Edit detail for numerical linear algebra revision 1 of 5

axiom
m := matrix([[random()$Integer for i in 1..10] for j in 1..10]); sm := m + transpose(m); smf:Matrix Float := sm

axiom
)set messages time on

axiom
eigen:=eigenvalues(sm)

axiom
Time: 0.55 (EV) + 0.15 (OT) + 0.30 (GC) = 1.00 sec
solve(rhs(eigen.1),15)

axiom
Time: 0.02 (IN) + 0.48 (EV) + 0.02 (OT) + 0.35 (GC) = 0.87 sec

axiom
charpol := reduce(*, [ rhs(x) - lhs(x) for x in % ])

axiom
Time: 0 sec

axiom
solve(x+11/10,3)

axiom
Time: 0.02 (IN) + 0.01 (EV) + 0.01 (OT) = 0.04 sec
ev:= solve(rhs(eigen.1),1.0*10^(-50))

axiom
Time: 0.01 (IN) + 0.49 (EV) + 0.07 (OT) + 0.28 (GC) = 0.85 sec
cp:= reduce(*, [rhs(x)-lhs(x) for x in ev])

axiom
Time: 0 sec

axiom
A:=[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0.02 (IN) + 0.02 (EV) + 0.08 (OT) = 0.12 sec

axiom
A:=[[a,b],[c,d]]

axiom
Time: 0.01 (OT) = 0.01 sec

axiom
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0.01 (EV) = 0.01 sec

axiom
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0 sec
eigen:=eigenvalues(A)
   There are 1 exposed and 0 unexposed library operations named 
      eigenvalues having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op eigenvalues
      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 
      eigenvalues with argument type(s) 
                          Matrix Expression Integer
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0 sec
\end{axiom
  Line   2: \end{axiom
           ....AB
  Error  A: Missing mate.
  Error  B: syntax error at top level
  Error  B: Possibly missing a } 
   3 error(s) parsing 
<div class="commentsheading"><a name="msg20050624075917-0500@page.axiom-developer.org"></a><b>test</b> --unknown,  <a href="http://axiom-wiki.newsynthesis.org/NumericalLinearAlgebra#msg20050624075917-0500@page.axiom-developer.org">Fri, 24 Jun 2005 07:59:17 -0500</a> <a href="http://axiom-wiki.newsynthesis.org/NumericalLinearAlgebra?subject=test&in_reply_to=%3C20050624075917-0500%40page.axiom-developer.org%3E#bottom">reply</a></div>\begin{axiom}
   There are no library operations named < having 1 argument(s) though 
      there are 4 exposed operation(s) and 1 unexposed operation(s) 
      having a different number of arguments. Use HyperDoc Browse, or 
      issue
                                 )what op <
      to learn what operations contain " < " in their names, or issue
                                )display op <
      to learn more about the available operations.
   Cannot find a definition or applicable library operation named < 
      with argument type(s) 
                                 Variable b
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0.01 (IN) = 0.01 sec

axiom
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

axiom
Time: 0.01 (OT) = 0.01 sec
A(1,1)

axiom
Time: 0 sec

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0.01 (IN) = 0.01 sec
A(1,1)*A(2,2)-A(2,1)*A(1,2)

axiom
Time: 0 sec

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0 sec
A(1,1)*A(2,2)

axiom
Time: 0 sec
A(2,1)*A(1,2)

axiom
Time: 0 sec

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0.01 (OT) = 0.01 sec
solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

axiom
Time: 0.02 (IN) + 0.10 (EV) + 0.03 (OT) + 0.07 (GC) = 0.22 sec

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0 sec
solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

axiom
Time: 0.01 (IN) = 0.01 sec
L

axiom
Time: 0 sec

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0.01 (OT) = 0.01 sec
B=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)
   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      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 
      equation with argument type(s) 
                                 Variable B
                      List Equation Expression Integer
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0.01 (OT) = 0.01 sec
solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

axiom
Time: 0 sec
L(1)
   There are no library operations named L 
      Use HyperDoc Browse or issue
                                 )what op L
      to learn if there is any operation containing " L " in its name.
   Cannot find a definition or applicable library operation named L 
      with argument type(s) 
                               PositiveInteger
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

axiom
Time: 0 sec
solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

axiom
Time: 0.01 (OT) = 0.01 sec
L.1
   There are no library operations named L 
      Use HyperDoc Browse or issue
                                 )what op L
      to learn if there is any operation containing " L " in its name.
   Cannot find a definition or applicable library operation named L 
      with argument type(s) 
                               PositiveInteger
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
solve(x^2,x)

axiom
Time: 0.01 (IN) = 0.01 sec

axiom
sqrt(2)

axiom
Time: 0 sec

axiom
solve(x^2=4,x)

axiom
Time: 0.02 (IN) + 0.01 (OT) = 0.03 sec

axiom
solve(x^2=4,x)

axiom
Time: 0 sec
x

axiom
Time: 0 sec

axiom
e=vector[1,2]
   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      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 
      equation with argument type(s) 
                                 Variable e
                           Vector PositiveInteger
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
e=solve(x^2=4,x)
   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      equation with argument type(s) 
                                 Variable e
                  List Equation Fraction Polynomial Integer
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
e=solve(x^2=4,x)
   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      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 
      equation with argument type(s) 
                                 Variable e
                  List Equation Fraction Polynomial Integer
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom
P:=matrix[[a, b], [1.0 - a, 1.0 - b]]

axiom
Time: 0.01 (IN) = 0.01 sec
eigenvectors(P)

axiom
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec