Edit detail for SandBox Matrix revision 1 of 6

Symbolic Matrices

\begin{axiom}
A:=matrix [[x,y],[z,w]]
A+1
\end{axiom}


test --unknown,  Fri, 24 Jun 2005 04:29:59 -0500 reply
\begin{axiom}
A+2
\end{axiom}


Use the Edit and Preview Functions
  Hey, why not learn to use the edit function
instead of entering such a large number of similar
comments?
Look at the top right hand side of the page.

test --unknown,  Fri, 24 Jun 2005 13:46:29 -0500 reply
\begin{axiom}
N:=matrix[[0],[0]]
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
v:=matrix[[v11],[v12]]
C:=Av-L(1,1)v
solve(C(1,1)=0,v11)
solve(C(2,1)=0,v12)
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
W:=(V(1,1)V(2,2) - V(1,2)V(2,1))
\end{axiom}

test --unknown,  Fri, 24 Jun 2005 13:47:22 -0500 reply
\begin{axiom}
N:=matrix[[0],[0]]
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
v:=matrix[[v11],[v12]]
C:=Av-L(1,1)v
solve(C(1,1)=0,v11)
solve(C(2,1)=0,v12)
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
V(1,1)V(2,2)
V(1,2)V(2,1)
\end{axiom}

test --unknown,  Fri, 24 Jun 2005 13:54:11 -0500 reply
\begin{axiom}
N:=matrix[[0],[0]]
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
v:=matrix[[v11],[v12]]
C:=Av-L(1,1)v
solve(C(1,1)=0,v11)
solve(C(2,1)=0,v12)
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
a:=sqrt(T(1,1)^2+T(2,1)^2)
b=sqrt(T(1,2)^2+T(2,2)^2)
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
V(1,1)V(2,2)
V(1,2)V(2,1)
\end{axiom}

test --unknown,  Fri, 24 Jun 2005 13:55:30 -0500 reply
\begin{axiom}
N:=matrix[[0],[0]]
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
v:=matrix[[v11],[v12]]
C:=Av-L(1,1)v
solve(C(1,1)=0,v11)
solve(C(2,1)=0,v12)
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
sqrt(T(1,1)^2+T(2,1)^2)
sqrt(T(1,2)^2+T(2,2)^2)
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
V(1,1)V(2,2)
V(1,2)V(2,1)
\end{axiom}

... --unknown,  Wed, 26 Oct 2005 13:10:47 -0500 reply
\begin{axiom}
inverse([[1,2], [3,4]])
\end{axiom}

... --unknown,  Fri, 11 Nov 2005 10:34:24 -0600 reply
\begin{axiom}
A:=matrix[[1,1,0],[1,0,0],[0,0,1],[0,1,1],[1,1,1]]
\end{axiom}

... --unknown,  Fri, 11 Nov 2005 10:36:09 -0600 reply
\begin{axiom}
v:=matrix[[2],[1],[0],[1],[2]]
\end{axiom}

msm_test:=matrix[[a,b,c],[b,d,e],[c,e,f]] --isssso,  Wed, 04 Oct 2006 07:29:36 -0500 reply

my matrix test --isssso,  Wed, 04 Oct 2006 07:56:29 -0500 reply
\begin{axiom}
msm_test2:=matrix[[a,b,c,d,e],[b,f,g,h,i],[c,g,j,k,l],[d,h,k,m,n],[e,i,l,n,o]]
det:=determinant(msm_test2)
inv:=inverse(m)
\end{axiom}

my matrix test --isssso,  Wed, 04 Oct 2006 07:56:37 -0500 reply
\begin{axiom}
msm_test2:=matrix[[a,b,c,d,e],[b,f,g,h,i],[c,g,j,k,l],[d,h,k,m,n],[e,i,l,n,o]]
det:=determinant(msm_test2)
inv:=inverse(msm_test2)
\end{axiom}

