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mskalsi

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Not working !!!...

mskalsi 290
May 09 2016
0 0

@Carl Love 

The following code was sent by Ian Anderson himself and is not working as suggested:

Optimal1.mw

Stucked again......!!!!...

mskalsi 290
May 08 2016
0 0

@Markiyan Hirnyk 

What should I do after this?

What is this initilization ?

Please illustrate in Maple sheet attached with

That's good........but !...

mskalsi 290
May 05 2016
0 0

@Markiyan Hirnyk 

That really calculate position of stationary points, but how do one know whether this stationary point is for Maxima or Minima ??

Elegantly Answered !!!!!...

mskalsi 290
April 28 2016
0 0

@Kitonum 

That is nice and quick reponse.

But how do I subtitute 8 triplet into expression that is what I really asked for?

dsubs as alternative for subs...

mskalsi 290
April 27 2016
0 0

 Everything is explained by ecterrab except replacement of derivative u[t] in DetSys, that can be done by command "dsubs". This command do same job as "subs" do, but using "dsubs" one can replace derivative which one can not perform using "subs" command.

Regards

Yes...

mskalsi 290
April 13 2016
0 0

@John Fredsted 

I have tried that command but I think I am using it in wrong way.

See this decompositon...

mskalsi 290
April 12 2016
0 0

@Dmitry Lyakhov 

Please see following decompositon you requested


> 

fct := Matrix(6, 6, {(1, 1) = 0, (1, 2) = -2*L(4)+4*L(5)-(25/2)*L(6), (1, 3) = (1/2)*L(6), (1, 4) = L(2)-L(3)-4*L(5)+12*L(6), (1, 5) = L(4)-18*L(6), (1, 6) = L(5)-8*L(6), (2, 1) = `*`, (2, 2) = 0, (2, 3) = L(2)-L(3), (2, 4) = -L(4), (2, 5) = -L(5), (2, 6) = -L(6), (3, 1) = `*`, (3, 2) = `*`, (3, 3) = 0, (3, 4) = -L(4), (3, 5) = -L(5), (3, 6) = -L(6), (4, 1) = `*`, (4, 2) = `*`, (4, 3) = `*`, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (5, 1) = `*`, (5, 2) = `*`, (5, 3) = `*`, (5, 4) = `*`, (5, 5) = 0, (5, 6) = 0, (6, 1) = `*`, (6, 2) = `*`, (6, 3) = `*`, (6, 4) = `*`, (6, 5) = `*`, (6, 6) = 0})

fct := Matrix(6, 6, {(1, 1) = 0, (1, 2) = -2*L(4)+4*L(5)-(25/2)*L(6), (1, 3) = (1/2)*L(6), (1, 4) = L(2)-L(3)-4*L(5)+12*L(6), (1, 5) = L(4)-18*L(6), (1, 6) = L(5)-8*L(6), (2, 1) = `*`, (2, 2) = 0, (2, 3) = L(2)-L(3), (2, 4) = -L(4), (2, 5) = -L(5), (2, 6) = -L(6), (3, 1) = `*`, (3, 2) = `*`, (3, 3) = 0, (3, 4) = -L(4), (3, 5) = -L(5), (3, 6) = -L(6), (4, 1) = `*`, (4, 2) = `*`, (4, 3) = `*`, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (5, 1) = `*`, (5, 2) = `*`, (5, 3) = `*`, (5, 4) = `*`, (5, 5) = 0, (5, 6) = 0, (6, 1) = `*`, (6, 2) = `*`, (6, 3) = `*`, (6, 4) = `*`, (6, 5) = `*`, (6, 6) = 0})

 (1)
> 

xct := subs([L(1) = x1, L(2) = x2, L(3) = x3, L(4) = x4, L(5) = x5, L(6) = x6], fct)

xct := Matrix(6, 6, {(1, 1) = 0, (1, 2) = -2*x4+4*x5-(25/2)*x6, (1, 3) = (1/2)*x6, (1, 4) = x2-x3-4*x5+12*x6, (1, 5) = x4-18*x6, (1, 6) = x5-8*x6, (2, 1) = `*`, (2, 2) = 0, (2, 3) = x2-x3, (2, 4) = -x4, (2, 5) = -x5, (2, 6) = -x6, (3, 1) = `*`, (3, 2) = `*`, (3, 3) = 0, (3, 4) = -x4, (3, 5) = -x5, (3, 6) = -x6, (4, 1) = `*`, (4, 2) = `*`, (4, 3) = `*`, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (5, 1) = `*`, (5, 2) = `*`, (5, 3) = `*`, (5, 4) = `*`, (5, 5) = 0, (5, 6) = 0, (6, 1) = `*`, (6, 2) = `*`, (6, 3) = `*`, (6, 4) = `*`, (6, 5) = `*`, (6, 6) = 0})

 (2)
> 

with(DifferentialGeometry):with(LieAlgebras):
> 

VectStrEq := [[x1, x2] = xct[1, 2], [x1, x3] = xct[1, 3], [x1, x4] = xct[1, 4], [x1, x5] = xct[1, 5], [x1, x6] = xct[1, 6], [x2, x3] = xct[2, 3], [x2, x4] = xct[2, 4], [x2, x5] = xct[2, 5], [x2, x6] = xct[2, 6], [x3, x4] = xct[3, 4], [x3, x5] = xct[3, 5], [x3, x6] = xct[3, 6], [x4, x5] = xct[4, 5], [x4, x6] = xct[4, 6], [x5, x6] = xct[5, 6]], [x1, x2, x3, x4, x5, x6]

[[x1, x2] = -2*x4+4*x5-(25/2)*x6, [x1, x3] = (1/2)*x6, [x1, x4] = x2-x3-4*x5+12*x6, [x1, x5] = x4-18*x6, [x1, x6] = x5-8*x6, [x2, x3] = x2-x3, [x2, x4] = -x4, [x2, x5] = -x5, [x2, x6] = -x6, [x3, x4] = -x4, [x3, x5] = -x5, [x3, x6] = -x6, [x4, x5] = 0, [x4, x6] = 0, [x5, x6] = 0], [x1, x2, x3, x4, x5, x6]

 (3)
> 

L2 := LieAlgebraData(VectStrEq, Ex2)

_DG([["LieAlgebra", Ex2, [6, table( [ ] )]], [[[1, 2, 4], -2], [[1, 2, 5], 4], [[1, 2, 6], -25/2], [[1, 3, 6], 1/2], [[1, 4, 2], 1], [[1, 4, 3], -1], [[1, 4, 5], -4], [[1, 4, 6], 12], [[1, 5, 4], 1], [[1, 5, 6], -18], [[1, 6, 5], 1], [[1, 6, 6], -8], [[2, 3, 2], 1], [[2, 3, 3], -1], [[2, 4, 4], -1], [[2, 5, 5], -1], [[2, 6, 6], -1], [[3, 4, 4], -1], [[3, 5, 5], -1], [[3, 6, 6], -1]]])

 (4)
Alg1   > 

DGsetup(L2)
> 

MultiplicationTable("LieTable")

