Hi friends! Hope everything is fine here

I want to generate a piecewise function using some already computed functions. Like I compute B[0], B[1], B[2] and B[3] using some formula which are given as,

B[0] := (1/6)*x^3/h^3;
B[1] := (1/6)*(4*h^3-12*h^2*x+12*h*x^2-3*x^3)/h^3;
B[2] := -(1/6)*(44*h^3-60*h^2*x+24*h*x^2-3*x^3)/h^3;
B[3] := (1/6)*(64*h^3-48*h^2*x+12*h*x^2-x^3)/h^3;

Now, I want to define the corresponding piecewise function as

piecewise(x <= 0, 0, 0 < x and x <= h, B[0], `and`(h < x, x <= 2*h), B[1], `and`(2*h < x, x <= 3*h), B[2], `and`(3*h < x, x <= 4*h), (B[3], 0)

similarly for already computed functions B[0], B[1], B[2], B[3] and B[4] which are given as

B[0] := (1/24)*x^4/h^4;
B[1] := -(1/24)*(5*h^4-20*h^3*x+30*h^2*x^2-20*h*x^3+4*x^4)/h^4;
B[2] := (1/24)*(155*h^4-300*h^3*x+210*h^2*x^2-60*h*x^3+6*x^4)/h^4;
B[3] := -(1/24)*(655*h^4-780*h^3*x+330*h^2*x^2-60*h*x^3+4*x^4)/h^4;
B[4] := (1/24)*(625*h^4-500*h^3*x+150*h^2*x^2-20*h*x^3+x^4)/h^4;

I want to define the corresponding piecewise function as

piecewise(x <= 0, 0, 0 < x and x <= h, B[0], `and`(h < x, x <= 2*h), B[1], `and`(2*h < x, x <= 3*h), B[2], `and`(3*h < x, x <= 4*h), B[3], `and`(4*h < x, x <= 5*h), B[4], 0)

Can someone please let me know a general procedure (using seq command, loop etc.) to define piecewise function if B[0], B[1], B[2],...,B[M] are known? I shall be very thankful for your answer.

I have plain text file generated, where each line has mixed numbers and strings. Some of the strings are latex. So they have "\" in them. The data is rectangle. same number of fields on each line, separated by commas.  I use CSV format to read the data to Maple.

I simply want to read this file using Import , which reads it into a matrix (using CSV format), and export it back right away using either ExportMatrix or Export and end up with the same exact file.

But Maple always adds extra "\" each time I export the matrix back to the file. So if I have initially "\sin x" in the file, after reading/writing the file 5 times without touching the data inside Maple, I end up with something like "\\\\\\\\\\\sin x" in the file at the end.

I could ofcourse not use ExportMatrix nor Export and write the data back to the file manually using fprintf using correct format for each field. But it is easier if I can get ExportMatrix to work since there are many fields some are integers, some are real and some are strings.

Here is a simple MWE which shows the problem. Originally I have this file on disk. Called test.txt and has 2 lines in it

1,"\sin x"
2,"this is second line"

Now after doing the following

data:=Import("test.txt",format="CSV",output=Matrix):  
ExportMatrix("test.txt",data,target=csv);

The file on disk now becomes

1,"\\sin x"
2,"this is second line"

And repeating the above one more time, the file becomes

1,"\\\\sin x"
2,"this is second line"

This ofcourse breaks all the latex strings in there.

Is there a way to prevent Maple from doing this? I looked at all the options in help, but do not see on so far.  I also tried Export but that did not work at all. So I'd like to see if ExportMatrix can do it, without adding an extra "\", otherwise, will have to use fprintf directly to export the data back to file.

edit

fyi, I ended up using fprintf to write the data back to disk. May be if there is a solution using ExportMatrix, will change back. This is what I ended up doing

File before

1,"\sin x"
2,"this is second line"

Now run this code

data:=Import("test.txt",format="CSV",output=Matrix):  
file_id := fopen("test.txt",WRITE):
nRows:=LinearAlgebra:-RowDimension(data);
for n to nRows do
    if n<nRows then
       fprintf(file_id,"%d,\"%s\"\n",data[n,1],data[n,2]);
    else
       fprintf(file_id,"%d,\"%s\"",data[n,1],data[n,2]);
    fi;
od;
fclose(file_id);

File after

1,"\sin x"
2,"this is second line"

Now the file is exactly the same as before reading it.

My actual data is more than the above two fields, but that makes the format string longer, that is all.

Hey

Does Maple have the equivalent of the MROUND Excel command?

Or can someone kindly make a procedure.

eg

MROUND(1986,10)=1990

MROUND(492,5)=490

thanks!