    Some or all expressions may not have rendered properly,
    because Axiom returned the following error:
Error: export AXIOM=/usr/local/lib/axiom/target/x86_64-unknown-linux; ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; $AXIOM/bin/AXIOMsys < /var/zope2/var/LatexWiki/179881548081827695-25px.axm

GCL (GNU Common Lisp)  2.6.8 CLtL1    Nov  9 2007 07:47:56
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
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Dedicated to the memory of W. Schelter
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                 FriCAS (AXIOM fork) Computer Algebra System 
                         Version: FriCAS 2007-10-02
               Timestamp: Friday November 9, 2007 at 19:35:06 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------
(1) -> (1) -> (1) -> (1) -> (1) -> A:=matrix [[x,y],[z,w]]
$$
\left[
\begin{array}{cc}
x & y \ 
z & w 
\end{array}
\right]
\leqno(1)
$$
                                              Type: Matrix Polynomial Integer
A+1

$$
\left[
\begin{array}{cc}
{x+1} & y \ 
z & {w+1} 
\end{array}
\right]
\leqno(2)
$$
                                     Type: SquareMatrix(2,Polynomial Integer)
(3) -> A+2

$$
\left[
\begin{array}{cc}
{x+2} & y \ 
z & {w+2} 
\end{array}
\right]
\leqno(3)
$$
                                     Type: SquareMatrix(2,Polynomial Integer)
(4) -> N:=matrix[[0],[0]]

$$
\left[
\begin{array}{c}
0 \ 
0 
\end{array}
\right]
\leqno(4)
$$
                                                         Type: Matrix Integer
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$$
\left[
{\left[ {{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]},
\: {\left[ {-{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]}
\right]
\leqno(5)
$$
                                           Type: List List Expression Integer
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$$
\left[
\begin{array}{cc}
{\cos 
\left(
{x} 
\right)}
& -{\sin 
\left(
{x} 
\right)}
\ 
{\sin 
\left(
{x} 
\right)}
& {\cos 
\left(
{x} 
\right)}
\end{array}
\right]
\leqno(6)
$$
                                              Type: Matrix Expression Integer
v:=matrix[[v11],[v12]]

$$
\left[
\begin{array}{c}
v11 \ 
v12 
\end{array}
\right]
\leqno(7)
$$
                                              Type: Matrix Polynomial Integer
C:=Av-L(1,1)v

$$
\left[
\begin{array}{c}
{{\left( -{v11 \  {\sqrt {-1}}} -v12 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\ 
{{\left( -{v12 \  {\sqrt {-1}}}+v11 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\end{array}
\right]
\leqno(8)
$$
                                              Type: Matrix Expression Integer
solve(C(1,1)=0,v11)

$$
\left[
{v11=-{v12 \over {\sqrt {-1}}}} 
\right]
\leqno(9)
$$
                                       Type: List Equation Expression Integer
solve(C(2,1)=0,v12)

$$
\left[
{v12={v11 \over {\sqrt {-1}}}} 
\right]
\leqno(10)
$$
                                       Type: List Equation Expression Integer
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$$
\left[
\begin{array}{cc}
-{\sqrt {-1}} & 1 \ 
1 & {\sqrt {-1}} 
\end{array}
\right]
\leqno(11)
$$
                                                 Type: Matrix AlgebraicNumber
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$$
\left[
\begin{array}{cc}
{\sqrt {-1}} & -1 \ 
-1 & -{\sqrt {-1}} 
\end{array}
\right]
\leqno(12)
$$
                                                 Type: Matrix AlgebraicNumber
W:=(V(1,1)V(2,2) - V(1,2)V(2,1))

$$
0 
\leqno(13)
$$
                                                        Type: AlgebraicNumber
(14) -> N:=matrix[[0],[0]]

