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SandBoxNijenhuis  ← ↑ →  SandBoxNonZeroInteger

SandBoxNonAssociativeAlgebra
  
last edited 15 years ago by Bill Page

Edit detail for SandBoxNonAssociativeAlgebra revision 2 of 25
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Editor: Bill Page
Time: 2008/04/24 07:03:02 GMT-7
Note: Jordan 
changed:
-b:Vector MPOLY(all,INT):=[b1,b2,b3,b4]
-c:Vector MPOLY(all,INT):=[c1,c2,c3,c4]
-_*_*(x,y)==concat(x(1) * y(1) + dot(x(2..), y(2..)), x(1) * y(2..) -
-x(2..) * y(1) + cross(x(2..), y(2..)))
b:Vector DMP(all,INT):=[b1,b2,b3,b4]
c:Vector DMP(all,INT):=[c1,c2,c3,c4]
_*_*(x,y)==concat(x(1) * y(1) + dot(x(2..), y(2..)), x(1) * y(2..) - x(2..) * y(1) + cross(x(2..), y(2..)))

changed:
-b0:Vector MPOLY(all,INT):=[0,b2,b3,b4]
-c0:Vector MPOLY(all,INT):=[0,c2,c3,c4]
b0:Vector DMP(all,INT):=[0,b2,b3,b4]
c0:Vector DMP(all,INT):=[0,c2,c3,c4]


axiom
all:=[a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]
LatexWiki Image(1)
Type: List OrderedVariableList? [a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?
axiom
a:Vector DMP(all,INT):=[a1,a2,a3,a4]
LatexWiki Image(2)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
b:Vector DMP(all,INT):=[b1,b2,b3,b4]
LatexWiki Image(3)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
c:Vector DMP(all,INT):=[c1,c2,c3,c4]
LatexWiki Image(4)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
_*_*(x,y)==concat(x(1) * y(1) + dot(x(2..), y(2..)), x(1) * y(2..) - x(2..) * y(1) + cross(x(2..), y(2..)))
Type: Void
axiom
-- Jordan?
a ** (b ** c) + c ** (a ** b) + b ** (c ** a)
axiom
Compiling function ** with type (Vector 
      DistributedMultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,
      c3,c4],Integer),Vector DistributedMultivariatePolynomial([a1,a2,
      a3,a4,b1,b2,b3,b4,c1,c2,c3,c4],Integer)) -> Vector 
      DistributedMultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,
      c3,c4],Integer)
LatexWiki Image(5)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
a0:Vector DMP(all,INT):=[0,a2,a3,a4]
LatexWiki Image(6)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
b0:Vector DMP(all,INT):=[0,b2,b3,b4]
LatexWiki Image(7)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
c0:Vector DMP(all,INT):=[0,c2,c3,c4]
LatexWiki Image(8)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)
axiom
-- Jordan?
a0 ** (b0 ** c0) + c0 ** (a0 ** b0) + b0 ** (c0 ** a0)
LatexWiki Image(9)
Type: Vector DistributedMultivariatePolynomial?([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]?,Integer)