I am not getting the hemisphere which I thought was my expression (equation) represents.

Can anyone help me find my mistake.

with(plots);
implicitplot3d(z <= sqrt(-x^2 - y^2 + 9), x = -3 .. 3, y = -3 .. 3, z = 0 .. 3, coords = spherical);

Thanks in advance.

Doubt_ImplicitPlot.mw

Hello everyone

I observe the following "strange" case and I am wondering if I am missing something. So, any insights are more than appreciated. The case is the followin:

When I use

with(Optimization):
Interactive(x + y, {x = 0 .. 1, y = 0 .. 1, 1 <= x + y})

I get: objective =1, x=y=.5

However, If I run

with(Optimization):
Minimize(x + y, {x >=0,x<=1, y>=0,y<=1, 1 <= x + y})

then I get: objective =1, x=1, y=0

Why there is such a difference? Because of there are multiple solutions? 

Setup:
I am working with a 'large' data set( ~70MB .csv file).  Using the import command I can import the data into a maple worksheet.  After import the dimension of the imported object 434000 rows by 30 columns.  The first 2 columns contain time stamp strings, the rest are numeric. 

Issue:
Importing this data set takes about 5 minutes everytime the command is called, which is everytime the worksheet is opened or re executed.  This is a lot of redundent processing.

Question:
Is there a way that I can import the data once and have it saved as a variable in the variable manager associated with the worksheet?  I want to avoid using the import command in a reduent manner.

Dear Maple community,

I'm trying to solve iteratively a system of (non-)linear equations and, to better understand the dynamics behind this process, would like to know the new/updated values of the unknowns after each iteration. Unfortunately, I wasn't able to implement this myself and was wondering whether you could give me hand?

Specifically, consider the following system of 4 non-linear equations in 4 unknowns: y[1], y[2], y[3], y[4]:

(EQ1): y[1]=f(y[1], y[2], y[3], y[4])

(EQ2): y[2]=f(y[1], y[2], y[3], y[4])

(EQ3): y[3]=f(y[1], y[2], y[3], y[4])

(EQ4): y[4]=f(y[1], y[2], y[3], y[4])

The goal is to set-up an iterative process along the following lines:

Step 1: Set the values of y[1] through y[4] on the right-hand side (RHS) equal to 1 and calculate the respective values of y[1] through y[4] on the left-hand side (LHS). Store the latter LHS values as {y[1]^0, y[2]^0, y[3]^0, y[4]^0}.

Step 2: Substitute {y[1]^0, y[2]^0, y[3]^0, y[4]^0} on the RHS, update the LHS values and store those as {y[1]^1, y[2]^1, y[3]^1, y[4]^1}.

Iterate Step 2 until convergence (which should yield the exact same result as with solving numerically the above system of 4 equations using the fsolve(.) command). Importantly, I would like to "retrieve" the values of each variable y[k]^i at each iteration i, where k=1,2,3,4, and i=0,1,... and use them for further analysis. 

Iterative_solutionQ.mw

with your help i solved ODE for Elziki transform ...but now i am facing some issues for PDE...elziki transform is like laplace ...but having 1/v in product...if any one can solve pde for laplace ... then please help me out.pde_elziki.mw

I was tasked updating an old maple program (written +20 years ago using Maple version 3 I believe) and came across a line I'm unsure the meaning of. The line is: beta := [rhobar2$rowdim(A)]:

rhobar2 is the square of the mean of a data set and A is a Matrix with 3 columns and 12 rows. I'm just unsure what the $ operator is or is doing to the data. Any help would be appreciated. I'm new to this, sorry if this seems trivial.

hi, do you know how can we smooth this ellipse and make it more clear?

thickness, grid, numpoints don't help

restart;
with(plots);
f := (x, y) -> x^2 + y^2 - 12*x + 16*y;
display(plot3d(f(x, y), x = -9 .. 9, y = -9 .. 9), pointplot3d([[6, -8, f(6, -8)]], color = red, symbol = solidcircle, symbolsize = 18), view = [-4.2 .. 8.2, -8.2 .. 4.2, -100 .. 100], plot3d([cos(t), sin(t), 1 - 12*cos(t) + 15*sin(t)], t = 0 .. 2*Pi, orientation = [-15, 68, 5]));
 

Let (C):f(x)=1/(x^2-2x).Find the equation of the circle touching the graph  at three points?

Hi 

As the titel states: It is possible to create a asymptotic bode plot in maple?

I know how to do a normal bode plot with the DynamicSystem package. But is it possible to get a straight line approximation/ asymptotic bode plot instead?

I discovered the MRB constant (CMRB) while using Maple. Since then, I've found many formulas related to it, including its integrated analog the MKB constant (MKB). They're both found in Google scholar!