$$
\left[
\begin{array}{c}
0 \ 
0 
\end{array}
\right]
\leqno(14)
$$
                                                         Type: Matrix Integer
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$$
\left[
{\left[ {{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]},
\: {\left[ {-{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]}
\right]
\leqno(15)
$$
                                           Type: List List Expression Integer
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$$
\left[
\begin{array}{cc}
{\cos 
\left(
{x} 
\right)}
& -{\sin 
\left(
{x} 
\right)}
\ 
{\sin 
\left(
{x} 
\right)}
& {\cos 
\left(
{x} 
\right)}
\end{array}
\right]
\leqno(16)
$$
                                              Type: Matrix Expression Integer
v:=matrix[[v11],[v12]]

$$
\left[
\begin{array}{c}
v11 \ 
v12 
\end{array}
\right]
\leqno(17)
$$
                                              Type: Matrix Polynomial Integer
C:=Av-L(1,1)v

$$
\left[
\begin{array}{c}
{{\left( -{v11 \  {\sqrt {-1}}} -v12 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\ 
{{\left( -{v12 \  {\sqrt {-1}}}+v11 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\end{array}
\right]
\leqno(18)
$$
                                              Type: Matrix Expression Integer
solve(C(1,1)=0,v11)

$$
\left[
{v11=-{v12 \over {\sqrt {-1}}}} 
\right]
\leqno(19)
$$
                                       Type: List Equation Expression Integer
solve(C(2,1)=0,v12)

$$
\left[
{v12={v11 \over {\sqrt {-1}}}} 
\right]
\leqno(20)
$$
                                       Type: List Equation Expression Integer
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$$
\left[
\begin{array}{cc}
-{\sqrt {-1}} & 1 \ 
1 & {\sqrt {-1}} 
\end{array}
\right]
\leqno(21)
$$
                                                 Type: Matrix AlgebraicNumber
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$$
\left[
\begin{array}{cc}
{\sqrt {-1}} & -1 \ 
-1 & -{\sqrt {-1}} 
\end{array}
\right]
\leqno(22)
$$
                                                 Type: Matrix AlgebraicNumber
V(1,1)*V(2,2)

$$
1 
\leqno(23)
$$
                                                        Type: AlgebraicNumber
V(1,2)*V(2,1)

$$
1 
\leqno(24)
$$
                                                        Type: AlgebraicNumber
(25) -> N:=matrix[[0],[0]]

$$
\left[
\begin{array}{c}
0 \ 
0 
\end{array}
\right]
\leqno(25)
$$
                                                         Type: Matrix Integer
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$$
\left[
{\left[ {{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]},
\: {\left[ {-{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]}
\right]
\leqno(26)
$$
                                           Type: List List Expression Integer
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$$
\left[
\begin{array}{cc}
{\cos 
\left(
{x} 
\right)}
& -{\sin 
\left(
{x} 
\right)}
\ 
{\sin 
\left(
{x} 
\right)}
& {\cos 
\left(
{x} 
\right)}
\end{array}
\right]
\leqno(27)
$$
                                              Type: Matrix Expression Integer
v:=matrix[[v11],[v12]]

$$
\left[
\begin{array}{c}
v11 \ 
v12 
\end{array}
\right]
\leqno(28)
$$
                                              Type: Matrix Polynomial Integer
C:=Av-L(1,1)v

$$
\left[
\begin{array}{c}
{{\left( -{v11 \  {\sqrt {-1}}} -v12 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\ 
{{\left( -{v12 \  {\sqrt {-1}}}+v11 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\end{array}
\right]
\leqno(29)
$$
                                              Type: Matrix Expression Integer
solve(C(1,1)=0,v11)

$$
\left[
{v11=-{v12 \over {\sqrt {-1}}}} 
\right]
\leqno(30)
$$
                                       Type: List Equation Expression Integer
solve(C(2,1)=0,v12)

$$
\left[
{v12={v11 \over {\sqrt {-1}}}} 
\right]
\leqno(31)
$$
                                       Type: List Equation Expression Integer
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$$
\left[
\begin{array}{cc}
-{\sqrt {-1}} & 1 \ 
1 & {\sqrt {-1}} 
\end{array}
\right]
\leqno(32)
$$
                                                 Type: Matrix AlgebraicNumber
a:=sqrt(T(1,1)^2+T(2,1)^2)

