MaplePrimes Questions

The computer on which I have been executing Maple worksheets for the past six years (CPU: i7 - 5820K, 6 core, 3.3 GHz, 5th generation) is now significantly slower than new machines.

I don't know how to interpret public specifications of potential replacement machines into their actual future performance with Maple.

Please give me or direct me to any advice which would enable me to knowledgeably purchase a much faster processor of Maple code.

 

Hello there, 

Is there any chance to see that the 'eq_5_22_desired' expression shown below can be derived from a collection of the commands. similar to what's given in the 'eq_5_22a'? In other words, is it possible to make Maple aware of the point that 'L__ad/(L__ad + L__fd)' can be interpreted as 'L__ad*L__fd/(L__ad + L__fd) * 1/L__fd'?

restart;

with(LinearAlgebra):

interface(imaginaryunit=j):

eq_5_22 := Psi__ad = -L__ad*L__fd*i__d*1/(L__ad + L__fd) + L__ad*Psi__fd*1/(L__ad + L__fd);

Psi__ad = -L__ad*L__fd*i__d/(L__ad+L__fd)+L__ad*Psi__fd/(L__ad+L__fd)

(1)

eq_5_23x := L__ad__p = 1 / (1/L__ad + 1/L__fd);

L__ad__p = 1/(1/L__ad+1/L__fd)

(2)

eq_5_23 := L__ad__p = evala(rhs(eq_5_23x));

L__ad__p = L__ad*L__fd/(L__ad+L__fd)

(3)

eq_5_22a := Psi__ad = collect(expand(solve(eq_5_18x, Psi__ad)), rhs(eq_5_23)); # error

Error, invalid input: expand expects 1 argument, but received 0

 

eq_5_22_desired := Psi__ad = -L__ad__p*i__d + L__ad__p*Psi__fd/L__fd;

Psi__ad = -L__ad__p*i__d+L__ad__p*Psi__fd/L__fd

(4)

 

Download Q20220812.mw


 

restart;

assume(alpha>0)

assume(delta:: real)

assume(C>0)

 

f:= g->e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(g*(1-g^2));

proc (g) options operator, arrow; e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(g*(1-g^2)) end proc

(1)

convert(1/(g*(1-g^2)),parfrac,g);

-(1/2)/(g+1)+1/g-(1/2)/(g-1)

(2)

f1:= g->-e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(2*(g+1));

proc (g) options operator, arrow; -e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(2*g+2) end proc

(3)

f2 := g->e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/g;

proc (g) options operator, arrow; e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/g end proc

(4)

f3:= g->-e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(2*(g-1));

proc (g) options operator, arrow; -e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(2*g-2) end proc

(5)

int(f1(g),g=0..infinity);

int(-e^(-(1/2)*C^2*g^2*(-g^2+1)^2*(delta^2+1)-C*g*(-g^2+1)*alpha)/(2*g+2), g = 0 .. infinity)

(6)

 


 

Download 2022_integralIandJ.mw

I do not know why eq(6) does not evaluate. Could you help me?

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!

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