However, I am stuck on proving the following.

Also prove the above equation, ReMKB+NoMKB-CMRB=0.

All my similar proofs are found at

https://www.mapleprimes.com/posts/214522-Formulas-For-The-MRB-Constant?sp=214522

Dear Users!

Hope everything going find with you. I want to generate sequence of Spline[i,p], p=1…M as given bellow

restart; M := 3;
for p while p <= M do
(x-x[i])*B[i, p-1]/(x[i+p]-x[i])+(x[i+p+1]-x)*B[i+1, p-1]/(x[i+p+1]-x[i+1]);
B[i, p] := collect(%, [`$`(B[i+s, 0], s = 0 .. M)]);
B[i+1, p] := eval(%, i = i+1)
end do;
for p while p <= M do
Spline[i, p] := B[i, p]
end do

The expression for Spline[i,1] and Spline[i,2] are fine but the expressions of Spline [i,p] p>2 is not in simplified form I got the its simplification like given bellow for Spline[i,3]

Spline[i, 3]:=(x-x[i])^3*B[i, 0]/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+1]-x[i]))+(((x-x[i])*(x-x[i]))*(x[i+2]-x)/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+2]-x[i+1]))+(x-x[i])*(x[i+3]-x)*(x-x[i+1])/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1]))+(x[i+4]-x)*(x-x[i+1])^2/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1])))*B[i+1, 0]+((x-x[i])*(x[i+3]-x)^2/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+(x[i+4]-x)*(x-x[i+1])*(x[i+3]-x)/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+((x[i+4]-x)*(x[i+4]-x))*(x-x[i+2])/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+3]-x[i+2])))*B[i+2, 0]+(x[i+4]-x)^3*B[i+3, 0]/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+4]-x[i+3]));

I am waiting for positive respone. Please take care and thanks in advance

timelimit() has improved in Maple 2021, and I thought it works now for everything. 

https://www.mapleprimes.com/maplesoftblog/213986-Introducing-Maple-Learn-officially#comment204444

But unfortunately,, it still hangs on some dsolves when I was testing something. Here is an example

restart;
ode:=(y(x)^4-a^2*x^2)*diff(y(x),x)^2+2*a^2*x*y(x)*diff(y(x),x)+y(x)^2*(y(x)^2-a^2)=0;
timelimit(60,dsolve(ode,y(x)))

The above has one minute timeout. But its been running for 20 minutes now. Here is another example that hangs

restart;
ode:=(diff(y(x),x) = (-y(x)^2+4*a*x)^3/(-y(x)^2+4*a*x-1)/y(x));
timelimit(60,dsolve(ode,y(x)))

I have found many more dsolve examples that hang with timelimit. Will update later. May be they will help find the cause.

Hopefully this timelimit issue will be fixed in some future release.  hangs in Maple commands even when using timelimit makes it very hard to run long scripts that run over many problems, since do not know when/where it will hang and have to restart and clean things manually each time.

Window 10. Maple 2021

Update March 15,2022

Here is another example of timelimit taking so much longer than asking for, it is pretty much useless.

I will use this question to collect such examples in one place. Here I asked for one minute (60 seconds, CPU time) timeout. Maple actually timedout after using 1381 CPU seconds which is 23 times as much as requested.

Download timelimit_example_march_15_2022.mw

Help says

The timelimit function evaluates the expression x, but gives up if the evaluation takes longer than the number of seconds specified by t.
Note: In some cases, the execution may not abort at exactly the time limit imposed, but will abort as soon as it can do so safely.  This can happen when execution is in critical sections of certain built-in routines.

For me, the above makes no sense at all. What does "as soon as it can do safely"? I am not running the code to control an airplane flight full of people here. This is some code running on my PC at home to do some calculation. It can abort right away. It will not hurt me physically or hurt my PC to do so. 

So what does "do so safely" actually mean? Safety of what exactly?

Compare the above example to Mathematica where it times out at almost exactly to the requested timeout. Here I ask for 3 seconds timeout

I am not asking for exact timeout. But asking for 1 minute timeout and getting 8 minutes is not good at all.

1.5 minutes is OK. even 2 minutes is OK. 

I have more examples to add. But will do that later.

Update

Quick try with Maple 2022 shows timelimit has much improved. Here are 3 examples from above. First one asks for 60 seconds limit, it finishes in 288 seconds.   Second one asks for 60 seconds, it finishes in 96 seconds. Third one asks for 60 seconds and finishes in 73 second.

This is much much better than in Maple 2021. Thanks for the Maple engineers who improved this.

Download better_time_limit_with_maple_2022.mw