$$
0 
\leqno(33)
$$
                                                        Type: AlgebraicNumber
b=sqrt(T(1,2)^2+T(2,2)^2)

$$
b=0 
\leqno(34)
$$
                                    Type: Equation Polynomial AlgebraicNumber
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$$
\left[
\begin{array}{cc}
{\sqrt {-1}} & -1 \ 
-1 & -{\sqrt {-1}} 
\end{array}
\right]
\leqno(35)
$$
                                                 Type: Matrix AlgebraicNumber
V(1,1)*V(2,2)

$$
1 
\leqno(36)
$$
                                                        Type: AlgebraicNumber
V(1,2)*V(2,1)

$$
1 
\leqno(37)
$$
                                                        Type: AlgebraicNumber
(38) -> N:=matrix[[0],[0]]

$$
\left[
\begin{array}{c}
0 \ 
0 
\end{array}
\right]
\leqno(38)
$$
                                                         Type: Matrix Integer
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$$
\left[
{\left[ {{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]},
\: {\left[ {-{{\sqrt {-1}} \  {\sin 
\left(
{x} 
\right)}}+{\cos
\left(
{x} 
\right)}}
\right]}
\right]
\leqno(39)
$$
                                           Type: List List Expression Integer
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$$
\left[
\begin{array}{cc}
{\cos 
\left(
{x} 
\right)}
& -{\sin 
\left(
{x} 
\right)}
\ 
{\sin 
\left(
{x} 
\right)}
& {\cos 
\left(
{x} 
\right)}
\end{array}
\right]
\leqno(40)
$$
                                              Type: Matrix Expression Integer
v:=matrix[[v11],[v12]]

$$
\left[
\begin{array}{c}
v11 \ 
v12 
\end{array}
\right]
\leqno(41)
$$
                                              Type: Matrix Polynomial Integer
C:=Av-L(1,1)v

$$
\left[
\begin{array}{c}
{{\left( -{v11 \  {\sqrt {-1}}} -v12 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\ 
{{\left( -{v12 \  {\sqrt {-1}}}+v11 
\right)}
\  {\sin 
\left(
{x} 
\right)}}
\end{array}
\right]
\leqno(42)
$$
                                              Type: Matrix Expression Integer
solve(C(1,1)=0,v11)

$$
\left[
{v11=-{v12 \over {\sqrt {-1}}}} 
\right]
\leqno(43)
$$
                                       Type: List Equation Expression Integer
solve(C(2,1)=0,v12)

$$
\left[
{v12={v11 \over {\sqrt {-1}}}} 
\right]
\leqno(44)
$$
                                       Type: List Equation Expression Integer
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$$
\left[
\begin{array}{cc}
-{\sqrt {-1}} & 1 \ 
1 & {\sqrt {-1}} 
\end{array}
\right]
\leqno(45)
$$
                                                 Type: Matrix AlgebraicNumber
sqrt(T(1,1)^2+T(2,1)^2)

$$
0 
\leqno(46)
$$
                                                        Type: AlgebraicNumber
sqrt(T(1,2)^2+T(2,2)^2)

$$
0 
\leqno(47)
$$
                                                        Type: AlgebraicNumber
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$$
\left[
\begin{array}{cc}
{\sqrt {-1}} & -1 \ 
-1 & -{\sqrt {-1}} 
\end{array}
\right]
\leqno(48)
$$
                                                 Type: Matrix AlgebraicNumber
V(1,1)*V(2,2)

$$
1 
\leqno(49)
$$
                                                        Type: AlgebraicNumber
V(1,2)*V(2,1)

$$
1 
\leqno(50)
$$
                                                        Type: AlgebraicNumber
(51) -> inverse([[1,2], [3,4]])

