MaplePrimes Questions

Using allvalues (twice) I can uncover the three roots of this expression: 1 real, 2 complex. But fsolve gives me just one real and 1 complex. Interestingly the free version of Woldframalpha.com gives the same single complex root.

Is there any way of coercing fsolve to give both?

Many thanks for any advice

Fsolve5.mw
 

 

Examples of the fsolve command: not all complex roots found

restart

expr := exp(x)+sin(x)-2

exp(x)+sin(x)-2

(1)

w := solve(expr)

RootOf(_Z-ln(-sin(_Z)+2))

(2)

w1 := evalf(allvalues(w))

.4486719164

(3)

w2 := allvalues(w)

RootOf(_Z-ln(-sin(_Z)+2), .4486719164), RootOf(_Z-ln(-sin(_Z)+2), 1.837819685+2.792964964*I), RootOf(_Z-ln(-sin(_Z)+2), -4.707337346-1.315656030*I)

(4)

q0 := evalf(w2[1])

.4486719164

(5)

q1 := evalf(w2[2])

1.837819685+2.792964964*I

(6)

q2 := evalf(w2[3])

-4.707337346-1.315656030*I

(7)

eval(expr, x = q0); eval(expr, x = q1); eval(expr, x = q2)

0.

 

0.1e-8+0.1e-8*I

 

0.-0.786e-9*I

(8)

r1 := fsolve(expr)

.4486719164

(9)

r2 := fsolve(expr, complex)

1.837819685+2.792964964*I

(10)

NULL

``


 

Download Fsolve5.mw

 

What is the simplest method for adding a color bar for plottings? (a scale that shows the correspondence 
between numbers and colors)

and could you interpret the graphics and the color bar?  I need your valuable comments.


I use Maple 2018.

For example;  

question.mw

I mean

Hello Everyone,

First of all I want to thank you to pay attention to my post.

For some reasons I want to know when does the root of my solution is equal to 0 isolating α, which yields the following equation
 

(6*alpha^4*l^2-7*alpha^3*l^2+6*alpha^3*l+2*alpha^2*l^2-6*alpha^2*l+alpha*l+3*alpha-2*sqrt(alpha^3*l^2*(alpha*l-l+1)*(9*alpha^4*l-13*alpha^3*l+9*alpha^3+6*alpha^2*l-12*alpha^2-alpha*l+6*alpha-1))-1)*(-1+2*alpha)/(alpha^2*l-3*alpha+1)^2 = 0
``

  1/2, -1/l, (1/8)*(3*l+(9*l^2-16*l)^(1/2))/l, -(1/8)*(-3*l+(9*l^2-16*l)^(1/2))/l``

``

NULL

 

NULL

``

 

 

When I substitute 1/2 it verifies the equation, but when I substitute other solutions my equation is not verified. For instance substituting "α=-1/l" I get something different from 0 as you can see

``

``

(6*alpha^4*l^2-7*alpha^3*l^2+6*alpha^3*l+2*alpha^2*l^2-6*alpha^2*l+alpha*l+3*alpha-2*sqrt(alpha^3*l^2*(alpha*l-l+1)*(9*alpha^4*l-13*alpha^3*l+9*alpha^3+6*alpha^2*l-12*alpha^2-alpha*l+6*alpha-1))-1)*(2*alpha-1)/(alpha^2*l-3*alpha+1)^2
"(->)"(-2/l-2*(1/l^2)^(1/2))*(-2/l-1)/(4/l+1)^2"(=)"2*((1/l^2)^(1/2)*l+1)*(2+l)/(4+l)^2

``

My question is what are these "solutions" if they are not solutions ?

I attach the file in case you would take a look at it

Download Maple_question2.mw

This code used to work OK in an earlier version of Maple 2018. I do not know what changed and if it some change in Physics package that caused it.

restart;
pde:=diff(u(r,theta),r$2)+1/r*diff(u(r,theta),r)+1/r^2*diff(u(r,theta),theta$2)=0;
bc:=u(r,0)=0,u(r,Pi)=0,u(0,theta)=0,u(1,theta)=f(theta);
sol:=pdsolve([pde,bc],u(r,theta),HINT = boundedseries(r = 0));

Now it gives the error 

Error, (in assuming) when calling 'assume'. Received: 'invalid arguments'

Workaround is to remove the HINT above. So the following now works

restart;
pde:=diff(u(r,theta),r$2)+1/r*diff(u(r,theta),r)+1/r^2*diff(u(r,theta),theta$2)=0;
bc:=u(r,0)=0,u(r,Pi)=0,u(0,theta)=0,u(1,theta)=f(theta);
sol:=pdsolve([pde,bc],u(r,theta));

Should this error message show up when using the HINT option?

