Edit detail for SandBoxNonAssociativeAlgebra revision 1 of 25

axiom
all:=[a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4]

axiom
a:Vector DMP(all,INT):=[a1,a2,a3,a4]

axiom
b:Vector MPOLY(all,INT):=[b1,b2,b3,b4]

axiom
c:Vector MPOLY(all,INT):=[c1,c2,c3,c4]

axiom
_*_*(x,y)==concat(x(1) * y(1) + dot(x(2..), y(2..)), x(1) * y(2..) -
  Line   5: _*_*(x,y)==concat(x(1) * y(1) + dot(x(2..), y(2..)), x(1) * y(2..) -
           .................A.................................................B
  Error  A: Missing mate.
  Error  B: syntax error at top level
  Error  B: Possibly missing a ) 
   3 error(s) parsing 
x(2..) * y(1) + cross(x(2..), y(2..)))
  Line   6: x(2..) * y(1) + cross(x(2..), y(2..)))
           .....................................A
  Error  A: Improper syntax.
   1 error(s) parsing 
-- Jordan?
a ** (b ** c) + c ** (a ** b) + b ** (c ** a)
   There are 20 exposed and 18 unexposed library operations named ** 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op **
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named ** 
      with argument type(s) 
Vector MultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4],Integer)
Vector MultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4],Integer)
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
a0:Vector DMP(all,INT):=[0,a2,a3,a4]

axiom
b0:Vector MPOLY(all,INT):=[0,b2,b3,b4]

axiom
c0:Vector MPOLY(all,INT):=[0,c2,c3,c4]

axiom
-- Jordan?
a0 ** (b0 ** c0) + c0 ** (a0 ** b0) + b0 ** (c0 ** a0)
   There are 20 exposed and 18 unexposed library operations named ** 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op **
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named ** 
      with argument type(s) 
Vector MultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4],Integer)
Vector MultivariatePolynomial([a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4],Integer)
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.