MaplePrimes Questions

I do not know if this caused by same crash in Reproducible--Server-Crash-Kernel-Connection-Has-Been-Lost  or not.

Could someone be able to find out? It happens each time the code is run on windows 10. 

 

26028

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715 and is the same as the version installed in this computer, created 2024, April 3, 20:27 hours Pacific Time.`

restart;

10168

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);


Download another_server_crash_on_int_maple_2024_april_4_2024.mw

ps. reported to Maplesoft.

The above is new crash in Maple 2024. Below shows no crash in Maple 2023:

26028

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715. The version installed in this computer is 1672 created 2024, February 7, 18:34 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

restart;

23104

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);

int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

 

 

Download int_on_maple_2023.mw

Update:

Here is a movie showing the crash. It also happens from the command line. All on windows 10.

My ini file has  nothing in it, other than one command which prints the process ID which I had there for over a year now.  This is after restarting Maple fresh and nothing else running other than this one worksheet.

 

Here is movie showing the crash from command line also. On windows 10 pro.

 

 

Absolute beginner here - please bear with me.

I would like to generate an 81 rows x 24 columns table from three nested "for" loops. I would like each entry of this table to be a list of 4 numbers. My code (which does not work) is as follows:

local M, templist;
for i to 81 do
    for j to 24 do
        for k to 4 do
        M[i][j]:=[op(templist[k]), indice(C[i][1][k],rorder(orders[j],Sets[k]));];
        end do;
    end do;
end do;

In the above "indice" is a procedure that works fine and returns a number, and it works fine.

I would like the 4 numbers that are generated by the k loop to be stringed together into a list, so i thought I could use the temporary list "templist" to append to it the 4 numbers, which would then become the entry in row i and column j of matrix M, but it does not work, and instead I get a table of 81 tables. So for instance the first of these 81 tables is:

1 = table([1 = [4, 1], 2 = [4, 1], 3 = [4, 2], 4 = [4, 3], 5 = [4, 2], 6 = [4, 3], 7 = [4, 1], 9 = [4, 1], 8 = [4, 1], 11 = [4, 1], 10 = [4, 1], 13 = [4, 2], 12 = [4, 1], 15 = [4, 2], 14 = [4, 3], 18 = [4, 3], 19 = [4, 2], 16 = [4, 2], 17 = [4, 3], 22 = [4, 2], 23 = [4, 3], 20 = [4, 3], 21 = [4, 2], 24 = [4, 3]])

and I only have 2 values in each list, rather then the 4 I am after.

If I declare M as a 81x24 matrix, I get retunred a matrix of zeroes. Where am I going wrong?

If anyone could lend a hand, I'd be forever grateful. Thank you!

I just discoverd today the step solutions for series in Student package 

Now i try to solve this with my own steps here ..

Note: SummationSteps(Sum(1/n^2, n = 1 .. infinity))was not capable to get a closed form?

"maple.ini in users"

(1)

NULL

Euler's Basel Problem
In the Student Basics package, there is a command :

 

SummationSteps

generate steps for evaluating summations

NULL

help("SummationSteps")

The SummationSteps command accepts an expression that is expected to contain summations and displays the steps required to evaluate each summation given.

2024

with(Student[Basics])

 

" restart; with(Student[Basics])"

"maple.ini in users"

 

[CompleteSquareSteps, CurveSketchSteps, ExpandSteps, FactorSteps, FractionSteps, GCDSteps, LCMSteps, LinearSolveSteps, LongDivision, ModuloSteps, OutputStepsRecord, PartialFractionSteps, PowerSteps, PracticeSheet, SimplifySteps, SolveSteps, SummationSteps, TrigSteps]

(2)

Try this out this SummationStepscommand for the Basel problem series  ( p-series example)

SummationSteps(Sum(1/n, n = 1 .. infinity))

"[[,,[]],["&bullet;",,"Apply the P-test on" (1)/(n)", which shows the summation diverges if" p<=1 "for" (&sum;)1/((n)^p)],[,,p=1],["&bullet;",,"Since" 0<1 "and" 1<=1", we get that the summation diverges"],[,,([[(&sum;)(1)/(n)" diverges"]])],["&bullet;",,"We know the summation diverges, so now we should find what it diverges to"],[,,[]],["&bullet;",,"Evaluate sum" (&sum;)1/n],[,,infinity]]"

(3)

Now the Basel Problem from Euler

SummationSteps(Sum(1/n^2, n = 1 .. infinity))

"[[,,[]],["&bullet;",,"Apply the P-test on" (n)^(-2)", which shows the summation diverges if" p<=1 "for" (&sum;)1/((n)^p)],[,,p=2],["&bullet;",,"Since" 1<2", we get that the summation converges"],[,,([[(&sum;)(n)^(-2)" converges"]])]]"

