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complex tensor expression with Pauli matrices...

Asked by: illuminates 65
physics tensor
February 02 2017
0  0

I attempt to understand is it possible whether to calculate the next expression by means of mathematica:

where

{,}- anti-communicator;

 a=0,1,2,3;

\tau^{0}-unity matrix; \tau^{i} - Pauli matrix;

and:
 

 

 


 
finally - Levi-Civita symbol; -Hermitian conjugation.

 

Thank you for your kind replies .

How to execute a set of values in a program...

Asked by: shakuntala 25
February 02 2017
0  10

Hello, Sir 

I tried to execute the program for a set values for more than one parameter but it is not existing, please can you do a favor for me in this case, that is how to write a program to execute set of values for more than one parameter at a time and how to plot the graph?

 

stretching_cylinder_new.mw

 

Scientific engineering notation implementation sug...

Asked by: Christopher2222 6030
February 01 2017
1  8

Way back in Maple 10 (I'd like to pay special attention to http://www.mapleprimes.com/questions/43066-Maple-10-How-Do-I-Change-Number-Formats) it was suggested even hinted by a Maplesoft employee that this availability would be in a future version of Maple. 

Since then there have been numerous requests on how to get Maple to change to scientific or engineering notation of the sorts. 

So what is that now, v11 v12 v13 v14 v15 v16 v17 v18 v2015 v2016 ... 10 versions!  and no implementation of engineering / scientific notation conversions. 

We rely today on printf or sprintf for e notations however I could't come up with an output of converting 3530 to simply 3.53 x 103 .  Can someone produce a proc to do so, I have tried and I can not. 

How to obtain accurate rotation matrices?...

Asked by: Lhunatic 15
tensor rotation
February 01 2017
0  4

Hey guys,

I'm trying to build up some program to manage my composites data. But I am struggling with my compliance/stiffness in the global coordinates:

-Basically, I have the lamina's properties in local coordinates.

-When I make walls out of them with 30degress fibers orientation, I need to rotate the local stiffness several times to get the the stiffness of that particular wall.

-While I do understand the concept and manage to get the final rotation matrix correctly, I often find myself making mistakes regarding the sense of rotation of my local axis relatively to the global one.

I try to stick with one direction of rotation but if Maple has a smart way whereas I can plug in the initial configuration of the local coords relatively to the global one, show the final configuration (local aligned to the global), and get the rotation matrix that made it happen, it would be more helpful.

Thank you

Update:

I enclosed an example of the kind of operations I do:

And here is the kind of code I'm using:

PB2_W1.mw
 

NULL

> 

restart:
> 

with(LinearAlgebra):
> 

Stiffness:=Matrix(6,6): Stiffness:=Matrix(6, 6, {(1, 1) = 20.4, (1, 2) = .537, (1, 3) = 1.01, (1, 4) = 0., (1, 5) = 0., (1, 6) = -0., (2, 1) = .537, (2, 2) = 1.59, (2, 3) = .73, (2, 4) = 0., (2, 5) = 0., (2, 6) = -0., (3, 1) = 1.01, (3, 2) = .73, (3, 3) = 2.86, (3, 4) = 0., (3, 5) = 0., (3, 6) = -0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 1.5, (4, 5) = 0., (4, 6) = -0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 2., (5, 6) = -0., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = .8});

Stiffness := Matrix(6, 6, {(1, 1) = 20.4, (1, 2) = .537, (1, 3) = 1.01, (1, 4) = 0., (1, 5) = 0., (1, 6) = -0., (2, 1) = .537, (2, 2) = 1.59, (2, 3) = .73, (2, 4) = 0., (2, 5) = 0., (2, 6) = -0., (3, 1) = 1.01, (3, 2) = .73, (3, 3) = 2.86, (3, 4) = 0., (3, 5) = 0., (3, 6) = -0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 1.5, (4, 5) = 0., (4, 6) = -0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 2., (5, 6) = -0., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = .8})

 (1)
> 

Q1:=Matrix(3,3): Q1[1,1]:=sin(Pi/4); Q1[1,2]:=0; Q1[1,3]:=cos(Pi/4); Q1[2,1]:=cos(Pi/4); Q1[2,2]:=0; Q1[2,3]:=-sin(Pi/4); Q1[3,1]:=0; Q1[3,2]:=1; Q1[3,3]:=0;

(1/2)*2^(1/2)

  

0

  

(1/2)*2^(1/2)

  

(1/2)*2^(1/2)

  

0

  

-(1/2)*2^(1/2)

  

0

  

1

  

0

 (2)
> 

Q1;

