Initial population.

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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input tutChap67.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1996.
+@
+<<*>>=
+<<license>>
+(vecA,vecB) : Vector Integer
+vecA := vector [3,0,4]
+vecB := vector [2,4,-2]
+vecA + vecB
+vecA - vecB
+5*vecA
+vecB*7
+vecB/2
+1/2 * vecB
+vecA * (1/2)
+dot(vecA,vecB)
+sqrt dot(vecA,vecA)
+magnitude vecA
+direction x == 1/magnitude x * x
+direction vecA
+magnitude direction vecB
+p := vector [u1*t,u2*t,u3*t-1/2*g*t^2]
+D(p,t)
+DV(s,t) == map(x+->D(x,t),s)
+v := DV(p,t) -- the velocity,
+a := DV(v,t) -- acceleration
+j := DV(a,t) -- and jerk
+)clear properties all
+s := operator 's;
+sSol := solve(D(s(t),t,2) - aF + r/m*D(s(t),t),s,t=0,[0,u])
+u := vector [ux,uy]
+aF := vector [0,-g]
+function(sSol ,'s,'t)
+s t
+function(numerator sSol,'n,'t)
+function(1/denominator sSol*n(t),'s,'t)
+s t
+outputGeneral 6
+map(x+->eval(x,[m=1,ux=20,uy=10,r=0.1,g=9.8]),s t)
+draw(curve(%.1,%.2),t=0..2)
+map(x+->eval(x,[m=1,ux=20,uy=10,r=0,g=9.8]),s t)
+map(x+->limit(x,r=0),s t)
+map(x+->eval(x,[m=1,ux=20,uy=10,g=9.8]),%::Vector Expression Integer)
+draw(curve(%.1,%.2),t=0..2)
+Integer has Ring
+PositiveInteger has Ring 
+has(Fraction Integer,DivisionRing)
+has(Integer,DivisionRing)
+List has Group
+List ? has Group
+Field has Ring                   
+Group has Ring
+vecC := vector [0,x +-> x,[a,b,c]]  
+matA := matrix [[x,0],[7.3,%i]]     
+vecC(1)
+vecC.2
+vecC 3
+vecD : Vector Integer := [1,2,3,4,5,6]
+matB : Matrix Integer := [[1,2,3],[4,5,6]]
+vector [1,2,3] :: Matrix Integer
+matA(1,2)
+matrix [[matA]]
+matrix [[matA::SquareMatrix(2,Polynomial Complex Float)]]
+matrix [[squareMatrix matA]]
+matC := matrix [[a,b,c],[d,e,f]]
+lvec := vector [2,3]            
+rvec := vector [4,5,6]
+lvec * matC
+matC * rvec
+lrvec := vector [1,2]
+lrvec * ((matrix [[a,b],[c,d]] * lrvec) :: Matrix Polynomial Integer)
+vecD := new(5,0)          
+new(3,3,0)$Matrix Integer
+Z3 := %;
+I3 := Z3; I3(1,1) := 1; I3(2,2) := 1; I3(3,3) := 1;
+I3
+I3 := Z3; for k in [1,2,3] repeat I3(k,k) := 1
+I3
+I3 := Z3; for k in 1..3 repeat I3(k,k) := 1
+I3
+expand(-7/2..7/3)
+for i in 11..20 repeat _
+           ( print i; _
+             if prime? i then messagePrint(" (That was prime.)")$OutputForm )
+poly := 0;
+for i in [1,2,3,4] for c in ['a,'b,'c,'d] repeat poly := poly + i*c
+poly
+vecC := vector [n^2 for n in 1..3]
+hilbert3 := matrix [[1/(i+j) for i in 1..3] for j in 1..3]
+I3 := matrix [[((m,n)+->if m=n then 1 else 0)(i,j) _
+                                             for i in 1..3] for j in 1..3]
+diagonalMatrix [1,1,1]
+inverse hilbert3                            
+% * hilbert3                                
+matC := matrix [[a,b],[c,d]]
+inverse matC
+determinant matC
+(x-a)^2 + (y-b)^2 - r^2 = 0
+row1 := [1,x,y,x^2+y^2]
+row2 := [eval(row1.i,[x,y],[0,1]) for i in 1..4]
+row3 := [eval(row1.i,[x,y],[1,0]) for i in 1..4];
+row4 := [eval(row1.i,[x,y],[-1,-1]) for i in 1..4];
+determinant [row1,row2,row3,row4] = 0
+solve([[1/(i+j) for i in 1..3] for j in 1..3],[3,5,7])
+matD := matrix [[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,7]]
+c := vector [5,6,7,8]
+solve(matD,c)
+horizConcat(matD,c)
+rank %
+rank matD
+solve([[2,3,4,5],[3,4,5,6],[4,5,6,7]],[5,6,7])  
+subMatrix(matD,1,3,1,4)
+rank horizConcat(matD,vector [5,6,7,9])  
+solve(matD,[5,6,7,9])            
+hilbert3 :: Matrix DoubleFloat -- continuing the previous session
+% * inverse %                             
+matrix [[1/(i+j) for i in 1..11] for j in 1..11]::Matrix DoubleFloat;
+badUnit := % * inverse %;
+diagEls := set [%(i,i) for i in 1..11];                                
+min diagEls
+max diagEls
+offDiags := empty()$Set DoubleFloat
+for i in 1..11 repeat _
+            for j in 1..11 | i ~= j repeat _
+               offDiags := union(offDiags,badUnit(i,j))
+min offDiags
+max offDiags
+hilbert11 := matrix [[1/(i+j) for i in 1..11] for j in 1..11];
+% * inverse %
+detHilbert3 := determinant hilbert3
+detHilbert11 := determinant hilbert11
+% :: DoubleFloat                                              
+determinant(hilbert11::Matrix DoubleFloat)                    
+test3 := hilbert3 :: Matrix Polynomial Fraction Integer;
+test3(1,1) := (1 + eps)/2;
+determinant test3        
+(% - detHilbert3)/detHilbert3
+for i in 1..3 repeat for j in 1..3 repeat _
+            test3(i,j) := hilbert3(i,j) + (2*randnum(2) - 1)*eps
+test3
+(determinant test3 - detHilbert3)/detHilbert3
+error3 := matrix [[eps[i,j] for i in 1..3] for j in 1..3]
+test3 := hilbert3 + t*error3;                                          
+detErr := (determinant test3 - detHilbert3)/detHilbert3;
+detErrReduced := coefficient(%,'t,1)
+coefficient(detErr,'t,0)
+epses := variables detErrReduced
+coefs := coefficients detErrReduced
+index := first sort((i,j)+->abs coefs.i > abs coefs.j, expand(1..9)) 
+epses.5
+coefs.5
+sort((i,j)+->abs i > abs j, coefs).2
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}