(4)

f := sum(1/n^2, n = 1 .. infinity)

(1/6)*Pi^2

(5)

How do we get this value from Euler ( The Basel Problem)

# Step 1: Define the series f
f := sum(1/n^2, n = 1 .. infinity);

# Step 2: Write the series as a product of terms (1 - 1/p)
g := convert(product(1 - 1/p, p = primes), hypergeom);

# Step 3: Compare with the Taylor series of the sine function
h := series(sin(x), x = 0, 10);

# Step 4: Set up equations between corresponding terms
eq := seq(coeff(h, x, 2*k)/k!, k = 1 .. 5) =
      seq(coeff(g, x, k), k = 1 .. 5);

# Step 5: Solve the equations to find the value of the series
sol := solve({eq, seq(coeff(g, x, k) = 0, k = 6 .. 10)});

# Step 6: Replace x with pi/2 to find the value
sol_pi := subs(x = Pi/2, sol);

# Step 7: Compute the value of the series
value := sol_pi[1][2];

value;

(1/6)*Pi^2

 

1-1/primes

 

series(x-(1/6)*x^3+(1/120)*x^5-(1/5040)*x^7+(1/362880)*x^9+O(x^11),x,11)

 

(0, 0, 0, 0, 0) = (0, 0, 0, 0, 0)

 

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, rtable, algebraic, relation(algebraic), relation({rtable, algebraic}), {list, set}({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {0 = 0, (0, 0, 0, 0, 0) = (0, 0, 0, 0, 0)}

 

sol

 

Error, attempting to assign to `value` which is protected.  Try declaring `local value`; see ?protect for details.

 

value

(6)

NULL

Download Het_Basel_Probleem_van_Euler.mw

1.mw.....can anyone hlep to sovle this equation...for omega(t)...
(-limit((1 - omega)^(k + 2), omega = 1, left) + 1)/(k + 2) = C*int((1 - `&sigma;_a`*sin(2*pi*N))^k, N = 0 .. N)...in solution..integral didn't get rid

This is for my understanding (and the proper use of Maple terms)

?simplify refers to them (sqrt in this case) as procedures

simplify[sqrt](16^(3/2));
                               64

`simplify/sqrt`(16^(3/2));
                               64

simplify(16^(3/2), sqrt);
                               64

?combine calls them (this time exp and trig) names of options

combine(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)),[trig,exp]);#why the list?
                        exp(sin(a + b))

combine(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)),trig,exp);#no list
                        exp(sin(a + b))

combine[trig](exp(sin(a)*cos(b))*exp(cos(a)*sin(b)));#no exp required?!?
                        exp(sin(a + b))

(`combine/exp`@`combine/trig`)(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)));
                        exp(sin(a + b))

If the terms command options and command procedures can be used interchangeably, how does evalf[4](...) fit into this scheme? 

Is there a special Maple term for the construct "proc[n]" where proc is a procedure/command name and n is not a name but of type numeric?

@ecterrab

Fetching package "Physics Updates" from MapleCloud...

ID: 5137472255164416
Version: 1713
URL: https://maple.cloud

An error occurred, the package was not installed:
Could not open workbook: /tmp/cloudDownload3108059082303936092/Physics Updates_1712064079729.maple

 

Same problem on Maple 2024 for Windows and Linux!!!

Hi,

I am trying to generate a plot using a procedure. A dummy code is as follows:

***

fun := piecewise(x+y > 1, (x+y)^2, x-y);

temp_proc := proc(x, y)
local out, ind:

ind := 9:

if x > y then ind := 1 else ind := 0 end if; 

if ind = 1 then out := eval(5*fun, {:-x=x, :-y=y}) else out := eval(-5*fun, {:-x=x, :-y=y}) end if:

return(out);
end proc:

xt := 5: yt := 2:
out1_fin := temp_proc(xt, yt);

plot(out1_fin, z=-2..3);
 

***

The issue is as follows:

1. I am getting an error message for the code above: "Error, (in temp_proc) cannot determine if this expression is true or false: 2 < z".

2. The entire procedure and the plot command work well for a fixed "z". However, it is not useful for me as I am looking for a plot for various values of z. 

3. I hope I don't have to run the procedure by manually creating a list of z and then plotting the lists of z and out1_fin. 

4. I am using the "ind" variable because it simplifies my actual code, which involves multiple conditions defining the function "fun" that I need to plot. 

I would appreciate your input on how to resolve the issue. 

Regards,

Omkar

 

I am unable to change the font on the Palette menus or the pop up context boxes.

It is very frustrating, as I can hardly read them.

I am not sure if it is a computer setting or a Maple setting.