Matrix(3, 3, {(1, 1) = (1/2)*sqrt(2), (1, 2) = 0, (1, 3) = (1/2)*sqrt(2), (2, 1) = (1/2)*sqrt(2), (2, 2) = 0, (2, 3) = -(1/2)*sqrt(2), (3, 1) = 0, (3, 2) = 1, (3, 3) = 0})

 (3)
> 

Q2:=Matrix(3,3): Q2[1,1]:=0; Q2[1,2]:=0; Q2[1,3]:=1; Q2[2,1]:=1; Q2[2,2]:=0; Q2[2,3]:=0; Q2[3,1]:=0; Q2[3,2]:=1; Q2[3,3]:=0;

0

  

0

  

1

  

1

  

0

  

0

  

0

  

1

  

0

 (4)
> 

Q2;

Matrix(3, 3, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 1, (2, 1) = 1, (2, 2) = 0, (2, 3) = 0, (3, 1) = 0, (3, 2) = 1, (3, 3) = 0})

 (5)
> 

Q3:=Matrix(3,3): Q3[1,1]:=0; Q3[1,2]:=-1; Q3[1,3]:=0; Q3[2,1]:=1; Q3[2,2]:=0; Q3[2,3]:=0; Q3[3,1]:=0; Q3[3,2]:=0; Q3[3,3]:=1;

0

  

-1

  

0

  

1

  

0

  

0

  

0

  

0

  

1

 (6)
> 

Q3;

Matrix(3, 3, {(1, 1) = 0, (1, 2) = -1, (1, 3) = 0, (2, 1) = 1, (2, 2) = 0, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 (7)
> 

S1:=Transpose(Q1); S2:=Transpose(Q2); S3:=Transpose(Q3);

S1 := Matrix(3, 3, {(1, 1) = (1/2)*sqrt(2), (1, 2) = (1/2)*sqrt(2), (1, 3) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (3, 1) = (1/2)*sqrt(2), (3, 2) = -(1/2)*sqrt(2), (3, 3) = 0})

  

S2 := Matrix(3, 3, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (3, 1) = 1, (3, 2) = 0, (3, 3) = 0})

  

S3 := Matrix(3, 3, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (2, 1) = -1, (2, 2) = 0, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 (8)
> 

S4:=Multiply(S3,S2);

S4 := Matrix(3, 3, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 1, (2, 1) = 0, (2, 2) = -1, (2, 3) = 0, (3, 1) = 1, (3, 2) = 0, (3, 3) = 0})

 (9)
> 

S5:=Multiply(S4,S1);

S5 := Matrix(3, 3, {(1, 1) = (1/2)*sqrt(2), (1, 2) = -(1/2)*sqrt(2), (1, 3) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = -1, (3, 1) = (1/2)*sqrt(2), (3, 2) = (1/2)*sqrt(2), (3, 3) = 0})

 (10)
> 

R:=Matrix(6,6): R[1,1]:=S5[1,1]^2; R[1,2]:=S5[1,2]^2; R[1,3]:=S5[1,3]^2; R[2,1]:=S5[2,1]*S5[1,1]; R[2,2]:=S5[2,2]*S5[1,2]; R[2,3]:=S5[2,3]*S5[1,3]; R[3,1]:=S5[2,1]^2; R[3,2]:=S5[2,2]^2; R[3,3]:=S5[2,3]^2; R[1,4]:=2*S5[1,2]*S5[1,3]; R[1,5]:=2*S5[1,1]*S5[1,3]; R[1,6]:=2*S5[1,1]*S5[1,2]; R[2,4]:=S5[2,2]*S5[1,3]+S5[2,3]*S5[1,2]; R[2,5]:=S5[2,1]*S5[1,3]+S5[2,3]*S5[1,1]; R[2,6]:=S5[2,1]*S5[1,2]+S5[2,2]*S5[1,1]; R[3,4]:=2*S5[2,2]*S5[2,3]; R[3,5]:=2*S5[2,1]*S5[2,3]; R[3,6]:=2*S5[2,1]*S5[2,2];
> 