$$
\left[
\begin{array}{cc}
-2 & 1 \ 
{3 \over 2} & -{1 \over 2} 
\end{array}
\right]
\leqno(51)
$$
                                     Type: Union(Matrix Fraction Integer,...)
(52) -> A:=matrix[[1,1,0],[1,0,0],[0,0,1],[0,1,1],[1,1,1]]

$$
\left[
\begin{array}{ccc}
1 & 1 & 0 \ 
1 & 0 & 0 \ 
0 & 0 & 1 \ 
0 & 1 & 1 \ 
1 & 1 & 1 
\end{array}
\right]
\leqno(52)
$$
                                                         Type: Matrix Integer
(53) -> v:=matrix[[2],[1],[0],[1],[2]]

$$
\left[
\begin{array}{c}
2 \ 
1 \ 
0 \ 
1 \ 
2 
\end{array}
\right]
\leqno(53)
$$
                                                         Type: Matrix Integer
(54) -> msm_test2:=matrix[[a,b,c,d,e],[b,f,g,h,i],[c,g,j,k,l],[d,h,k,m,n],[e,i,l,n,o]]

$$
\left[
\begin{array}{ccccc}
0 & b & c & d & e \ 
b & f & g & h & i \ 
c & g & j & k & l \ 
d & h & k & m & n \ 
e & i & l & n & o 
\end{array}
\right]
\leqno(54)
$$
                                      Type: Matrix Polynomial AlgebraicNumber
det:=determinant(msm_test2)

$$
{{\left( {{\left( -{{b \sp 2} \  j}+{2 \  b \  c \  g} -{{c \sp 2} \  f} 
\right)}
\  m}+{{b \sp 2} \  {k \sp 2}}+{{\left( -{2 \  b \  c \  h} -{2 \  b \  d \  
g}+{2 \  c \  d \  f} 
\right)}
\  k}+{{\left( {2 \  b \  d \  h} -{{d \sp 2} \  f} 
\right)}
\  j}+{{c \sp 2} \  {h \sp 2}} -{2 \  c \  d \  g \  h}+{{d \sp 2} \  {g \sp 
2}} 
\right)}
\  o}+{{\left( {{b \sp 2} \  j} -{2 \  b \  c \  g}+{{c \sp 2} \  f} 
\right)}
\  {n \sp 2}}+{{\left( {{\left( -{2 \  {b \sp 2} \  k}+{2 \  b \  c \  h}+{2 
\  b \  d \  g} -{2 \  c \  d \  f} 
\right)}
\  l}+{{\left( {2 \  b \  c \  i}+{2 \  b \  e \  g} -{2 \  c \  e \  f} 
\right)}
\  k}+{{\left( -{2 \  b \  d \  i} -{2 \  b \  e \  h}+{2 \  d \  e \  f} 
\right)}
\  j}+{{\left( -{2 \  {c \sp 2} \  h}+{2 \  c \  d \  g} 
\right)}
\  i}+{2 \  c \  e \  g \  h} -{2 \  d \  e \  {g \sp 2}} 
\right)}
\  n}+{{\left( {{b \sp 2} \  {l \sp 2}}+{{\left( -{2 \  b \  c \  i} -{2 \  b 
\  e \  g}+{2 \  c \  e \  f} 
\right)}
\  l}+{{\left( {2 \  b \  e \  i} -{{e \sp 2} \  f} 
\right)}
\  j}+{{c \sp 2} \  {i \sp 2}} -{2 \  c \  e \  g \  i}+{{e \sp 2} \  {g \sp 
2}} 
\right)}
\  m}+{{\left( -{2 \  b \  d \  h}+{{d \sp 2} \  f} 
\right)}
\  {l \sp 2}}+{{\left( {{\left( {2 \  b \  d \  i}+{2 \  b \  e \  h} -{2 \  
d \  e \  f} 
\right)}
\  k}+{{\left( {2 \  c \  d \  h} -{2 \  {d \sp 2} \  g} 
\right)}
\  i} -{2 \  c \  e \  {h \sp 2}}+{2 \  d \  e \  g \  h} 
\right)}
\  l}+{{\left( -{2 \  b \  e \  i}+{{e \sp 2} \  f} 
\right)}
\  {k \sp 2}}+{{\left( -{2 \  c \  d \  {i \sp 2}}+{{\left( {2 \  c \  e \  
h}+{2 \  d \  e \  g} 
\right)}
\  i} -{2 \  {e \sp 2} \  g \  h} 
\right)}
\  k}+{{\left( {{d \sp 2} \  {i \sp 2}} -{2 \  d \  e \  h \  i}+{{e \sp 2} \  
{h \sp 2}} 
\right)}
\  j} 
\leqno(55)
$$
                                             Type: Polynomial AlgebraicNumber
inv:=inverse(m)
   There are 4 exposed and 3 unexposed library operations named inverse
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op inverse
      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 
      inverse with argument type(s) 
                                 Variable m
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
(56) -> msm_test2:=matrix[[a,b,c,d,e],[b,f,g,h,i],[c,g,j,k,l],[d,h,k,m,n],[e,i,l,n,o]]


$$
\left[
\begin{array}{ccccc}
0 & b & c & d & e \ 
b & f & g & h & i \ 
c & g & j & k & l \ 
d & h & k & m & n \ 
e & i & l & n & o 
\end{array}
\right]
\leqno(56)
$$
                                      Type: Matrix Polynomial AlgebraicNumber
det:=determinant(msm_test2)

$$
{{\left( {{\left( -{{b \sp 2} \  j}+{2 \  b \  c \  g} -{{c \sp 2} \  f} 
\right)}
\  m}+{{b \sp 2} \  {k \sp 2}}+{{\left( -{2 \  b \  c \  h} -{2 \  b \  d \  
g}+{2 \  c \  d \  f} 
\right)}
\  k}+{{\left( {2 \  b \  d \  h} -{{d \sp 2} \  f} 
\right)}
\  j}+{{c \sp 2} \  {h \sp 2}} -{2 \  c \  d \  g \  h}+{{d \sp 2} \  {g \sp 
2}} 
\right)}
\  o}+{{\left( {{b \sp 2} \  j} -{2 \  b \  c \  g}+{{c \sp 2} \  f} 
\right)}
\  {n \sp 2}}+{{\left( {{\left( -{2 \  {b \sp 2} \  k}+{2 \  b \  c \  h}+{2 
\  b \  d \  g} -{2 \  c \  d \  f} 
\right)}
\  l}+{{\left( {2 \  b \  c \  i}+{2 \  b \  e \  g} -{2 \  c \  e \  f} 
\right)}
\  k}+{{\left( -{2 \  b \  d \  i} -{2 \  b \  e \  h}+{2 \  d \  e \  f} 
\right)}
\  j}+{{\left( -{2 \  {c \sp 2} \  h}+{2 \  c \  d \  g} 
\right)}
\  i}+{2 \  c \  e \  g \  h} -{2 \  d \  e \  {g \sp 2}} 
\right)}
\  n}+{{\left( {{b \sp 2} \  {l \sp 2}}+{{\left( -{2 \  b \  c \  i} -{2 \  b 
\  e \  g}+{2 \  c \  e \  f} 
\right)}
\  l}+{{\left( {2 \  b \  e \  i} -{{e \sp 2} \  f} 
\right)}
\  j}+{{c \sp 2} \  {i \sp 2}} -{2 \  c \  e \  g \  i}+{{e \sp 2} \  {g \sp 
2}} 
\right)}
\  m}+{{\left( -{2 \  b \  d \  h}+{{d \sp 2} \  f} 
\right)}
\  {l \sp 2}}+{{\left( {{\left( {2 \  b \  d \  i}+{2 \  b \  e \  h} -{2 \  
d \  e \  f} 
\right)}
\  k}+{{\left( {2 \  c \  d \  h} -{2 \  {d \sp 2} \  g} 
\right)}
\  i} -{2 \  c \  e \  {h \sp 2}}+{2 \  d \  e \  g \  h} 
\right)}
\  l}+{{\left( -{2 \  b \  e \  i}+{{e \sp 2} \  f} 
\right)}
\  {k \sp 2}}+{{\left( -{2 \  c \  d \  {i \sp 2}}+{{\left( {2 \  c \  e \  
h}+{2 \  d \  e \  g} 
\right)}
\  i} -{2 \  {e \sp 2} \  g \  h} 
\right)}
\  k}+{{\left( {{d \sp 2} \  {i \sp 2}} -{2 \  d \  e \  h \  i}+{{e \sp 2} \  
{h \sp 2}} 
\right)}
\  j} 
\leqno(57)
$$
                                             Type: Polynomial AlgebraicNumber
inv:=inverse(msm_test2)