"[[[,`| `,e1,e2,e3,e4,e5,e6],[,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`],[e1,`| `,0,_DG([["vector",Ex2,[]],[[[4],-2],[[5],4],[[6],-25/2]]]),_DG([["vector",Ex2,[]],[[[6],1/2]]]),_DG([["vector",Ex2,[]],[[[2],1],[[3],-1],[[5],-4],[[6],12]]]),_DG([["vector",Ex2,[]],[[[4],1],[[6],-18]]]),_DG([["vector",Ex2,[]],[[[5],1],[[6],-8]]])],[e2,`| `,_DG([["vector",Ex2,[]],[[[4],2],[[5],-4],[[6],25/2]]]),0,_DG([["vector",Ex2,[]],[[[2],1],[[3],-1]]]),_DG([["vector",Ex2,[]],[[[4],-1]]]),_DG([["vector",Ex2,[]],[[[5],-1]]]),_DG([["vector",Ex2,[]],[[[6],-1]]])],[e3,`| `,_DG([["vector",Ex2,[]],[[[6],-1/2]]]),_DG([["vector",Ex2,[]],[[[2],-1],[[3],1]]]),0,_DG([["vector",Ex2,[]],[[[4],-1]]]),_DG([["vector",Ex2,[]],[[[5],-1]]]),_DG([["vector",Ex2,[]],[[[6],-1]]])],[e4,`| `,_DG([["vector",Ex2,[]],[[[2],-1],[[3],1],[[5],4],[[6],-12]]]),_DG([["vector",Ex2,[]],[[[4],1]]]),_DG([["vector",Ex2,[]],[[[4],1]]]),0,0,0],[e5,`| `,_DG([["vector",Ex2,[]],[[[4],-1],[[6],18]]]),_DG([["vector",Ex2,[]],[[[5],1]]]),_DG([["vector",Ex2,[]],[[[5],1]]]),0,0,0],[e6,`| `,_DG([["vector",Ex2,[]],[[[5],-1],[[6],8]]]),_DG([["vector",Ex2,[]],[[[6],1]]]),_DG([["vector",Ex2,[]],[[[6],1]]]),0,0,0]]]"

 (5)

 

Alg1 > 

decomposition := Decompose(factoralgebras = true)

decomposition := [Matrix(6, 6, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1, (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 1, (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 1}), [_DG([["vector", Ex2, []], [[[1], 1]]]), _DG([["vector", Ex2, []], [[[2], 1]]]), _DG([["vector", Ex2, []], [[[3], 1]]]), _DG([["vector", Ex2, []], [[[4], 1]]]), _DG([["vector", Ex2, []], [[[5], 1]]]), _DG([["vector", Ex2, []], [[[6], 1]]])], [[[e1, e2] = -(25/2)*e6+4*e5-2*e4, [e1, e3] = (1/2)*e6, [e1, e4] = 12*e6-4*e5+e2-e3, [e1, e5] = e4-18*e6, [e1, e6] = e5-8*e6, [e2, e3] = e2-e3, [e2, e4] = -e4, [e2, e5] = -e5, [e2, e6] = -e6, [e3, e4] = -e4, [e3, e5] = -e5, [e3, e6] = -e6]]]

 (6)
Ex2 > 

``


Download fct-Decomposition.mw

Book...

mskalsi 290
April 12 2016
0 0

@John Fredsted 

Thank you so much.

Pavel Winternitz and Peter Olver both suggested me following book on classification of Lie algebras:

L. Snobl and P. Winternitz, Classification and Identification of Lie
algebras, CRM Monograph Series, Vol 33, AMS, Providence, RI, 2014.

I believe this book could be helpful in understanding classification problems in Lie algebra, but unfortunately I can not afford this book.

Decomposition...

mskalsi 290
April 11 2016
0 0

@John Fredsted 

Following may also be suitable


> 

with(DifferentialGeometry):
> 

with(LieAlgebras):
> 

DGsetup([x, y, z, t, u]):
Euc > 

VectorFields := [y*D_y, z*D_z, z*D_y, y*D_z, D_t, 3*D_t*t+D_x*x, D_x, u*D_u]

[y*_DG([["vector", "Euc", []], [[[2], 1]]]), z*_DG([["vector", "Euc", []], [[[3], 1]]]), z*_DG([["vector", "Euc", []], [[[2], 1]]]), y*_DG([["vector", "Euc", []], [[[3], 1]]]), _DG([["vector", "Euc", []], [[[4], 1]]]), 3*_DG([["vector", "Euc", []], [[[4], 1]]])*t+_DG([["vector", "Euc", []], [[[1], 1]]])*x, _DG([["vector", "Euc", []], [[[1], 1]]]), u*_DG([["vector", "Euc", []], [[[5], 1]]])]