R[4,1]:=S5[3,1]*S5[1,1]; R[4,2]:=S5[3,2]*S5[1,2]; R[4,3]:=S5[3,3]*S5[1,3]; R[4,4]:=S5[3,2]*S5[1,3]+S5[3,3]*S5[1,2]; R[4,5]:=S5[3,1]*S5[1,3]+S5[3,3]*S5[1,1]; R[4,6]:=S5[3,1]*S5[1,2]+S5[3,2]*S5[1,1]; R[5,1]:=S5[3,1]*S5[2,1]; R[5,2]:=S5[3,2]*S5[2,2]; R[5,3]:=S5[3,3]*S5[2,3]; R[5,4]:=S5[3,2]*S5[2,3]+S5[3,3]*S5[2,2]; R[5,5]:=S5[3,1]*S5[2,3]+S5[3,3]*S5[2,1]; R[5,6]:=S5[3,1]*S5[2,2]+S5[3,2]*S5[2,1];R[6,1]:=S5[3,1]^2; R[6,2]:=S5[3,2]^2; R[6,3]:=S5[3,3]^2; R[6,4]:=2*S5[3,3]*S5[3,2]; R[6,5]:=2*S5[3,1]*S5[3,3]; R[6,6]:=2*S5[3,1]*S5[3,2];

1/2

  

1/2

  

0

  

0

  

0

  

0

  

0

  

0

  

1

  

0

  

0

  

-1

  

(1/2)*2^(1/2)

  

-(1/2)*2^(1/2)

  

0

  

0

  

0

  

0

  

1/2

  

-1/2

  

0

  

0

  

0

  

0

  

0

  

0

  

0

  

-(1/2)*2^(1/2)

  

-(1/2)*2^(1/2)

  

0

  

1/2

  

1/2

  

0

  

0

  

0

  

1

 (11)
> 

print(R);

Matrix(6, 6, {(1, 1) = 1/2, (1, 2) = 1/2, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = -1, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = (1/2)*sqrt(2), (2, 5) = -(1/2)*sqrt(2), (2, 6) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 1/2, (4, 2) = -1/2, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -(1/2)*sqrt(2), (5, 5) = -(1/2)*sqrt(2), (5, 6) = 0, (6, 1) = 1/2, (6, 2) = 1/2, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 1})

 (12)
> 

RTrans:=Transpose(R);

RTrans := Matrix(6, 6, {(1, 1) = 1/2, (1, 2) = 0, (1, 3) = 0, (1, 4) = 1/2, (1, 5) = 0, (1, 6) = 1/2, (2, 1) = 1/2, (2, 2) = 0, (2, 3) = 0, (2, 4) = -1/2, (2, 5) = 0, (2, 6) = 1/2, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = (1/2)*sqrt(2), (4, 3) = 0, (4, 4) = 0, (4, 5) = -(1/2)*sqrt(2), (4, 6) = 0, (5, 1) = 0, (5, 2) = -(1/2)*sqrt(2), (5, 3) = 0, (5, 4) = 0, (5, 5) = -(1/2)*sqrt(2), (5, 6) = 0, (6, 1) = -1, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 1})

 (13)
> 

Stiff1:=Matrix(6,6): Stiff1:=Multiply(Stiffness, RTrans);

Stiff1 := Matrix(6, 6, {(1, 1) = 10.46850000, (1, 2) = 0., (1, 3) = 1.01, (1, 4) = 9.931500000, (1, 5) = 0., (1, 6) = 10.46850000, (2, 1) = 1.063500000, (2, 2) = 0., (2, 3) = .73, (2, 4) = -.5265000000, (2, 5) = 0., (2, 6) = 1.063500000, (3, 1) = .8700000000, (3, 2) = 0., (3, 3) = 2.86, (3, 4) = .1400000000, (3, 5) = 0., (3, 6) = .8700000000, (4, 1) = 0., (4, 2) = .7500000000*sqrt(2), (4, 3) = 0., (4, 4) = 0., (4, 5) = -.7500000000*sqrt(2), (4, 6) = 0., (5, 1) = 0., (5, 2) = -1.000000000*sqrt(2), (5, 3) = 0., (5, 4) = 0., (5, 5) = -1.000000000*sqrt(2), (5, 6) = 0., (6, 1) = -.8, (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = .8})

 (14)
> 

StiffnessW1:=Matrix(6,6): StiffnessW1:=Multiply(R,Stiff1); evalf(StiffnessW1,3);

StiffnessW1 := Matrix(6, 6, {(1, 1) = 6.566000000, (1, 2) = 0., (1, 3) = .8700000000, (1, 4) = 4.702500000, (1, 5) = 0., (1, 6) = 4.966000000, (2, 1) = 0., (2, 2) = 1.750000000, (2, 3) = 0., (2, 4) = 0., (2, 5) = .2500000000, (2, 6) = 0., (3, 1) = .8700000000, (3, 2) = 0., (3, 3) = 2.86, (3, 4) = .1400000000, (3, 5) = 0., (3, 6) = .8700000000, (4, 1) = 4.702500000, (4, 2) = 0., (4, 3) = .1400000000, (4, 4) = 5.229000000, (4, 5) = 0., (4, 6) = 4.702500000, (5, 1) = 0., (5, 2) = .2500000000, (5, 3) = 0., (5, 4) = 0., (5, 5) = 1.750000000, (5, 6) = 0., (6, 1) = 4.966000000, (6, 2) = 0., (6, 3) = .8700000000, (6, 4) = 4.702500000, (6, 5) = 0., (6, 6) = 6.566000000})

