Advanced Search

Aixleft math

120 Reputation

5 Badges

1 years, 35 days
Singapore
Contact Aixleft math

MaplePrimes Activity


These are replies submitted by Aixleft math

Thanks!...

Aixleft math 120
September 10 2024
0 0

@mmcdara Thanks for your reply! 

Thanks!...

Aixleft math 120
September 09 2024
0 0

@mmcdara Also thanks for the website you provide! it is very valuable!

Thanks!...

Aixleft math 120
September 09 2024
0 0

@nm I appreciate your answer, it's exactly what I needed.

Thanks!...

Aixleft math 120
August 27 2024
0 0

@Carl Love No wonder! This is a low-level mistake for me. Thanks for your remind!

Thanks you!...

Aixleft math 120
July 29 2024
0 0

@mmcdara Thanks you for patient answer! I just notice this reply lately!

Thanks!...

Aixleft math 120
July 26 2024
0 0

@dharr Thanks! it works! Thanks for your answer!

Thanks!...

Aixleft math 120
July 10 2024
0 0

@dharr Thanks for your reply! it seems that drawing such a large number of complex expressions must be slow.

this is the smart plot file...

Aixleft math 120
July 10 2024
0 0

This the file that I trigger the smartplot. It did meet up with my desired outcome. And I try the builderplot, try to get the 3d contour of the eq11, but no use (maple said cannot analyse the expression). I have searched the good post about contour plot in mapleprime, but they don't fit this issue cause after I add the command based on the smartplot, the smartplot didn't work. Also, the implicit 3d command is also 25mins evaluating no end.

Download 3D_smart_plot.mw

Thanks!...

Aixleft math 120
July 09 2024
0 0

@mmcdara Thanks for your valuable answer! I learn much more. So I just reckon that Maple can do anything if I give the correct command, but the fact is not .

cannot solve the expression to get the e...

Aixleft math 120
July 08 2024
0 0

@mmcdara  Really thanks for your modification such that I can do more about the eigenvalues. On the basis of your code, I wanna solve the range of which eigenvalues is less than 1. But my maple has beening running for 15mins and no outcome. But this command for solving eigenvalues is ok before for Taylor expansion. Maybe this time is not suitable for the new expression?evalf_the_value_of_eigenvalues.mw

> 

restart;
csgn(v)=1;

csgn(v) = 1

 (1)
> 

with(LinearAlgebra):
> 

A := Matrix([[0, 0, 0], [-(cos(alpha*v)-1)/v^2, 0, 0], [0, -(cos(beta*v)-1)/(cos(alpha*v)*v^2), 0]]):
> 

C := Matrix([0, alpha, -beta]):
> 

e := Vector(3, 1):
> 

E := IdentityMatrix(3):
> 

G := Matrix([[0], [sin(alpha*v)/(alpha*v)], [((sin(beta*v)*cos(alpha*v)+sin(alpha*v)*cos(beta*v)-sin(alpha*v)))/(v*cos(alpha*v)*(beta))]]):
> 

b := Vector(3, [1/24, (-sin(beta*v)*v^3+12*cos(beta*v)*v^2+24*cos(beta*v)*cos(v)-24*sin(beta*v)*sin(v)+24*sin(beta*v)*v-24*cos(beta*v))/(24*v^3*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v))), -(sin(alpha*v)*v^3+12*cos(alpha*v)*v^2+24*cos(v)*cos(alpha*v)+24*sin(v)*sin(alpha*v)-24*v*sin(alpha*v)-24*cos(alpha*v))/(24*v^3*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v)))]):
> 

bp := Vector(3, [1/12, -(sin(beta*v)*v^2+12*cos(beta*v)*sin(v)-12*cos(beta*v)*v+12*cos(v)*sin(beta*v)-12*sin(beta*v))/(12*v^2*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v))), -(sin(alpha*v)*v^2+12*cos(v)*sin(alpha*v)-12*cos(alpha*v)*sin(v)+12*cos(alpha*v)*v-12*sin(alpha*v))/(12*v^2*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v)))]):
> 

L0 := E + v^2 *~ A:
> 

L1 := simplify(L0^(-1)):
> 

AUX := simplify(L1 . G . C . e, size):
> 

N1 := simplify((1 - v^2/2) + v^4 * (b^+ . AUX), size):
> 

N2 := simplify(1 - v^2 * (b^+ . L1 . e), size):
> 

N3 := simplify(-v^2 + v^4 * (bp^+ . AUX), size):
> 

N4 := simplify(1 - v^2 * (bp^+ . L1 . e), size):
alpha:= 1/2 + 1/10*sqrt(5):
beta:= -1/2 + 1/10*sqrt(5):
det := simplify(N1*N4 - N2*N3, size):
tr := simplify(N1 + N4, size):
> 

v1 := simplify((N1+N4-sqrt((N1+N4)^2-4*(N1*N4-N2*N3)))*(1/2), size); v2 := simplify((N1+N4+sqrt((N1+N4)^2-4*(N1*N4-N2*N3)))*(1/2), size)
> 

_EnvExplicit := true; sols1 := solve(abs(v11) < 1); evalf(sols1)

RealRange(Open(-1.), Open(1.))

 (2)
> 

_EnvExplicit := true; sols2 := solve(abs(v22) < 1); evalf(sols2)
 

 
> 

#tr_tay := mtaylor(tr, v=0, 10):
#det_tay := mtaylor(det, v=0, 10):
> 

#TR := simplify(eval(mtaylor(tr, v=0, 10), {alpha=1/2+(1/10)*sqrt(5), beta=-1/2+(1/10)*sqrt(5)}));

#DET := simplify(eval(mtaylor(det, v=0, 10), {alpha=1/2+(1/10)*sqrt(5), beta=-1/2+(1/10)*sqrt(5)}));
> 

> 

``


 

 

 

 

Thanks!...

Aixleft math 120
July 08 2024
0 0

@mmcdara Thank you very much! yes, you do got my meanings. You made a good decision to make α and β pending first and then calculate it last and I just learned the usage of size. But why is your maple font color and style different from mine? is the version reason?

Thanks!...

Aixleft math 120
July 08 2024
0 0

@vv Thank you for your suggestion!

Replenish...

Aixleft math 120
July 08 2024
0 0

I have tried to use Taylor expansion on the polynomials containing trigonometric functions in the matrix's component before, and this method can indeed get the result, but the error is not accurate enough. Now I try to use Taylor expansion on the final result. But it shows that it cannot be computed series (is it because there are too many trigonometric functions?)

Thanks!...

Aixleft math 120
July 05 2024
0 0

@Kitonum Thank you!

Thanks!...

Aixleft math 120
July 05 2024
0 0

@C_R Thank you!

1 2 3 4 5 Page 4 of 5