 (1)
Euc > 

LD := LieAlgebraData(VectorFields)

_DG([["LieAlgebra", "L1", [8]], [[[1, 3, 3], -1], [[1, 4, 4], 1], [[2, 3, 3], 1], [[2, 4, 4], -1], [[3, 4, 1], -1], [[3, 4, 2], 1], [[5, 6, 5], 3], [[6, 7, 7], -1]]])

 (2)
Euc > 

DGsetup(LD)

`Lie algebra: L1`

 (3)
L1 > 

MultiplicationTable("LieTable")

"[[[,`| `,e1,e2,e3,e4,e5,e6,e7,e8],[,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`],[e1,`| `,0,0,_DG([["vector","L1",[]],[[[3],-1]]]),_DG([["vector","L1",[]],[[[4],1]]]),0,0,0,0],[e2,`| `,0,0,_DG([["vector","L1",[]],[[[3],1]]]),_DG([["vector","L1",[]],[[[4],-1]]]),0,0,0,0],[e3,`| `,_DG([["vector","L1",[]],[[[3],1]]]),_DG([["vector","L1",[]],[[[3],-1]]]),0,_DG([["vector","L1",[]],[[[1],-1],[[2],1]]]),0,0,0,0],[e4,`| `,_DG([["vector","L1",[]],[[[4],-1]]]),_DG([["vector","L1",[]],[[[4],1]]]),_DG([["vector","L1",[]],[[[1],1],[[2],-1]]]),0,0,0,0,0],[e5,`| `,0,0,0,0,0,_DG([["vector","L1",[]],[[[5],3]]]),0,0],[e6,`| `,0,0,0,0,_DG([["vector","L1",[]],[[[5],-3]]]),0,_DG([["vector","L1",[]],[[[7],-1]]]),0],[e7,`| `,0,0,0,0,0,_DG([["vector","L1",[]],[[[7],1]]]),0,0],[e8,`| `,0,0,0,0,0,0,0,0]]]"

 (4)
L1 > 

decomposition := Decompose()

decomposition := [Matrix(8, 8, {(1, 1) = 1/2, (1, 2) = -1/2, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 1, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 1, (5, 7) = 0, (5, 8) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 1, (6, 8) = 0, (7, 1) = 1/2, (7, 2) = 1/2, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 1}), [_DG([["vector", "L1", []], [[[1], 1], [[2], -1]]]), _DG([["vector", "L1", []], [[[3], 1]]]), _DG([["vector", "L1", []], [[[4], 1]]]), _DG([["vector", "L1", []], [[[5], 1]]]), _DG([["vector", "L1", []], [[[6], 1]]]), _DG([["vector", "L1", []], [[[7], 1]]]), _DG([["vector", "L1", []], [[[1], 1], [[2], 1]]]), _DG([["vector", "L1", []], [[[8], 1]]])]]

 (5)
L1 > 

``


Download Decomposition_of_abstract_Lie_Algebra_Better_way.mw

Wrong Judgement...

mskalsi 290
April 11 2016
0 0

@John Fredsted 

I made early judgement as I am beginner in Lie algebra. Actually my field is Lie group analysis of partial differential equations and during literature survey I come to realise that abstract Lie algebras are better suitable for classification of Lie algebras for group invariant solutions.

I do not even know how you could make decision about decomposition from multiplication table.

Can you please explain how you read mutliplication table for L_1 ?

Or please suggest any good graduate text on Lie algebra. I have books like of Nathan Jacobson but that seems to be too advance for me.