  

Matrix(6, 6, {(1, 1) = 6.57, (1, 2) = 0., (1, 3) = .870, (1, 4) = 4.70, (1, 5) = 0., (1, 6) = 4.97, (2, 1) = 0., (2, 2) = 1.75, (2, 3) = 0., (2, 4) = 0., (2, 5) = .250, (2, 6) = 0., (3, 1) = .870, (3, 2) = 0., (3, 3) = 2.86, (3, 4) = .140, (3, 5) = 0., (3, 6) = .870, (4, 1) = 4.70, (4, 2) = 0., (4, 3) = .140, (4, 4) = 5.23, (4, 5) = 0., (4, 6) = 4.70, (5, 1) = 0., (5, 2) = .250, (5, 3) = 0., (5, 4) = 0., (5, 5) = 1.75, (5, 6) = 0., (6, 1) = 4.97, (6, 2) = 0., (6, 3) = .870, (6, 4) = 4.70, (6, 5) = 0., (6, 6) = 6.57})

 (15)
> 

 

 

NULL


 

Download PB2_W1.mw

It is decent enough to get results if human mistakes don't happen when it comes to rotation orientation (which tends to happen more often than not). 

I am aware though that it is not written with wits or in an efficient format. If you have a suggestion, Im all ears.

 

Thanks again

 

 

Fractional Differential Transform method...

Asked by: ZAIN UL ABADIN ZAFAR 20
February 01 2017
0  2

Hi!

I hope every one is ok.

I am running this code (see below)

m := 2;


X[0] := 14;
                              
Y[0] := 18;
                        
a := 1; b := 1; c := .1; d := 1;

alpha := 1;

for k from 0 to m do X[k+1] := GAMMA(k*alpha+1)*(a*X(k)-b*(sum(X(s)*Y(k-s), s = 0 .. k)))/GAMMA(k*alpha+1+1); Y[k+1] := GAMMA(k*alpha+1)*(-c*Y(k)+d*(sum(X(s)*Y(k-s), s = 0 .. k)))/GAMMA(k*alpha+1+1) end do

x := 0; y := 0

The following message pop out.

PLease HELP! HELP!.....

\

 

Scientific output...

Asked by: amelscape 5
numeric
January 31 2017
1  0

Is there a way to change the numeric formatting of 'Scientific' to use a cdot instead of a cross to represent multiplication?

How do I integrate a large set of datapoints....

Asked by: Qwinzzi 10
plot integration
January 31 2017
2  23

Hello! 

I got a set of data imported from excel which is of the size 2001x2. I've use DataPlot to plot the graph of this data but I can't seem to find a way to integrate it. I've used BSplineCurve to make the discreate values continious but I cant seem to integrate this new curve. Can someone please give me a solution or an alternative way to find an approximative way to find the area under the curve.

Thanks

How to express a polynomial in cos(x) and sin(x) i...

Asked by: jga 15
rational trigonometric-identities
January 31 2017
1  7

Hello,

Say I have a rational function 

 

f:= q^4*(q^2+1)*((q^6+q^5-q^4-2*q^3+q+1)^6/q^13+(q^6+q^5-2*q^3-q^2+q+1)^6/q^25)/((1+q)^4*(-q^2+1)^2)

 

in a variable q, with big degrees in numerator and denominator. I happen to know that if I make a change of variable q=exp(Ix) this rational function can be written in the form

f(exp(Ix))=\sum_{k>0, n>=0} (coefficient(n,k)) sin^(2n-2)(kx/2), where this sum is finite.

I'm trying to find (1) what is the best way to simplify the rational function f and (2) how can I make the change of variable into these variables. 

I managed to put the rational function in terms of cos(x) and sin(x), however after a day of calculations the computer couldn't simplify the expression. 

For this I was using:  simplify(rationalize(convert(subs(q=exp(Ix),factor(rationalize(f))),trig)))

I appreciate any help.

Edit: Another way of getting this variables would be to force Maple to use multiple angle identities to write the powers of cosine(x) in terms of sin(kx). Is there any way to force this kind of simplification?

How would i start to write a procedure to decrypt ...

