Initial population.

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diff --git a/src/input/calculus2.input.pamphlet b/src/input/calculus2.input.pamphlet
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input calculus2.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{bugs}
+\subsection{bug1}
+exp: series expansion involves transcendental constants
+<<bug1>>=
+exp(2 + tan(y))
+@
+<<bugs>>=
+
+-- Input for page FormalDerivativePage
+)clear all
+
+differentiate(f, x)
+f := operator f
+x := operator x
+y := operator y
+a := f(x z, y z, z**2) + x y(z+1)
+dadz := differentiate(a, z)
+eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
+eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
+differentiate(%, z)
+
+-- Input for page SeriesArithmeticPage
+)clear all
+
+x := series x
+num := 3 + x
+den := 1 + 7 * x
+num / den
+base := 1 / (1 - x)
+expon := x * base
+base ** expon
+
+-- Input for page SeriesConversionPage
+)clear all
+
+f := sin(a*x)
+series(f,x = 0)
+g := y / (exp(y) - 1)
+series(g)
+h := sin(3*x)
+series(h,x,x = %pi/12)
+series(sqrt(tan(a*x)),x = 0)
+series(sec(x) ** 2,x = %pi/2)
+bern := t * exp(t*x) / (exp(t) - 1)
+series(bern,t = 0)
+
+-- Input for page SeriesDifferentialEquationPage
+)clear all
+
+)set streams calculate 7
+y := operator 'y
+eq := differentiate(y(x), x, 3) - sin(differentiate(y(x), x, 2)) * exp(y(x)) = cos(x)
+seriesSolve(eq, y, x = 0, [1, 0, 0])
+x := operator 'x
+eq1 := differentiate(x(t), t) = 1 + x(t)**2
+eq2 := differentiate(y(t), t) = x(t) * y(t)
+seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])
+
+-- Input for page LaplacePage
+)clear all
+
+sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
+laplace(%, t, s)
+laplace((exp(a*t) - exp(b*t))/t, t, s)
+laplace(2/t * (1 - cos(a*t)), t, s)
+laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
+laplace((cos(a*t) - cos(b*t))/t, t, s)
+laplace(exp(a*t+b)*ei(c*t), t, s)
+laplace(a*ci(b*t) + c*si(d*t), t, s)
+laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
+
+-- Input for page SeriesCoefficientPage
+)clear all
+
+x := series(x)
+y := exp(x) * sin(x)
+coefficient(y,6)
+coefficient(y,15)
+y
+
+-- Input for page SymbolicIntegrationPage
+)clear all
+
+f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2)
+integrate(f, x)
+g := log(1 + sqrt(a * x + b)) / x
+integrate(g, x)
+integrate(1/(x**2 - 2),x)
+integrate(1/(x**2 + 2),x)
+h := x**2 / (x**4 - a**2)
+integrate(h, x)
+complexIntegrate(h, x)
+expandLog %
+rootSimp %
+ratForm %
+
+-- Input for page DerivativePage
+)clear all
+
+f := exp exp x
+differentiate(f, x)
+differentiate(f, x, 4)
+g := sin(x**2 + y)
+differentiate(g, y)
+differentiate(g, [y, y, x, x])
+
+-- Input for page SeriesFormulaPage
+)clear all
+
+taylor(n +-> 1/factorial(n),x = 0)
+taylor(n +-> (-1)**(n-1)/n,x = 1,1..)
+taylor(n +-> (-1)**(n-1)/n,x = 1,1..7)
+laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..)
+puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)
+puiseux(j +-> j**2,x = 8,-4/3..,1/2)
+series(n +-> 1/factorial(n),x = 0)
+series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..)
+series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2)
+
+-- Input for page SeriesCreationPage
+)clear all
+
+x := series x
+1/(1 - x - x**2)
+sin(x)
+sin(1 + x)
+sin(a * x)
+series(1/log(y),y = 1)
+f : UTS(FLOAT,z,0) := exp(z)
+series(1/factorial(n),n,w = 0)
+
+-- Input for page SeriesFunctionPage
+)clear all
+
+x := series x
+rat := x**2 / (1 - 6*x + x**2)
+sin(rat)
+y : UTS(FRAC INT,y,0) := y
+exp(y)
+tan(y**2)
+cos(y + y**5)
+log(1 + sin(y))
+<<bug1>>
+z : UTS(EXPR INT,z,0) := z
+exp(2 + tan(z))
+w := taylor w
+exp(2 + tan(w))
+
+-- Input for page LimitPage
+)clear all
+
+f := sin(a*x) / tan(b*x)
+limit(f,x=0)
+g := csc(a*x) / csch(b*x)
+limit(g,x=0)
+h := (1 + k/x)**x
+limit(h,x=%plusInfinity)
+
+-- Input for page SeriesBernoulliPage
+)clear all
+
+reduce(+,[m**4 for m in 1..10])
+sum4 := sum(m**4, m = 1..k)
+eval(sum4, k = 10)
+f := t*exp(x*t) / (exp(t) - 1)
+)set streams calculate 5
+ff := taylor(f,t = 0)
