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Ronan

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13 years, 351 days
East Grinstead, United Kingdom
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Dual Quaternion Multiplication Table ...

Ronan 1396 Maple 18
algebra multiplication
February 29 2016
1 1


I am trying to setup a Dual Quaternion Multiplication Table. I found the table on Wikki. I  need some help here.

Have set

x1  =1   x2 = i   x3  =j   x4   =k   x5 =e   x6 = ei   x7 = ej   x8 =ek

 

restart

                                                                                                              #    x1   x2    x3   x4    x5   x6    x7   x8

with(DifferentialGeometry):

NULL

 

StructureEquations := [[x1, x1] = x1, [x1, x2] = x2, [x1, x3] = x3, [x1, x4] = x4, [x1, x5] = x1*x5, [x1, x6] = x6, [x1, x7] = x7, [x1, x8] = x8, [x2, x1] = x2, [x2, x2] = -1, [x2, x3] = x4, [x2, x4] = -x3, [x2, x5] = x6, [x2, x6] = -x5, [x2, x7] = x8, [x2, x8] = -x7, [x3, x1] = x3, [x3, x2] = -x4, [x3, x3] = -1, [x3, x4] = x2, [x3, x5] = x7, [x3, x6] = -x8, [x3, x7] = -x5, [x3, x8] = x6, [x4, x1] = x4, [x4, x2] = x3, [x4, x3] = -x2, [x4, x4] = -1, [x4, x5] = x8, [x4, x6] = x7, [x4, x7] = -x6, [x4, x8] = -x5, [x5, x1] = x5, [x5, x2] = x6, [x5, x3] = x7, [x5, x4] = x8, [x5, x5] = 0, [x6, x1] = x6, [x6, x2] = -x5, [x6, x3] = x8, [x6, x4] = -x7, [x7, x1] = x7, [x7, x2] = -x8, [x7, x3] = -x5, [x7, x4] = x6, [x8, x1] = x8, [x8, x2] = x7, [x8, x3] = -x6, [x8, x4] = -x5]

[[x1, x1] = x1, [x1, x2] = x2, [x1, x3] = x3, [x1, x4] = x4, [x1, x5] = x1*x5, [x1, x6] = x6, [x1, x7] = x7, [x1, x8] = x8, [x2, x1] = x2, [x2, x2] = -1, [x2, x3] = x4, [x2, x4] = -x3, [x2, x5] = x6, [x2, x6] = -x5, [x2, x7] = x8, [x2, x8] = -x7, [x3, x1] = x3, [x3, x2] = -x4, [x3, x3] = -1, [x3, x4] = x2, [x3, x5] = x7, [x3, x6] = -x8, [x3, x7] = -x5, [x3, x8] = x6, [x4, x1] = x4, [x4, x2] = x3, [x4, x3] = -x2, [x4, x4] = -1, [x4, x5] = x8, [x4, x6] = x7, [x4, x7] = -x6, [x4, x8] = -x5, [x5, x1] = x5, [x5, x2] = x6, [x5, x3] = x7, [x5, x4] = x8, [x5, x5] = 0, [x6, x1] = x6, [x6, x2] = -x5, [x6, x3] = x8, [x6, x4] = -x7, [x7, x1] = x7, [x7, x2] = -x8, [x7, x3] = -x5, [x7, x4] = x6, [x8, x1] = x8, [x8, x2] = x7, [x8, x3] = -x6, [x8, x4] = -x5]

 (1)

``

 (2)

DQ := LieAlgebraData(StructureEquations, [x1, x2, x3, x4, x5, x6, x7, x8])

_DG([["LieAlgebra", "L1", [8, table( [ ] )]], [[[1, 2, 2], 1], [[1, 3, 3], 1], [[1, 4, 4], 1], [[1, 5, 1], x5], [[1, 5, 5], x1], [[1, 6, 6], 1], [[1, 7, 7], 1], [[1, 8, 8], 1], [[1, 2, 2], -1], [[2, 3, 4], 1], [[2, 4, 3], -1], [[2, 5, 6], 1], [[2, 6, 5], -1], [[2, 7, 8], 1], [[2, 8, 7], -1], [[1, 3, 3], -1], [[2, 3, 4], 1], [[3, 4, 2], 1], [[3, 5, 7], 1], [[3, 6, 8], -1], [[3, 7, 5], -1], [[3, 8, 6], 1], [[1, 4, 4], -1], [[2, 4, 3], -1], [[3, 4, 2], 1], [[4, 5, 8], 1], [[4, 6, 7], 1], [[4, 7, 6], -1], [[4, 8, 5], -1], [[1, 5, 5], -1], [[2, 5, 6], -1], [[3, 5, 7], -1], [[4, 5, 8], -1], [[1, 6, 6], -1], [[2, 6, 5], 1], [[3, 6, 8], -1], [[4, 6, 7], 1], [[1, 7, 7], -1], [[2, 7, 8], 1], [[3, 7, 5], 1], [[4, 7, 6], -1], [[1, 8, 8], -1], [[2, 8, 7], -1], [[3, 8, 6], 1], [[4, 8, 5], 1]]])