Maple 2018.2 with Physics package cloud version 205.

Here is screen shot showing it was working in Physics 170

 

How can I calculate the Euler-Lagrange equation from the Lagrangian density from Gauged Baby Skyrme model in maple using the physics package? Here, the rules of the operation in the inner space are the same that of the vectors conventional: dot and cross products, etc...
Following below the Lagrangian density.

Errata:

Hello everyone!
Can you help me with my problem?
How can I automatically paste parts of denominator from one equations to another? Now I must do this manualy. Example of my problem is in file2.

File_2.mw

Hello! 

I have system of equations to solve. It has 118 equations and all variables have to be binary. I know for that system that the minial number for x=1 is 32 (I cheked it in solution chapter at the end of the book) but I always get 33 of ones. I changed MaxSols=500 and still got 33. If I change MaxSols to some bigger number the time for calculation is larger and I still don't get the correct solution. Is there any faster way to do this?

I'm thinking (but I don't know how to do in Maple): Is there any way to show solutions only with number of ones in interval, for example 30 to 33.

try1.mw

I have a question about Hilbert Series of the quotient of an algebra by a non-homogenous ideal. 

In maple help: https://www.maplesoft.com/support/help/maple/view.aspx?path=Groebner%2FHilbertSeries, it is said that 

The algorithms for HilbertSeries and HilbertPolynomial use the leading monomials of a total degree Groebner basis for J. Here J is an ideal.

I checked the following example. Let 

J:= [(x[2]-x[1])*(x[2]-x[3]), (x[4]-x[1])*(-x[5]+x[4]), (x[4]-x[2])*(x[4]-x[6]), (-x[3]+x[5])*(x[5]-x[6]), x[1]^3-1, x[2]^3-1, x[3]^3-1, x[4]^3-1, x[5]^3-1, x[6]^3-1];

and

t1:=map(LeadingMonomial, l, grlex(x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12]));

Then t1 is the ideal generated by the following monomials.
t1 := [x[1]*x[2], x[1]*x[4], x[2]*x[4], x[3]*x[5], x[1]^3, x[2]^3, x[3]^3, x[4]^3, x[5]^3, x[6]^3]

Using the commands:

l2:={x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[11],x[12]};

factor(HilbertSeries(J, l2, t));

factor(HilbertSeries(t1, l2, t));

We obtain Hilbert(J,t)=(t^2+t+1)*(5*t^4+11*t^3+11*t^2+5*t+1)
Hilbert(t1, t) = (t^2+t+1)*(3*t^2+3*t+1)*(2*t^2+2*t+1)

These two polynomials are not equal. How does maple compute Hilbert Series for the quotient of an algebra by a non-homogenous ideal? Thank you very much.

 

 


 

Is there any way to integrate this in maple?

lambda^2*t*(diff(theta(t), t, t)) = lambda^2*(diff(theta(t), t))-Pr*s*lambda*(diff(theta(t), t))+Pr*(diff(theta(t), t))-Pr*t*(diff(theta(t), t))

 

If I used factor, it didn't simplify to 0. As you may notice that this value should be 0.

Hello!

I need help, because I can't find solution.
How can I export data from Bode Plot to Excel? Two below solutions don't work.

 

with(DynamicSystems);

T2 := TransferFunction((1.224867518*10^(-7)*s+2.259345677*10^(-6))/(s^2+11.83692270*s+238.3951363)):

BP2 := BodePlot(T2);

with(ExcelTools);
ExcelTools:-Export(op([1, 1], BP2));

Export(BP2, "Employees13.xls", "Payroll1", "B2");
 

File_1.mw

Never really used the writeto command but what's with all the typesetting gobbledygook in the text file?  It occurs with document and worksheet mode.  Perhaps it's only meant for classic or command line maple?

Is there a way to log the terminal output to a .txt file?

Dear all

Trying to plot this expresion

f := epsilon-1.5+9.3*I = (a+I*b)*(26.+I*(-45.-1.0*Re(a+I*b)^2-1.0*Im(a+I*b)^2))

implicitplot (a^2+b^2) against epsilon

many thanks

I am trying to solve a linear system involving large number of equations with constant coefficients using Solve command from the LinearAlgebra package. The maple program is giving solutions for a smaller number of equations (T=10,Ne=20,Ng=15). But if I increase the number of equations to (T=20,Ne=30, Ng=25), then I got the error kernel connection has been lost. I need to increase the number of equations beyond this also. Any help to simplify the code or finding errors is appreciated.

solntosystem.mw

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