Asked by: Gibberish123 15
January 30 2017
2  11

Suppose i have a message X encrypted using RSA with public code (n,e) and ascii (Here we treat the message as an array so don't worry about block-length) how would one go about writing a procedure that given a public key (n,e) with small n and a ciphertext message x will decrypt x. I have been looking online to see how we can get maple to take ascii into consideration but to no avail any help would be appreciated

animating a cylinder bounded by a sphere...

Asked by: brian bovril 914
animate
January 30 2017
0  6

Guys

I can't seem to work out how the cylinder in my animation won't extend to of the bottom of the sphere initially. and how to make it stop at the maximum volume coordinates.

cylinder_in_sphere_ani.mw

 

 

Problem for solving system of ODEs...

Asked by: Muhammad Usman 240
January 30 2017
0  3

Dear friends! I am facing problem to solve the below system of ODEs numerically please find the mistake and correct it.

alpha := -1; R := 2; m := 2; Pr := 7; Le := 1.25; Nt := .2; Nb := .2; g := .5; K1 := .1; Q := .5

Eq1 := eta^3*(diff(F(eta), eta, eta, eta, eta))+alpha*(eta^4*(diff(F(eta), eta, eta, eta))+eta^3*(diff(F(eta), eta, eta))-eta^2*F(eta))-2*eta^2*(diff(F(eta), eta, eta, eta))+3*eta*(diff(F(eta), eta, eta))-3*(diff(F(eta), eta))+eta*R*(diff(F(eta), eta))^2-3*eta*R*F(eta)*(diff(F(eta), eta, eta))+3*R*F(eta)*(diff(F(eta), eta))+3*eta^2*R*F(eta)*(diff(F(eta), eta, eta, eta))-eta^2*(diff(F(eta), eta))*(diff(F(eta), eta, eta))-M^2*(eta^3*(diff(F(eta), eta, eta))-eta^2*(diff(F(eta), eta))); Eq2 := eta*(diff(G(eta), eta, eta))+alpha*Pr*eta^2*(diff(G(eta), eta))+R*Pr*F(eta)*(diff(G(eta), eta))+Nb*eta*(diff(G(eta), eta))*(diff(H(eta), eta))+Nt*eta*(diff(G(eta), eta))^2+diff(G(eta), eta)+Q*Pr*eta*G(eta) = 0; Eq3 := eta*(diff(H(eta), eta, eta))+alpha*Le*Pr*eta^2*(diff(H(eta), eta))+R*Le*Pr*F(eta)*(diff(H(eta), eta))+Nt*eta*(diff(G(eta), eta, eta))/Nb+Nt*(diff(G(eta), eta))/Nb+diff(H(eta), eta)-g*Le*Pr*eta*H(eta)-Le*Pr*K1*eta = 0;

IC1 := F(0) = 0, F(1) = 1, (D(F))(0) = 0, (D(F))(1) = 0, (D(G))(0) = 0, G(1) = 1, (D(H))(0) = 0, H(1) = lambda; dsys1 := {Eq1, Eq2, Eq3, IC1}; dsol1 := dsolve(dsys1, numeric, continuation = lambda, range = 0 .. 1);

dsol1x := subs(dsol1, F(eta));

dsol1y := subs(dsol1, G(eta)); dsol1z := subs(dsol1, H(eta));
 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

How to factor 4 - 2a and (2x^2 - 2x + sqrt(2))^2 ?...

Asked by: nguyenhuyenag 90
factorization
January 29 2017
2  2

Hi all

I have 4 - 2a and (2x^2 - 2x + sqrt(2))^2. How to factor it become 2(2-a) and 2(sqrt(2)x^2 - sqrt(2)x + 1)^2 ?

Thanks you very much.

 

How to to expand Index Notation...

Asked by: Lhunatic 15
index
January 29 2017
0  7

Hello people,

I am looking to use Maple and its loops, to develop the tensorial expressions in index notations such as this one:

My Sigma[11] is supposed to be a summation of the terms obtained when i then j are vary throughout the values, 1, 2 3 

 

Thanks

How can one export maple files to text in batch?...

Asked by: s31415 10
convert export batch
January 29 2017
2  6

Hi,

I am looking for a way of exporting a large number of Maple files (*.mw) into text files (*.txt) automatically. Here are two questions:

  • Is there a ready-made tool allowing to do this?
  • If not, is it possible to export a maple file to text from the command line interface?

Thanks!

Samuel

How do I factor a vector out of a matrix...

Asked by: Lhunatic 15
matrix linearalgebra
January 29 2017
1  2

Hey guys,

I have this (6x1) matrix:

And I wish to factor a vector of the recurring terms out of it, this particular vector:

So that I end up with a (6x6) Matrix multiplied to that vector.

 

Thank you

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