help links subscribe changes refresh edit

	SandBox
SandBox Mapping ←	↑	→ SandBox Monoid

SandBox Matrix

Edit detail for SandBox Matrix revision 5 of 6

	1 2 3 4 5 6
Editor: Bill Page Time: 2010/10/09 22:22:29 GMT-7
Note: Re: test

added:

From BillPage Sat Oct 9 22:22:21 -0700 2010
From: Bill Page
Date: Sat, 09 Oct 2010 22:22:21 -0700
Subject: Re: test
Message-ID: <20101009222221-0700@axiom-wiki.newsynthesis.org>

Write::

  !\begin{axiom}
  M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]
  \end{axiom}

\begin{axiom}
M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]
\end{axiom}

Symbolic Matrices

fricas

A:=matrix [[x,y],[z,w]]

$\label{eq1}\left[ \begin{array}{cc} x & y \ z & w$

(1)

Type: Matrix(Polynomial(Integer))

fricas

A+1

$\label{eq2}\left[ \begin{array}{cc} {x + 1}& y \ z &{w + 1}$

(2)

Type: SquareMatrix?(2,Polynomial(Integer))

test --unknown, Fri, 24 Jun 2005 04:29:59 -0500 reply

fricas

A+2

$\label{eq3}\left[ \begin{array}{cc} {x + 2}& y \ z &{w + 2}$

(3)

Type: SquareMatrix?(2,Polynomial(Integer))

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

fricas

N:=matrix[[0],[0]]

$\label{eq4}\left[ \begin{array}{c} 0 \ 0$

(4)

Type: Matrix(NonNegativeInteger?)

fricas

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq5}\left[{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}\right]$

(5)

Type: List(List(Expression(Integer)))

fricas

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

$\label{eq6}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(6)

Type: Matrix(Expression(Integer))

fricas

v:=matrix[[v11],[v12]]

$\label{eq7}\left[ \begin{array}{c} v 11 \ v 12$

(7)

Type: Matrix(Polynomial(Integer))

fricas

C:=A*v-L(1,1)*v

$\label{eq8}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(8)

Type: Matrix(Expression(Integer))

fricas

solve(C(1,1)=0,v11)

$\label{eq9}\left[{v 11 = -{v 12 \over{\sqrt{- 1}}}}\right]$

(9)

Type: List(Equation(Expression(Integer)))

fricas

solve(C(2,1)=0,v12)

$\label{eq10}\left[{v 12 ={v 11 \over{\sqrt{- 1}}}}\right]$

(10)

Type: List(Equation(Expression(Integer)))

fricas

V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$\label{eq11}\left[ \begin{array}{cc} -{\sqrt{- 1}}& 1 \ 1 &{\sqrt{- 1}}$

(11)

Type: Matrix(AlgebraicNumber?)

fricas

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$\label{eq12}\left[ \begin{array}{cc} {\sqrt{- 1}}& - 1 \ - 1 & -{\sqrt{- 1}}$

(12)

Type: Matrix(AlgebraicNumber?)

fricas

W:=(V(1,1)*V(2,2) - V(1,2)*V(2,1))

$\label{eq13}0$

(13)

Type: AlgebraicNumber?

test --unknown, Fri, 24 Jun 2005 13:47:22 -0500 reply

fricas

N:=matrix[[0],[0]]

$\label{eq14}\left[ \begin{array}{c} 0 \ 0$

(14)

Type: Matrix(NonNegativeInteger?)

fricas

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq15}\left[{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}\right]$

(15)

Type: List(List(Expression(Integer)))

fricas

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

$\label{eq16}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(16)

Type: Matrix(Expression(Integer))

fricas

v:=matrix[[v11],[v12]]

$\label{eq17}\left[ \begin{array}{c} v 11 \ v 12$

(17)

Type: Matrix(Polynomial(Integer))

fricas

C:=A*v-L(1,1)*v

$\label{eq18}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(18)

Type: Matrix(Expression(Integer))

fricas

solve(C(1,1)=0,v11)

