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Damon

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8 years, 361 days
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These are questions asked by Damon

Dot Product Commutativity...

Damon 20 Maple
vector product
September 25 2015
1 2

I want to make a dot product like

Eq6 := (sum(delta[i].v[i], i = 1 .. 3)).(sum(delta[j].w[j], j = 1 .. 3))

and get the complete result like

Eq7 := v[1].w[1]+v[2].w[2]+v[3].w[3]

but instead I get

Eq6 := ((Vector(3, {(1) = 1, (2) = 0, (3) = 0})).v[1]+(Vector(3, {(1) = 0, (2) = 1, (3) = 0})).v[2]+(Vector(3, {(1) = 0, (2) = 0, (3) = 1})).v[3]).((Vector(3, {(1) = 1, (2) = 0, (3) = 0})).w[1]+(Vector(3, {(1) = 0, (2) = 1, (3) = 0})).w[2]+(Vector(3, {(1) = 0, (2) = 0, (3) = 1})).w[3])

Is there a way to force the dot product operation all the way?

 DotProductCommutativity.mw

Epsilon-delta relationships...

Damon 20 Maple
tensor
September 25 2015
1 0

I’m trying to use Maple to develop tensor operations using the epsilon-delta notation as used in the attached document, which makes use of the following relationships

permutations.pdf    epsilondelta.pdf

I see how to generate permutations in Maple, and I see there is some mention of what I am trying to do in Maples definition of a signature.  But I am unable to see how to implement it.  Does anyone have any ideas?

Format of Vector Operation...

Damon 20
sum vector
September 23 2015
1 11

I define unit vectors as

delta[1] := Vector(3, {(1) = 1, (2) = 0, (3) = 0})

delta[2] := Vector(3, {(1) = 0, (2) = 1, (3) = 0})

delta[3] := Vector(3, {(1) = 0, (2) = 0, (3) = 1})

Then I manually take the dot product as

Eq3 := delta[1].delta[1]+delta[1].delta[2]+delta[1].delta[3]+delta[2].delta[1]+delta[2].delta[2]+delta[2].delta[3]+delta[3].delta[1]+delta[3].delta[2]+delta[3].delta[3]

and get

Eq3 := 3

But when I do this

Eq4 := sum(sum(delta[i].delta[j], j = 1 .. 3), i = 1 .. 3)

I get

Eq4 := Vector(3, {(1) = Vector(3, {(1) = 1, (2) = 1, (3) = 1}), (2) = Vector(3, {(1) = 1, (2) = 1, (3) = 1}), (3) = Vector(3, {(1) = 1, (2) = 1, (3) = 1})})

How can I make Maple give me the first result using the sum command?

 

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