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#174 (1 . failed) cannot be coerced to mode (Integer) in TriangularMatrixOperations ←	↑	→ #176 Factored Polynomials aren't differentiated correctly

#175 Works on implementation and/or documentation of LieSquareMatrix

Edit detail for #175 Works on implementation and/or documentation of LieSquareMatrix revision 1 of 2

	1 2
Editor: Time: 2007/11/17 22:02:41 GMT-8
Note:

changed:
-
From the implementation of LieSquareMatrix::

    Exports ==> Join(SquareMatrixCategory(n,R,Row,Col), CoercibleTo Matrix R,_
      FramedNonAssociativeAlgebra R)


\begin{axiom}
lieAlgebra?()$LieSquareMatrix(2,FRAC INT)
a:=matrix([[1/2,3/4],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)
a*a
b:=matrix([[2,4/7],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)
a*b
1$LieSquareMatrix(2,FRAC INT)
\end{axiom}
\begin{axiom}
a:=matrix([[1/2,3/4],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)
minRowIndex a
\end{axiom}

From the implementation of LieSquareMatrix?:

    Exports ==> Join(SquareMatrixCategory(n,R,Row,Col), CoercibleTo Matrix R,_
      FramedNonAssociativeAlgebra R)

axiom

lieAlgebra?()$LieSquareMatrix(2,FRAC INT)

   algebra is anti-commutative
   Jacobi identity holds
   this is a Lie algebra

$\label{eq1} \mbox{\rm true}$

(1)

Type: Boolean

axiom

a:=matrix([[1/2,3/4],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)

$\label{eq2}\left[ \begin{array}{cc} {1 \over 2}&{3 \over 4} \ {7 \over 2}&{5 \over 7}$

(2)

Type: LieSquareMatrix?(2,Fraction(Integer))

axiom

a*a

$\label{eq3}\left[ \begin{array}{cc} 0 & 0 \ 0 & 0$

(3)

Type: LieSquareMatrix?(2,Fraction(Integer))

axiom

b:=matrix([[2,4/7],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)

$\label{eq4}\left[ \begin{array}{cc} 2 &{4 \over 7} \ {7 \over 2}&{5 \over 7}$

(4)

Type: LieSquareMatrix?(2,Fraction(Integer))

axiom

a*b

$\label{eq5}\left[ \begin{array}{cc} {5 \over 8}& -{{213}\over{196}} \ {{21}\over 4}& -{5 \over 8}$

(5)

Type: LieSquareMatrix?(2,Fraction(Integer))

axiom

1$LieSquareMatrix(2,FRAC INT)

   Internal Error
   The function One with signature () -> % is missing from domain 
      LieSquareMatrix2(Fraction (Integer))

axiom

a:=matrix([[1/2,3/4],[7/2,5/7]])$LieSquareMatrix(2,FRAC INT)

$\label{eq6}\left[ \begin{array}{cc} {1 \over 2}&{3 \over 4} \ {7 \over 2}&{5 \over 7}$

(6)

Type: LieSquareMatrix?(2,Fraction(Integer))

axiom

minRowIndex a

   Internal Error
   The function minRowIndex with signature hashcode is missing from 
      domain LieSquareMatrix2(Fraction (Integer))