$\label{eq19}\left[{v 11 = -{v 12 \over{\sqrt{- 1}}}}\right]$

(19)

Type: List(Equation(Expression(Integer)))

fricas

solve(C(2,1)=0,v12)

$\label{eq20}\left[{v 12 ={v 11 \over{\sqrt{- 1}}}}\right]$

(20)

Type: List(Equation(Expression(Integer)))

fricas

V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$\label{eq21}\left[ \begin{array}{cc} -{\sqrt{- 1}}& 1 \ 1 &{\sqrt{- 1}}$

(21)

Type: Matrix(AlgebraicNumber?)

fricas

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$\label{eq22}\left[ \begin{array}{cc} {\sqrt{- 1}}& - 1 \ - 1 & -{\sqrt{- 1}}$

(22)

Type: Matrix(AlgebraicNumber?)

fricas

V(1,1)*V(2,2)

$\label{eq23}1$

(23)

Type: AlgebraicNumber?

fricas

V(1,2)*V(2,1)

$\label{eq24}1$

(24)

Type: AlgebraicNumber?

test --unknown, Fri, 24 Jun 2005 13:54:11 -0500 reply

fricas

N:=matrix[[0],[0]]

$\label{eq25}\left[ \begin{array}{c} 0 \ 0$

(25)

Type: Matrix(NonNegativeInteger?)

fricas

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq26}\left[{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}\right]$

(26)

Type: List(List(Expression(Integer)))

fricas

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

$\label{eq27}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(27)

Type: Matrix(Expression(Integer))

fricas

v:=matrix[[v11],[v12]]

$\label{eq28}\left[ \begin{array}{c} v 11 \ v 12$

(28)

Type: Matrix(Polynomial(Integer))

fricas

C:=A*v-L(1,1)*v

$\label{eq29}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(29)

Type: Matrix(Expression(Integer))

fricas

solve(C(1,1)=0,v11)

$\label{eq30}\left[{v 11 = -{v 12 \over{\sqrt{- 1}}}}\right]$

(30)

Type: List(Equation(Expression(Integer)))

fricas

solve(C(2,1)=0,v12)

$\label{eq31}\left[{v 12 ={v 11 \over{\sqrt{- 1}}}}\right]$

(31)

Type: List(Equation(Expression(Integer)))

fricas

T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$\label{eq32}\left[ \begin{array}{cc} -{\sqrt{- 1}}& 1 \ 1 &{\sqrt{- 1}}$

(32)

Type: Matrix(AlgebraicNumber?)

fricas

a:=sqrt(T(1,1)^2+T(2,1)^2)

$\label{eq33}0$

(33)

Type: AlgebraicNumber?

fricas

b=sqrt(T(1,2)^2+T(2,2)^2)

$\label{eq34}b = 0$

(34)

Type: Equation(Polynomial(AlgebraicNumber?))

fricas

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$\label{eq35}\left[ \begin{array}{cc} {\sqrt{- 1}}& - 1 \ - 1 & -{\sqrt{- 1}}$

(35)

Type: Matrix(AlgebraicNumber?)

fricas

V(1,1)*V(2,2)

$\label{eq36}1$

(36)

Type: AlgebraicNumber?

fricas

V(1,2)*V(2,1)

$\label{eq37}1$

(37)

Type: AlgebraicNumber?

test --unknown, Fri, 24 Jun 2005 13:55:30 -0500 reply

fricas

N:=matrix[[0],[0]]

$\label{eq38}\left[ \begin{array}{c} 0 \ 0$

(38)

Type: Matrix(NonNegativeInteger?)

fricas

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq39}\left[{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}\right]$

(39)

Type: List(List(Expression(Integer)))

fricas

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

$\label{eq40}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(40)

Type: Matrix(Expression(Integer))

fricas

v:=matrix[[v11],[v12]]

$\label{eq41}\left[ \begin{array}{c} v 11 \ v 12$

(41)

Type: Matrix(Polynomial(Integer))

fricas

C:=A*v-L(1,1)*v

$\label{eq42}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(42)

Type: Matrix(Expression(Integer))

fricas

solve(C(1,1)=0,v11)

