mskalsi

290 Reputation

7 Badges

9 years, 342 days

MaplePrimes Activity


These are questions asked by mskalsi

Dear All


As a result of certain computation, Maple produce following result:

exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]^2/exp(epsilon[3]):

How can I force Maple to produce result like:

exp(epsilon[10]-epsilon[3])*a[2]*epsilon[6]*epsilon[9]^2:

Similar to this; Maple produce result:

(exp(epsilon[10]))^2*a[1]:

How I can force Maple to produce it like:

exp(2*epsilon[10])*a[1]:

As an example; I need to simplify following expression in manner as described above

-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]*epsilon[2]/exp(epsilon[3])-2*a[10]*epsilon[7]*epsilon[9]-a[10]*epsilon[7]*epsilon[2]-a[3]*epsilon[9]^2*epsilon[11]-a[3]*epsilon[11]*epsilon[5]+exp(epsilon[10])*a[7]*epsilon[2]+a[10]*epsilon[6]*epsilon[4]-2*a[3]*epsilon[6]*epsilon[4]+(exp(epsilon[10]))^2*a[1]/exp(epsilon[3])+exp(epsilon[3])*a[11]*epsilon[9]^2+exp(epsilon[3])*a[11]*epsilon[5]+2*exp(epsilon[10])*a[7]*epsilon[9]-(exp(epsilon[10]))^2*a[5]*epsilon[11]/(exp(epsilon[3]))^2-exp(epsilon[10])*a[2]*epsilon[7]/exp(epsilon[3])-2*exp(epsilon[10])*a[9]*epsilon[7]/exp(epsilon[3])+a[10]*epsilon[6]*epsilon[8]*epsilon[2]-a[3]*epsilon[11]*epsilon[9]*epsilon[2]-2*a[3]*epsilon[6]*epsilon[8]*epsilon[2]+2*a[10]*epsilon[6]*epsilon[8]*epsilon[9]-4*a[3]*epsilon[6]*epsilon[8]*epsilon[9]-(exp(epsilon[10]))^3*a[4]*epsilon[6]/(exp(epsilon[3]))^3+(exp(epsilon[3]))^2*a[6]*epsilon[4]/exp(epsilon[10])+exp(epsilon[3])*a[11]*epsilon[9]*epsilon[2]-2*a[10]*epsilon[1]+a[3]*epsilon[1]-2*exp(epsilon[10])*a[9]*epsilon[11]*epsilon[9]/exp(epsilon[3])-(exp(epsilon[10]))^2*a[8]*epsilon[6]*epsilon[2]/(exp(epsilon[3]))^2-exp(epsilon[10])*a[9]*epsilon[11]*epsilon[2]/exp(epsilon[3])-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]^2/exp(epsilon[3])+2*(exp(epsilon[3]))^2*a[6]*epsilon[8]*epsilon[9]/exp(epsilon[10])-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[5]/exp(epsilon[3])+(exp(epsilon[3]))^2*a[6]*epsilon[8]*epsilon[2]/exp(epsilon[10])-2*(exp(epsilon[10]))^2*a[8]*epsilon[6]*epsilon[9]/(exp(epsilon[3]))^2


Download Expression.mwExpression.mw

Regards

Dear All

I have started exploring Lie Algebra package in Maple 18 and it wonderful experience for me. But as I am in learning stage so I feel little difficulty to understand even its basic enviroment.

I am trying to fing quotient algebra for Normalizer of certain element W1 in Lie algebra and I don't how to do it. I have expected answer for quotient of Normlizer but don't know to obtain it. Please see following details:

 

with(DifferentialGeometry):with(LieAlgebras):``

L1 := _DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 1], -1], [[1, 6, 2], -1], [[2, 3, 2], -1], [[2, 4, 1], 1], [[2, 5, 2], 1], [[4, 5, 4], -1], [[4, 6, 3], -1], [[4, 6, 5], -2], [[5, 6, 6], -1]]])

_DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 1], -1], [[1, 6, 2], -1], [[2, 3, 2], -1], [[2, 4, 1], 1], [[2, 5, 2], 1], [[4, 5, 4], -1], [[4, 6, 3], -1], [[4, 6, 5], -2], [[5, 6, 6], -1]]])

(1)

DGsetup(L1)

`Lie algebra: Alg1`

(2)
Alg1 > 

MultiplicationTable("LieTable")

"[[[,`| `,e1,e2,e3,e4,e5,e6],[,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`],[e1,`| `,0,0,_DG([["vector",Alg1,[]],[[[1],-1]]]),0,0,_DG([["vector",Alg1,[]],[[[2],-1]]])],[e2,`| `,0,0,_DG([["vector",Alg1,[]],[[[2],-1]]]),_DG([["vector",Alg1,[]],[[[1],1]]]),_DG([["vector",Alg1,[]],[[[2],1]]]),0],[e3,`| `,_DG([["vector",Alg1,[]],[[[1],1]]]),_DG([["vector",Alg1,[]],[[[2],1]]]),0,0,0,0],[e4,`| `,0,_DG([["vector",Alg1,[]],[[[1],-1]]]),0,0,_DG([["vector",Alg1,[]],[[[4],-1]]]),_DG([["vector",Alg1,[]],[[[3],-1],[[5],-2]]])],[e5,`| `,0,_DG([["vector",Alg1,[]],[[[2],-1]]]),0,_DG([["vector",Alg1,[]],[[[4],1]]]),0,_DG([["vector",Alg1,[]],[[[6],-1]]])],[e6,`| `,_DG([["vector",Alg1,[]],[[[2],1]]]),0,0,_DG([["vector",Alg1,[]],[[[3],1],[[5],2]]]),_DG([["vector",Alg1,[]],[[[6],1]]]),0]]]"

(3)
Alg1 > 

W1 := [a*e3+e5]

[a*_DG([["vector", Alg1, []], [[[3], 1]]])+_DG([["vector", Alg1, []], [[[5], 1]]])]

(4)
Alg1 > 

Nor[W1] := SubalgebraNormalizer(W1)

[_DG([["vector", Alg1, []], [[[5], 1]]]), _DG([["vector", Alg1, []], [[[3], 1]]])]

(5)

How one can find Quotient alegebra "(Nor[W1])/(W1)....???`? ``The expected answer is {e3}.`"

I am trying verify 4th 2-dimensional subalgebra results given in research artcle by Coggeshall and Meyer-ter-Vehn (See pp. 3592 in article).

Download [670]_Normalizer_in_Abstract_Lie_Algebra.mw

Regards

Dear All

I intend to convert Lie algebra into abstract Lie algebra with the aid of Maple packages DifferentialGeometry and Lie algebras. I want to do this for classification of Lie algebra for group inavriant solution, can anybody help me out.....?

Regards

Dear All

Please see following:

 

Suppose we have

M := proc (i) options operator, arrow; i/(i+1) end proc

proc (i) options operator, arrow; i/(i+1) end proc

(1)

and

F := proc (i, j) options operator, arrow; M(i)/(M(i)+j) end proc

proc (i, j) options operator, arrow; M(i)/(M(i)+j) end proc

(2)

 For i from 1 to 5 and j from 1 to 5, how one can display all values of F(i,j) using "loop" ???

 

Download loop.mw

Regards

Dear All

Please see following query:

 

 

 For following Algeraic expression

 

(3*a[1]+5*a[2])*U[1]+(-6*a[1]+2*a[2])*U[2]

 

How one can construct a matrix of the following form:

 

Matrix([[3, 5], [-6, 2]])

Matrix(2, 2, {(1, 1) = 3, (1, 2) = 5, (2, 1) = -6, (2, 2) = 2})

(1)

 

Where first row corresponds to U[1]and second row corresponds to U[2] and the entries of matrix are coefficients of a[1]and a[2]

 

 

Download Constructing_matrix_from_algebraic_expression.mw

Regards

First 6 7 8 9 10 11 12 Page 8 of 13