 

But I Guess.........!!!...

mskalsi 290
April 11 2016
0 0

@John Fredsted 

But I guess the decomposition must be like

L = L_1 + L_2 + L_3 + L_4

with

L_1 = { V-2-V_1, V_3, V_4} = sl(2,R), 

L_2 = {{V_6, V_7, V_5} , L_3 },

L_3= {V_1+V_2},

L_3 ={{V_8}

Please correct me if I am wrong.

Wow........!!!!...

mskalsi 290
April 11 2016
0 0

@John Fredsted 

Thank you So much.

One more thing, can you please tell how to express this abstract Lie algebra as direct sum of indecomposable Lie algebras.

and how to perform in reverse manner i.e. to convert this abstract Lie algebra to Lie algebra?

Amazing...........

mskalsi 290
April 06 2016
0 0

@Carl Love 

Thanks for help.

I am really grateful to you and I wish for your healthy and peaceful life.

I failed to explain..................

mskalsi 290
April 06 2016
0 0

@Carl Love 

I am carrying put succssive adjoints on linear combination of vectors. These adjoint actions are being carried out with the aid of Matrix called adjoint matrix. Please see following:


> 

M := Matrix([[v[1], v[2], v[3], -epsilon*v[1]+v[4]], [v[1], v[2], -epsilon*v[1]+v[3], -3*epsilon*v[2]+v[4]], [v[1], epsilon*v[1]+v[2], v[3], 2*epsilon*v[3]+v[4]], [exp(epsilon)*v[1], exp(3*epsilon)*v[2], exp(-2*epsilon)*v[3], v[4]]])

M := Matrix(4, 4, {(1, 1) = v[1], (1, 2) = v[2], (1, 3) = v[3], (1, 4) = -epsilon*v[1]+v[4], (2, 1) = v[1], (2, 2) = v[2], (2, 3) = -epsilon*v[1]+v[3], (2, 4) = -3*epsilon*v[2]+v[4], (3, 1) = v[1], (3, 2) = epsilon*v[1]+v[2], (3, 3) = v[3], (3, 4) = 2*epsilon*v[3]+v[4], (4, 1) = exp(epsilon)*v[1], (4, 2) = exp(3*epsilon)*v[2], (4, 3) = exp(-2*epsilon)*v[3], (4, 4) = v[4]})

 (1)

Step I
 
> 

F[4] := expand(t[4]*(a[1]*v[1]+a[2]*v[2]+a[3]*v[3]+a[4]*v[4]))

a[1]*t[4]*v[1]+a[2]*t[4]*v[2]+a[3]*t[4]*v[3]+a[4]*t[4]*v[4]

 (1.1)
> 

for i to 4 do for j to 4 do F[4] := expand(algsubs(t[i]*v[j] = M[i, j], expand(F[4]))) end do end do; 1; F[4]

a[4]*v[4]+a[2]*(exp(epsilon))^3*v[2]+a[1]*exp(epsilon)*v[1]+a[3]*v[3]/(exp(epsilon))^2

 (1.2)
> 

expand(subs(epsilon = E[4], a[4]*v[4]+a[2]*(exp(epsilon))^3*v[2]+a[1]*exp(epsilon)*v[1]+a[3]*v[3]/(exp(epsilon))^2))

a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]+a[3]*v[3]/(exp(E[4]))^2

 (1.3)

Step II
 
> 

F[1] := expand(t[1]*(a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]+a[3]*v[3]/(exp(E[4]))^2))

The expression from previous step is used here

t[1]*a[4]*v[4]+t[1]*a[2]*(exp(E[4]))^3*v[2]+t[1]*a[1]*exp(E[4])*v[1]+t[1]*a[3]*v[3]/(exp(E[4]))^2

 (2.1)
> 

for i to 4 do for j to 4 do F[1] := expand(algsubs(t[i]*v[j] = M[i, j], expand(F[1]))) end do end do; 1; F[1]

a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-a[4]*epsilon*v[1]+a[3]*v[3]/(exp(E[4]))^2