$\label{eq43}\left[{v 11 = -{v 12 \over{\sqrt{- 1}}}}\right]$

(43)

Type: List(Equation(Expression(Integer)))

fricas

solve(C(2,1)=0,v12)

$\label{eq44}\left[{v 12 ={v 11 \over{\sqrt{- 1}}}}\right]$

(44)

Type: List(Equation(Expression(Integer)))

fricas

T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

$\label{eq45}\left[ \begin{array}{cc} -{\sqrt{- 1}}& 1 \ 1 &{\sqrt{- 1}}$

(45)

Type: Matrix(AlgebraicNumber?)

fricas

sqrt(T(1,1)^2+T(2,1)^2)

$\label{eq46}0$

(46)

Type: AlgebraicNumber?

fricas

sqrt(T(1,2)^2+T(2,2)^2)

$\label{eq47}0$

(47)

Type: AlgebraicNumber?

fricas

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

$\label{eq48}\left[ \begin{array}{cc} {\sqrt{- 1}}& - 1 \ - 1 & -{\sqrt{- 1}}$

(48)

Type: Matrix(AlgebraicNumber?)

fricas

V(1,1)*V(2,2)

$\label{eq49}1$

(49)

Type: AlgebraicNumber?

fricas

V(1,2)*V(2,1)

$\label{eq50}1$

(50)

Type: AlgebraicNumber?

fricas

)clear all

   All user variables and function definitions have been cleared.
B := %i*sqrt(a^2 + b^2 + c^2)

$\label{eq51}i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}$

(51)

Type: Expression(Complex(Integer))

fricas

A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]

$\label{eq52}\left[ \begin{array}{ccc} {i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}& c & - b \ - c &{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}& a \ b & - a &{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}$

(52)

Type: Matrix(Expression(Complex(Integer)))

fricas

rowEchelon(A)

$\label{eq53}\left[ \begin{array}{ccc} 1 & 0 &{{{a \ c \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}+{i \ b \ {{c}^{2}}}+{i \ {{b}^{3}}}+{i \ {{a}^{2}}\ b}}\over{{\left({{b}^{2}}+{{a}^{2}}\right)}\ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}} \ 0 & 1 &{{-{i \ a \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}+{b \ c}}\over{{{b}^{2}}+{{a}^{2}}}} \ 0 & 0 & 0$

(53)

Type: Matrix(Expression(Complex(Integer)))

fricas

B := -%i*sqrt(a^2 + b^2 + c^2)

$\label{eq54}-{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}$

(54)

Type: Expression(Complex(Integer))

fricas

A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]

$\label{eq55}\left[ \begin{array}{ccc} -{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}& c & - b \ - c & -{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}& a \ b & - a & -{i \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}$

(55)

Type: Matrix(Expression(Complex(Integer)))

fricas

rowEchelon(A)

$\label{eq56}\left[ \begin{array}{ccc} 1 & 0 &{{{a \ c \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}-{i \ b \ {{c}^{2}}}-{i \ {{b}^{3}}}-{i \ {{a}^{2}}\ b}}\over{{\left({{b}^{2}}+{{a}^{2}}\right)}\ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}} \ 0 & 1 &{{{i \ a \ {\sqrt{{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}}+{b \ c}}\over{{{b}^{2}}+{{a}^{2}}}} \ 0 & 0 & 0$

(56)

Type: Matrix(Expression(Complex(Integer)))

test --jcv, Sat, 09 Oct 2010 16:10:48 -0700 reply

M := matrix [[1,1,1,1],[a,a,b,b]?,[1,1,1,1]?,[a,a,b,b]]?

Re: test --Bill Page, Sat, 09 Oct 2010 22:22:21 -0700 reply

Write:

  \begin{axiom}
  M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]
  \end{axiom}

fricas

M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]

$\label{eq57}\left[ \begin{array}{cccc} 1 & 1 & 1 & 1 \ a & a & b & b \ 1 & 1 & 1 & 1 \ a & a & b & b$

(57)

Type: Matrix(Polynomial(Integer))