161786__0 := proc(m::nonnegint, n::posint := 1, ` $`)::'Vector'(prime):
	#(*
	    kernelopts(opaquemodules = false):
	# *)
	local p := ifelse(n = 1, 1, ithprime(n - 1)), vec := Vector('datatype' = prime);
	to m do
		if ormap(`=`, MultiSet(`convert/base`:-MakeSplit(length((p := nextprime(p))), 1, 10)(p)):-hash, 4) then
			vec ,= p
		fi
	od;
	vec
end:

Nevertheless, this version is still inefficient: 

time[real](A161786__0(10**6, 10**6));
 = 
                            182.414

Another choice is converting each of integers into a string: 

A161786__1 := proc(m::nonnegint, n::posint := 1, ` $`)::'Vector'(prime):
	options no_options:
	local p := ifelse(n = 1, 1, ithprime(n - 1)), vec := DEQueue();
	to m do
		if member(4, rhs~({StringTools['CharacterFrequencies'](nprintf("%d", (p := nextprime(p))), 'digit')})) then
			vec ,= p
		fi
	od;
	Vector([vec[]], 'datatype' = prime)
end:

This time the elapsed time is reduced to nearly two minutes: 

time[real](A161786__1(10**6, 10**6));
 = 
                            118.409

But can this task be accomplished within (a quarter of) a minute in modern Maple? In other words, is there a way to make further improvement on the performance? (Note that the reference time is mesured using a adjusted version (i.e., ) of the Mma code provided in that OEIS page.) 

preview print function not working correct after ...

Asked by: 2cUniverse 115
print export osx
October 09 2023
2  0

When printing a Maple Worksheet  often I go in the PrintPrewiev of the Mac and then select some sides to print.

This is not working anymore since I have updated from Maple 2021 to Maple 2023.

Is this known ?

Any help for his ?

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