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Question: Use Maple to find a matrix formulation of expression

Question:Use Maple to find a matrix formulation of expression

Harry Garst 239 Maple
matrix
November 16 2017
0


 

NULL

> 

restart; with(LinearAlgebra)
> 

kernelopts(version); interface(version)

`Maple 2017.3, X86 64 WINDOWS, Sep 27 2017, Build ID 1265877`

  

`Standard Worksheet Interface, Maple 2017.3, Windows 10, September 27 2017 Build ID 1265877`

 (1)



The following equation contains so many regularities, that it is tantalizing to find a compact matrix formulation.
I found a matrix expression, but it seems unnecessairy complex. Is there a Maple procedure that can help me to find a more concise matrix formulation?

> 

eq1 := i2*i3*i4*(i2+i3+i4)+i1*i3*i4*(i1+i3+i4)+i1*i2*i4*(i1+i2+i4)+i1*i2*i3*(i1+i2+i3)

i2*i3*i4*(i2+i3+i4)+i1*i3*i4*(i1+i3+i4)+i1*i2*i4*(i1+i2+i4)+i1*i2*i3*(i1+i2+i3)

 (2)
> 

expand(eq1)

i1^2*i2*i3+i1^2*i2*i4+i1^2*i3*i4+i1*i2^2*i3+i1*i2^2*i4+i1*i2*i3^2+i1*i2*i4^2+i1*i3^2*i4+i1*i3*i4^2+i2^2*i3*i4+i2*i3^2*i4+i2*i3*i4^2

 (3)
> 

V := Matrix(4, 1, [i1, i2, i3, i4])

Matrix(%id = 18446745919887783806)

 (4)
> 

one := Matrix(4, 1, 1)

Matrix(%id = 18446745919887784886)

 (5)

This matrix expression works, but seems overly complex. Using Maple, is there a way to simplify it?

> 

Trace(MatrixScalarMultiply(one^%T.(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T))).convert(Diagonal(Adjoint(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T)))), Matrix), 1/2))-eq1

0

 (6)

Alternatively, but also not very simple:

> 

Trace(DiagonalMatrix(Diagonal(MatrixScalarMultiply(1/(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T))), (1/2)*Determinant(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T)))))).(KroneckerProduct(V^%T.one, IdentityMatrix(4))-DiagonalMatrix(V)))-eq1

0

 (7)

Obviously, this does not help:

> 

A, B := LinearAlgebra:-GenerateMatrix([eq1], [x])

Matrix(%id = 18446745919887762006), Vector[column](%id = 18446745919887761886)

 (8)

NULL


 

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