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# Edit detail for SandBoxMatrixExample revision 1 of 1

 1 Editor: Bill Page Time: 2009/10/16 12:10:59 GMT-7 Note: clean up

changed:
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Matrix Example

\begin{axiom}
m1 := matrix([ [1, x/y, 0], [0, 1, 0], [0, 0, 1] ])
m2 := matrix([ [1, 0, 0], [0, 1, y/x], [0, 0, 1] ])
m3 := matrix([ [-1/y, 0, 0], [0, y/(x*z), 0], [0, 0, x/(x*y-z*y)] ])
m4 := matrix([ [1, 0, 0], [0, 1, 0], [0, y/x, 1] ])
m5 := matrix([ [1, 0, 0], [z/y, 1, 0], [0, 0, 1] ])
m6 := matrix([ [0, 0, 1], [0, 1, 0], [1, 0, 0] ])

T := m1*m2*m3*m4*m5*m6
M := matrix([ [0, -z, y], [z, 0, -x], [-y, x, 0] ])
R := matrix([ [r, 0, 0], [0, r, 0], [0, 0, r] ])

T - R
determinant(%)

T * vector([bx, by, bc])

\end{axiom}

\begin{axiom}
R := matrix([ [cos(t), -sin(t), 0], [sin(t), cos(t), 0], [0,0,1] ])
T := transpose(R)

e11 := matrix( [ [1,0,0], [0,0,0], [0,0,0] ] )
e12 := matrix( [ [0,1,0], [0,0,0], [0,0,0] ] )
e13 := matrix( [ [0,0,1], [0,0,0], [0,0,0] ] )
e21 := matrix( [ [0,0,0], [1,0,0], [0,0,0] ] )
e22 := matrix( [ [0,0,0], [0,1,0], [0,0,0] ] )
e23 := matrix( [ [0,0,0], [0,0,1], [0,0,0] ] )
e31 := matrix( [ [0,0,0], [0,0,0], [1,0,0] ] )
e32 := matrix( [ [0,0,0], [0,0,0], [0,1,0] ] )
e33 := matrix( [ [0,0,0], [0,0,0], [0,0,1] ] )

T*e11*R
T*e12*R
T*e13*R
T*e21*R
T*e22*R
T*e23*R
T*e31*R
T*e32*R
T*e33*R
\end{axiom}


Matrix Example

fricas
m1 := matrix([ [1, x/y, 0], [0, 1, 0], [0, 0, 1] ])
 (1)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
m2 := matrix([ [1, 0, 0], [0, 1, y/x], [0, 0, 1] ])
 (2)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
m3 := matrix([ [-1/y, 0, 0], [0, y/(x*z), 0], [0, 0, x/(x*y-z*y)] ])
 (3)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
m4 := matrix([ [1, 0, 0], [0, 1, 0], [0, y/x, 1] ])
 (4)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
m5 := matrix([ [1, 0, 0], [z/y, 1, 0], [0, 0, 1] ])
 (5)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
m6 := matrix([ [0, 0, 1], [0, 1, 0], [1, 0, 0] ])
 (6)
Type: Matrix(NonNegativeInteger?)
fricas
T := m1*m2*m3*m4*m5*m6
 (7)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
M := matrix([ [0, -z, y], [z, 0, -x], [-y, x, 0] ])
 (8)
Type: Matrix(Polynomial(Integer))
fricas
R := matrix([ [r, 0, 0], [0, r, 0], [0, 0, r] ])
 (9)
Type: Matrix(Polynomial(Integer))
fricas
T - R
 (10)
Type: Matrix(Fraction(Polynomial(Integer)))
fricas
determinant(%)
 (11)
Type: Fraction(Polynomial(Integer))
fricas
T * vector([bx, by, bc])
 (12)
Type: Vector(Fraction(Polynomial(Integer)))

fricas
R := matrix([ [cos(t), -sin(t), 0], [sin(t), cos(t), 0], [0,0,1] ])
 (13)
Type: Matrix(Expression(Integer))
fricas
T := transpose(R)
 (14)
Type: Matrix(Expression(Integer))
fricas
e11 := matrix( [ [1,0,0], [0,0,0], [0,0,0] ] )
 (15)
Type: Matrix(NonNegativeInteger?)
fricas
e12 := matrix( [ [0,1,0], [0,0,0], [0,0,0] ] )
 (16)
Type: Matrix(NonNegativeInteger?)
fricas
e13 := matrix( [ [0,0,1], [0,0,0], [0,0,0] ] )
 (17)
Type: Matrix(NonNegativeInteger?)
fricas
e21 := matrix( [ [0,0,0], [1,0,0], [0,0,0] ] )
 (18)
Type: Matrix(NonNegativeInteger?)
fricas
e22 := matrix( [ [0,0,0], [0,1,0], [0,0,0] ] )
 (19)
Type: Matrix(NonNegativeInteger?)
fricas
e23 := matrix( [ [0,0,0], [0,0,1], [0,0,0] ] )
 (20)
Type: Matrix(NonNegativeInteger?)
fricas
e31 := matrix( [ [0,0,0], [0,0,0], [1,0,0] ] )
 (21)
Type: Matrix(NonNegativeInteger?)
fricas
e32 := matrix( [ [0,0,0], [0,0,0], [0,1,0] ] )
 (22)
Type: Matrix(NonNegativeInteger?)
fricas
e33 := matrix( [ [0,0,0], [0,0,0], [0,0,1] ] )
 (23)
Type: Matrix(NonNegativeInteger?)
fricas
T*e11*R
 (24)
Type: Matrix(Expression(Integer))
fricas
T*e12*R
 (25)
Type: Matrix(Expression(Integer))
fricas
T*e13*R
 (26)
Type: Matrix(Expression(Integer))
fricas
T*e21*R
 (27)
Type: Matrix(Expression(Integer))
fricas
T*e22*R
 (28)
Type: Matrix(Expression(Integer))
fricas
T*e23*R
 (29)
Type: Matrix(Expression(Integer))
fricas
T*e31*R
 (30)
Type: Matrix(Expression(Integer))
fricas
T*e32*R
 (31)
Type: Matrix(Expression(Integer))
fricas
T*e33*R
 (32)
Type: Matrix(Expression(Integer))