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l.54 a:=sqrt(T(1,1)^
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\OML/cmm/m/it/10 T\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)[])\OM
L/cmm/m/it/10 b \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 sqrt\OT1/cmr/m/n/10 (\OML/cm
m/m/it/10 T\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2)[] + \OML/cmm
/m/it/10 T\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2)[])\OML/cmm/m/
it/10 Z \OT1/cmr/m/n/10 := \OML/cmm/m/it/10 matrix\OT1/cmr/m/n/10 [[\OML/cmm/m/
it/10 V\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2)\OML/cmm/m/it/10 
; \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \O
T1/cmr/m/n/10 2)]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 ^^@\OML/c
mm/m/it/10 V\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML/cmm/m/i
t/10 ; V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)]]\OML/cmm/m/it/
10 V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1) \OMS/cmsy/m/n/10 ^^
C
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l.70 sqrt(T(1,1)^
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qrt(T(1,1)$[] + \OML/cmm/m/it/10 T\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr
/m/n/10 1)[])\OML/cmm/m/it/10 sqrt\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 T\OT1/cmr/m
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L/cmm/m/it/10 Z \OT1/cmr/m/n/10 := \OML/cmm/m/it/10 matrix\OT1/cmr/m/n/10 [[\OM
L/cmm/m/it/10 V\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2)\OML/cmm/
m/it/10 ; \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 (1\OML/cmm/m/it
/10 ; \OT1/cmr/m/n/10 2)]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 ^
^@\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML
/cmm/m/it/10 ; V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)]]\OML/c
mm/m/it/10 V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1) \OMS/cmsy/m
/n/10 ^^C \OML/cmm/m/it/10 V\OT1/cmr/m/n/10 (2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/1
0 2)\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2) \
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l.90 msm_
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10 matrix\OT1/cmr/m/n/10 [[\OML/cmm/m/it/10 a; b; c; d; e\OT1/cmr/m/n/10 ]\OML/
cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 b; f; g; h; i\OT1/cmr/m/n/10 ]\
OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 c; g; j; k; l\OT1/cmr/m/n/1
0 ]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 d; h; k; m; n\OT1/cmr/m
/n/10 ]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 e; i; l; n; o\OT1/c
mr/m/n/10 ]]\OML/cmm/m/it/10 det \OT1/cmr/m/n/10 :=
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10 matrix\OT1/cmr/m/n/10 [[\OML/cmm/m/it/10 a; b; c; d; e\OT1/cmr/m/n/10 ]\OML/
cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 b; f; g; h; i\OT1/cmr/m/n/10 ]\
OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 c; g; j; k; l\OT1/cmr/m/n/1
0 ]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 d; h; k; m; n\OT1/cmr/m
/n/10 ]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 e; i; l; n; o\OT1/c
mr/m/n/10 ]]\OML/cmm/m/it/10 det \OT1/cmr/m/n/10 :=
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
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