+factorial(6) * coefficient(ff,6)
+g := eval(f, x = x + 1) - f
+normalize(g)
+taylor(g,t = 0)
+B5 := factorial(5) * coefficient(ff,5)
+1/5 * (eval(B5, x = k + 1) - eval(B5, x = 1))
+sum4
+@
+<<*>>=
+
+-- Input for page FormalDerivativePage
+)clear all
+
+differentiate(f, x)
+f := operator f
+x := operator x
+y := operator y
+a := f(x z, y z, z**2) + x y(z+1)
+dadz := differentiate(a, z)
+eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
+eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
+differentiate(%, z)
+
+-- Input for page SeriesArithmeticPage
+)clear all
+
+x := series x
+num := 3 + x
+den := 1 + 7 * x
+num / den
+base := 1 / (1 - x)
+expon := x * base
+base ** expon
+
+-- Input for page SeriesConversionPage
+)clear all
+
+f := sin(a*x)
+series(f,x = 0)
+g := y / (exp(y) - 1)
+series(g)
+h := sin(3*x)
+series(h,x,x = %pi/12)
+series(sqrt(tan(a*x)),x = 0)
+series(sec(x) ** 2,x = %pi/2)
+bern := t * exp(t*x) / (exp(t) - 1)
+series(bern,t = 0)
+
+-- Input for page SeriesDifferentialEquationPage
+)clear all
+
+)set streams calculate 7
+y := operator 'y
+eq := differentiate(y(x), x, 3) - sin(differentiate(y(x), x, 2)) * exp(y(x)) = cos(x)
+seriesSolve(eq, y, x = 0, [1, 0, 0])
+x := operator 'x
+eq1 := differentiate(x(t), t) = 1 + x(t)**2
+eq2 := differentiate(y(t), t) = x(t) * y(t)
+seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])
+
+-- Input for page LaplacePage
+)clear all
+
+sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
+laplace(%, t, s)
+laplace((exp(a*t) - exp(b*t))/t, t, s)
+laplace(2/t * (1 - cos(a*t)), t, s)
+laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
+laplace((cos(a*t) - cos(b*t))/t, t, s)
+laplace(exp(a*t+b)*ei(c*t), t, s)
+laplace(a*ci(b*t) + c*si(d*t), t, s)
+laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
+
+-- Input for page SeriesCoefficientPage
+)clear all
+
+x := series(x)
+y := exp(x) * sin(x)
+coefficient(y,6)
+coefficient(y,15)
+y
+
+-- Input for page SymbolicIntegrationPage
+)clear all
+
+f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2)
+integrate(f, x)
+g := log(1 + sqrt(a * x + b)) / x
+integrate(g, x)
+integrate(1/(x**2 - 2),x)
+integrate(1/(x**2 + 2),x)
+h := x**2 / (x**4 - a**2)
+integrate(h, x)
+complexIntegrate(h, x)
+expandLog %
+rootSimp %
+ratForm %
+
+-- Input for page DerivativePage
+)clear all
+
+f := exp exp x
+differentiate(f, x)
+differentiate(f, x, 4)
+g := sin(x**2 + y)
+differentiate(g, y)
+differentiate(g, [y, y, x, x])
+
+-- Input for page SeriesFormulaPage
+)clear all
+
+taylor(n +-> 1/factorial(n),x = 0)
+taylor(n +-> (-1)**(n-1)/n,x = 1,1..)
+taylor(n +-> (-1)**(n-1)/n,x = 1,1..7)
+laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..)
+puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)
+puiseux(j +-> j**2,x = 8,-4/3..,1/2)
+series(n +-> 1/factorial(n),x = 0)
+series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..)
+series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2)
+
+-- Input for page SeriesCreationPage
+)clear all
+
+x := series x
+1/(1 - x - x**2)
+sin(x)
+sin(1 + x)
+sin(a * x)
+series(1/log(y),y = 1)
+f : UTS(FLOAT,z,0) := exp(z)
+series(1/factorial(n),n,w = 0)
+
+-- Input for page SeriesFunctionPage
+)clear all
+
+x := series x
+rat := x**2 / (1 - 6*x + x**2)
+sin(rat)
+y : UTS(FRAC INT,y,0) := y
+exp(y)
+tan(y**2)
+cos(y + y**5)
+log(1 + sin(y))
+z : UTS(EXPR INT,z,0) := z
+exp(2 + tan(z))
+w := taylor w
+exp(2 + tan(w))
+
+-- Input for page LimitPage
+)clear all
+
+f := sin(a*x) / tan(b*x)
+limit(f,x=0)
+g := csc(a*x) / csch(b*x)
+limit(g,x=0)
+h := (1 + k/x)**x
+limit(h,x=%plusInfinity)
+
+-- Input for page SeriesBernoulliPage
+)clear all
+
+reduce(+,[m**4 for m in 1..10])
+sum4 := sum(m**4, m = 1..k)
+eval(sum4, k = 10)
+f := t*exp(x*t) / (exp(t) - 1)
+)set streams calculate 5
+ff := taylor(f,t = 0)
+factorial(6) * coefficient(ff,6)
+g := eval(f, x = x + 1) - f
+normalize(g)
+taylor(g,t = 0)
+B5 := factorial(5) * coefficient(ff,5)
+1/5 * (eval(B5, x = k + 1) - eval(B5, x = 1))
+sum4
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}