Any help would be appreciated

The following is a simple example of what I would like to do: 

M := Array(1 .. 10, 1 .. 2);

for i to 10 do
    M[i, 1] := i;
    M[i, 2] := 3*i;
end do;

Mt := Interpolation:-LinearInterpolation(M);
E := t -> Mt(t);
diffeq := D(C)(t) = E(t);
dsolve({diffeq, C(0) = 0}, {C(t)}, numeric);
Error, (in dsolve/numeric/process_input) unknown Interpolation:-LinearInterpolation([Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]))])],Vector(10, [3.,6.,9.,12.,15.,18.,21.,24.,27.,30.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]),uniform = true,verify = false) present in ODE system is not a specified dependent variable or evaluatable procedure

Hi, 
I am struggling with the output of a procedure. A dummy code is as follows:

*****

fun := x^2+y^2;

temp_proc := proc(x, y)
local out1, out2, out3:

if x > 0 then out1 := fun; out2 := 2*fun; out3 := k*fun;
elif x <= 0 then out1 := fun; out2 := -2*fun; out3 := -k*fun;
end if:

return(out1, out2, out3);
end proc:

xt := -1: yt := 2:
out1_fin := temp_proc(xt, yt)[1];
out2_fin := temp_proc(xt, yt)[2];
out3_fin := temp_proc(xt, yt)[3];


*****

xt and yt are numerical input parameters. I expect to obtain "out1_fin" and "out2_fin" in numerical form and "out3_fin" in symbolic form. All three outputs should substitute xt and yt for x and y, respectively, wherever relevant. 

However, currently, the output I am getting is not after substituting the values of xy and yt. The output is as follows:

*****

out1_fin := x^2+y^2

out2_fin := -2*x^2-2*y^2          

out3_fin := -k*(x^2+y^2)

*****

May I get some help in resolving the issue? 

Also, would a procedure be a good idea for this task, or would a module be better? 

I would appreciate any guidance in this regard. Thank you. 

Regards,

Omkar

I keep getting an error: invalid subscript selector on specifically this part of my code:

MuligIndgange := subsop(RemoveList\[i\]=NULL, MuligIndgange).
Whenever I comment out the MuligIndgange := part it works.

I can't for the life of me see why it's happening, and whenever I use this code outside my proc it works aswell.

Any help is appreciated, and if you need more context I'll be happy to give it.

for i to numelems(MuligIndgange) do
     if M1[MuligIndgange[i][1], MuligIndgange[i][2]] =/= 0 then
         RemoveList := [op(RemoveList), i];
      end if;
end do;
for i from numelems(RemoveList) by -1 to 1 do
    MuligIndgange := subsop(RemoveList[i] = NULL, MuligIndgange);
end do;

When I use evala(Minpoly(sqrt(3) + sqrt(2), x)), then I get a right answer: x^4 - 10*x^2 + 1

But when I want to get the minimal polynomial of cos((2*Pi)/7) by evala(Minpoly(cos((2*Pi)/7), x)), I will get a result:

x - cos((2*Pi)/7)

It clearly does not follow the definition of a minimal polynomial. Is it a bug of Minpoly or I have missed something?

Question 1
Let theta a real number in the range 0..2*Pi.
Is there a way to "convert" 

f := theta -> arccos(cos(theta))+arcsin(sin(theta))

into 

f1 := theta -> piecewise(theta < 0, 0, theta < (1/2)*Pi, 2*theta, theta < Pi, Pi, theta <= (3/2)*Pi, 3*Pi-2*theta, 0)


Question 2
As f1 is  2*Pi periodic, is there a way to convert f into a periodic function where the "pattern" is f1(theta)?
To be clearer I thought to something close to what we get when we do this

solve(cos(x)=1, allsolutions);
                            2 Pi _Z2 
about(_Z1);
Originally _Z1, renamed _Z1~:
  is assumed to be: integer

and I imagined 

Some_Transformation(f(theta))
    f1(theta+2*Pi*_Z1~)
about(_Z1); 
Originally _Z1, renamed _Z1~: 
  is assumed to be: integer

For the moment I build the periodized f1 this way

f2 := (theta, K) -> int(f1(theta-z)*add(Dirac(z-2*Pi*k), k=-K..K), z=-infinity..+infinity);
# or
f2 := (theta, K) -> sum(int(f1(theta-z)*Dirac(z-2*Pi*k), z=-infinity..+infinity), k=-K..K);

Thanks in advance.

How do I solve the problem below using maple commands? I'm having trouble finding the commands and believe my answer is incorrect. I am currentley on maple 2022. 
How would I find an equation of the line tangent to the graph of f(x) when x =3?
f(x)= (1-kx)/(1+x^2)
f := x -> x^2 + 2*x + 1;

Thank you.

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