 (3)

DGsetup(DQ)

`Lie algebra: L1`

 (4)

MultiplicationTable(DQ, "AlgebraTable")

Error, (in DifferentialGeometry:-LieAlgebras:-MultiplicationTable) invalid input: DifferentialGeometry:-ChangeFrame expects its 1st argument, frame_name, to be of type {name, string}, but received _DG([["LieAlgebra", "L1", [8, table( [ ] )]], [[[1, 2, 2], 1], [[1, 3, 3], 1], [[1, 4, 4], 1], [[1, 5, 1], x5], [[1, 5, 5], x1], [[1, 6, 6], 1], [[1, 7, 7], 1], [[1, 8, 8], 1], [[1, 2, 2], -1], [[2, 3, 4], 1], [[2, 4, 3], -1], [[2, 5, 6], 1], [[2, 6, 5], -1], [[2, 7, 8], 1], [[2, 8, 7], -1], [[1, 3, 3], -1], [[2, 3, 4], 1], [[3, 4, 2], 1], [[3, 5, 7], 1], [[3, 6, 8], -1], [[3, 7, 5], -1], [[3, 8, 6], 1], [[1, 4, 4], -1], [[2, 4, 3], -1], [[3, 4, 2]...

  

NULL

 

Download Dual_Quaternion_Defining_Algebra.mw

 

Listing monomials...

Ronan 1396 Maple 18
February 13 2016
2 9

I an experimenting with Groebner basis. Have a set 17 equations. There are 12 unknowns. Using 14 of the equations and tdeg, the system produced 65 equations. How do I get a list of the monomials in this new list?

How do I preform a particular substituti...

Ronan 1396 Maple 18
simplify substitution applyrule
December 24 2014
2 1


I am trying to do a substitution as shown in the attached document. I know variants of this question have been asked before but dont quiet get what to do. It is problem with algsubs and how it handles denominators I think. Can get substiturion to work for simple fractions but more complicated ones fail. Would appreciate any guidance here.

restart 

``

``

CR := proc (a, b, c, d) options operator, arrow; (a-c)*(b-d)/((a-d)*(b-c)) end proc

proc (a, b, c, d) options operator, arrow; (a-c)*(b-d)/((a-d)*(b-c)) end proc

 (1)

eqns := CR(a, b, c, d)

(a-c)*(b-d)/((a-d)*(b-c))

 (2)

e1 := CR(b, a, c, d)

(b-c)*(a-d)/((b-d)*(a-c))

 (3)

simplify(e1, {(a-c)*(b-d)/((a-d)*(b-c)) = lambda})

(a*b-a*c-b*d+c*d)/(a*b-a*d-b*c+c*d)

 (4)

e1

(b-c)*(a-d)/((b-d)*(a-c))

 (5)

``

lambda

lambda

 (6)

applyrule((a-c)*(b-d)/((a-d)*(b-c)) = lambda, e1)

(b-c)*(a-d)/((b-d)*(a-c))

 (7)

alias(lambda = (a-c)*(b-d)/((a-d)*(b-c)))

lambda

 (8)

e1

(b-c)*(a-d)/((b-d)*(a-c))

 (9)

``

NULL

``

f := a/b

a/b

 (10)

``

f := algsubs(a/b = alpha, f)

alpha

 (11)

f

alpha

 (12)

algsubs((a-c)*(b-d)/((a-d)*(b-c)) = lambda, e1)

Error, (in algsubs) cannot compute degree of pattern in a

  

``

 

Download UHG5_substitution.mw

Work Sheet issue...

Ronan 1396 Maple
worksheet
May 27 2014
1 2

Using maple 16. When I run a worksheet it adds in extra rows of the red >s. The attached example was run 3 times. How do I stop this happening?

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solve(x^(2*x)+6)

(1/2)*(ln(6)+I*Pi)/LambertW((1/2)*ln(6)+((1/2)*I)*Pi)

 (1)
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solve(y+4 = 0)

-4

 (2)
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Download worksheet_issue.mw

Obtain output in matrix format...

Ronan 1396 Maple 16
matrix
November 01 2013
0 0

Hello

Am trying to convert a vector projection to matrix type output.

Attached is a sample worksheet.

 

Transformation_matri.mw 

 

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