 (2.2)
> 

expand(subs(epsilon = E[1], a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-a[4]*epsilon*v[1]+a[3]*v[3]/(exp(E[4]))^2))

a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-a[4]*E[1]*v[1]+a[3]*v[3]/(exp(E[4]))^2

 (2.3)

Step III
 
> 

F[2] := expand(t[2]*(a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-a[4]*E[1]*v[1]+a[3]*v[3]/(exp(E[4]))^2))

t[2]*a[4]*v[4]+t[2]*a[2]*(exp(E[4]))^3*v[2]+t[2]*a[1]*exp(E[4])*v[1]-t[2]*a[4]*E[1]*v[1]+t[2]*a[3]*v[3]/(exp(E[4]))^2

 (3.1)
> 

for i to 4 do for j to 4 do F[2] := expand(algsubs(t[i]*v[j] = M[i, j], expand(F[2]))) end do end do; 1; F[2]

a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-3*a[4]*epsilon*v[2]-a[4]*E[1]*v[1]-a[3]*epsilon*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2

 (3.2)
> 

expand(subs(epsilon = E[2], a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-3*a[4]*epsilon*v[2]-a[4]*E[1]*v[1]-a[3]*epsilon*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2))

a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-3*a[4]*E[2]*v[2]-a[4]*E[1]*v[1]-a[3]*E[2]*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2

 (3.3)

Step IV
 
> 

F[3] := expand(t[3]*(a[4]*v[4]+a[2]*(exp(E[4]))^3*v[2]+a[1]*exp(E[4])*v[1]-3*a[4]*E[2]*v[2]-a[4]*E[1]*v[1]-a[3]*E[2]*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2))

t[3]*a[4]*v[4]+t[3]*a[2]*(exp(E[4]))^3*v[2]+t[3]*a[1]*exp(E[4])*v[1]-3*t[3]*a[4]*E[2]*v[2]-t[3]*a[4]*E[1]*v[1]-t[3]*a[3]*E[2]*v[1]/(exp(E[4]))^2+t[3]*a[3]*v[3]/(exp(E[4]))^2

 (4.1)
> 

for i to 4 do for j to 4 do F[3] := expand(algsubs(t[i]*v[j] = M[i, j], expand(F[3]))) end do end do; 1; F[3]

a[4]*v[4]+(exp(E[4]))^3*v[1]*epsilon*a[2]+a[2]*(exp(E[4]))^3*v[2]-3*a[4]*E[2]*epsilon*v[1]+a[1]*exp(E[4])*v[1]+2*a[4]*epsilon*v[3]-a[4]*E[1]*v[1]-3*a[4]*E[2]*v[2]-a[3]*E[2]*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2

 (4.2)
> 

expand(subs(epsilon = E[3], a[4]*v[4]+(exp(E[4]))^3*v[1]*epsilon*a[2]+a[2]*(exp(E[4]))^3*v[2]-3*a[4]*E[2]*epsilon*v[1]+a[1]*exp(E[4])*v[1]+2*a[4]*epsilon*v[3]-a[4]*E[1]*v[1]-3*a[4]*E[2]*v[2]-a[3]*E[2]*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2))

a[4]*v[4]+(exp(E[4]))^3*v[1]*E[3]*a[2]+a[2]*(exp(E[4]))^3*v[2]-3*a[4]*E[2]*E[3]*v[1]+a[1]*exp(E[4])*v[1]+2*a[4]*E[3]*v[3]-a[4]*E[1]*v[1]-3*a[4]*E[2]*v[2]-a[3]*E[2]*v[1]/(exp(E[4]))^2+a[3]*v[3]/(exp(E[4]))^2

 (4.3)

Can we combine above four step in single sequence ?


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My Code is Flawed...

mskalsi 290
April 05 2016
0 0

@Carl Love 

The code given by you is perfect. It was mine code that I written as flawed.

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