MaplePrimes Questions

When trying to construct objects like SU(3)xSU(2)xU(1), one needs parameters to satisfy SU(n,q)xSU(n,q)xU(n,q).  What are the values of 'q' for these group constructions using the group theory package?  

thanks

in Maple 2022.1 on windows 10

interface(version);

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1288 and is the same as the version installed in this computer, created 2022, August 6, 16:9 hours Pacific Time.`

restart;

int(x^5*(a+b*arctan(c*x^2))^2,x)

Error, (in gcdex) invalid arguments

 


Why it happens and is there a workaround?

Does it happen on earlier versions? I do not have an earlier Maple installed on my current PC as it is new to check. 

Download int_problem_8_10_2022.mw

When I use rsolve() to obtain the direct formula for calculating the mean `u` from its recursive definition:

u(n + 1) = u(n) + (x[n + 1] - u(n))/(n + 1)

u(1) = x[1]

and plug it into rsolve() then I receive the output:

rsolve({ u(n + 1) = u(n) + (x[n + 1] - u(n))/(n + 1), u(1) = x[1]}, u(n))

which is correct, but I would like to see it further simplified to:

sum(x[n1], n1 = 1 .. n)/n

Further calls to simplify() don't achieve this. Is there a way to do this, or did I hit some kind of limitation of rsolve() and is this as good as can be expected?

Thanks!

I want to change the output of the mtaylor command, eg for 3 series terms

ftaylor:=mtaylor(f(x,y),[x,y],3);

gives

ftaylor := f(0,0)+D[1](f)(0,0)*x+D[2](f)(0,0)*y+1/2*D[1,1](f)(0,0)*x^2+D[1,2](f)(0,0)*x*y+1/2*D[2,2](f)(0,0)*y^2;

I want the output as ftaylor := g(x,y) + D[1](g(x,y)) *x + D[2](g(x,y))*y + .... etc for all the terms in ftaylor.

Later on g(x,y) can be defined and terms like D[1](g(x,y)) evaluated.

I tried

subs(f(0,0)=g(x,y),ftaylor);

but it doesn't work. Using eval doesn't work either.

Is there a way to do this?

Thank you in advance.

I want to modify the code such that it works with

with(LinearAlgebra);
with(VectorCalculus);

How to do that? What is radical? 

with(linalg);
readlib(coeftayl);
A := matrix(2, 2, [0, a, b, 0]);
v := eigenvects(map(eval, A), 'radical');
q := ev[1][3][1];
et := eigenvects(map(eval, transpose(A)), 'radical');
P := et[2][3][1];

The maple did not give output

Question.mw

A simple tutorial task on optimization from one of the forums. We need to find the minimum of the function 
g1 = (x1-x2)*(x2-x3)*(x3-x4)*(x4-x1) with the following constraint g2 = x1^2+x2^2+x3^2+x4^2-1
It reduces to solving polynomial equations.  
Minimum = - 0.25. It's  solution:
[x1 = .683012702, x2 = .183012702, x3 = -.183012702, x4 = -.683012702],
[x1 = .183012702, x2 = .683012702, x3 = -.683012702, x4 = -.183012702],
[x1 = -.183012702, x2 = .183012702, x3 = .683012702, x4 = -.683012702],
[x1 = -.683012702, x2 = .683012702, x3 = .183012702, x4 = -.183012702],
[[x1 = .683012702, x2 = -.683012702, x3 = -.183012702, x4 = .183012702],
[x1 = .183012702, x2 = -.183012702, x3 = -.683012702, x4 = .683012702],
[x1 = -.183012702, x2 = -.683012702, x3 = .683012702, x4 = .183012702],
[x1 = -.683012702, x2 = -.183012702, x3 = .183012702, x4 = .683012702]
when x5 =0 .25

But so far I have not found an easy way to solve it using Maple. First we need to be able to successfully use fsolve, and only then "polynomial" functions.

restart; with(RootFinding):
g1 := (x1-x2)*(x2-x3)*(x3-x4)*(x4-x1); 
g2 := x1^2+x2^2+x3^2+x4^2-1;
 g :=g1+x5*g2; 
f1 := diff(g, x1); 
f2 := diff(g, x2); 
f3 := diff(g, x3); 
f4 := diff(g, x4); 
f5 := diff(g, x5); 
#solve([f1, f2, f3, f4, f5], [x1, x2, x3, x4, x5]);
Isolate([f1, f2, f3, f4, f5], [x1, x2, x3, x4, x5]); 
S := fsolve([f1, f2, f3, f4, f5], {x1, x2, x3, x4, x5}, maxsols = 8); 
x5 := rhs(op(5, S));
Isolate([f1, f2, f3, f4], [x1, x2, x3, x4]); 
solve([f1, f2, f3, f4], [x1, x2, x3, x4])

The optimization package doesn't help much either.
The task itself is of no interest, it is interesting to look at its simplest solution in Maple.
(By the way, Draghilev's method works well, but, of course, this is not the easiest way).

Hellow maple users, I am getting an error while solving system of differential equations analytically. Please help to recify the error. Thanks in advance. Here is my codes;

restart:
with(DETools):
# S, N  are constant
Eq1:=diff(u(y),y,y)-u(y)=C(y):
Eq2:=diff(T(y),y,y)=u(y)-diff(u(y),y)^2-u(y)^2+S*T(y)+N*T(y):
Eq3:=diff(C(y),y,y)-C(y)=0:
desys:={Eq1,Eq2,Eq3};ics:={u(0)=0,D(u)(0)=h,T(1)=h,D(T)(0)=0,C(1)=h,D(C)(0)=0}:
combine(dsolve(desys union ics,{u(y),T(y),C(y)}));

Dear all

How can I solve the system of equations with unknowns  c[2] and Z

system_eqs.mw

Maybe the question can be solved by hand.

thanks

Hello Everyone;

Hope you are fine. I need to solve the system of equation. I am using fsolve command but it is not working. Kindly guide me.

Thanks

ques.mw

restart

``

``

Eq[0, 0] := 1.33120000000000000000000000000*lambda[0, 1]+1.33120000000000000000000000000*lambda[0, 2]+1.33120000000000000000000000000*lambda[0, 3]+1.33120000000000000000000000000*lambda[0, 4] = .916487142969312002551492271668:

Eq[0, 1] := 1.32901933598375616624661615670*lambda[0, 1]+1.32901933598375616624661615670*lambda[0, 2]+1.32901933598375616624661615670*lambda[0, 3]+1.32901933598375616624661615670*lambda[0, 4] = 1.09232395220587507357427365904:

Eq[0, 2] := 1.37120000000000000000000000000*lambda[0, 1]+1.37120000000000000000000000000*lambda[0, 2]+1.37120000000000000000000000000*lambda[0, 3]+1.37120000000000000000000000000*lambda[0, 4] = 1.25415129307905065856083635281:

Eq[0, 3] := .966980664016243833753383843299*lambda[0, 1]+.966980664016243833753383843299*lambda[0, 2]+.966980664016243833753383843299*lambda[0, 3]+.966980664016243833753383843299*lambda[0, 4] = 1.37114174964252179339832329224:

``

``

fsolve({seq(Eq[0, ii1], ii1 = 0 .. 3)});

fsolve({.966980664016243833753383843299*lambda[0, 1]+.966980664016243833753383843299*lambda[0, 2]+.966980664016243833753383843299*lambda[0, 3]+.966980664016243833753383843299*lambda[0, 4] = 1.37114174964252179339832329224, 1.32901933598375616624661615670*lambda[0, 1]+1.32901933598375616624661615670*lambda[0, 2]+1.32901933598375616624661615670*lambda[0, 3]+1.32901933598375616624661615670*lambda[0, 4] = 1.09232395220587507357427365904, 1.33120000000000000000000000000*lambda[0, 1]+1.33120000000000000000000000000*lambda[0, 2]+1.33120000000000000000000000000*lambda[0, 3]+1.33120000000000000000000000000*lambda[0, 4] = .916487142969312002551492271668, 1.37120000000000000000000000000*lambda[0, 1]+1.37120000000000000000000000000*lambda[0, 2]+1.37120000000000000000000000000*lambda[0, 3]+1.37120000000000000000000000000*lambda[0, 4] = 1.25415129307905065856083635281}, {lambda[0, 1], lambda[0, 2], lambda[0, 3], lambda[0, 4]})

(1)

``

``

Download ques.mw

Fitting procedures in Maple are self explaning and easy to perform. However, I was wondering if it is possible to fit data vectors with units. For example one vector would have units of seconds and the other units of length. Thank you for your help.

Is there any command that allows me to extract the input number of any function f?

exmple:

f: (x1; x2;...;xn)-> y

command (f)=n

thanks for the help!

I have string of length

StringTools:-Length(str);
                            1073105

When doing

p:=StringTools:-LengthSplit(str,100):

Maple gives

 

From help:

LengthSplit
split a string into equal length pieces

 

This is all done in .mpl  file actually, not interactive, but I made the above worksheet to show  the problem. The string is read from a file by a program and it wants to split it to 100 length smaller strings.

I have lots of RAM. 128 GB.  So why does Maple crash and is there a workaround this?

This string was generated by another software.

I have attached the above example below as worksheet.  Maple 2022.1 on windows 10.

Here is a simpler way to generate this problem

restart;
str:=StringTools:-Random(1073104,'upper'):
str[1..10];

StringTools:-Length(str);
p:=StringTools:-LengthSplit(str,100):

 

Using trial and error, the crash happens when the length reaches 1073101. At 1073100 there was no crash.

 

 

I need to define a simple recursive algorithm (i'm not a programmer) such that:

xi=xi-1+b 

 

with i=0,1,...,n; 

and with all xi's elements of a Set A

how can i achieve this?

I have some expressions like 3%/5 and would like to get the numerator and denominators numer(3%/5) does not return 3.

I cannot evaluate it since it might reduce the fraction which will make my results invalid.

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