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Diffstat (limited to 'src/input/tutchap3.input.pamphlet')
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diff --git a/src/input/tutchap3.input.pamphlet b/src/input/tutchap3.input.pamphlet new file mode 100644 index 00000000..7ddc0bff --- /dev/null +++ b/src/input/tutchap3.input.pamphlet @@ -0,0 +1,103 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input tutChap3.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1996. +@ +<<*>>= +<<license>> +D(x^2,x) +D(sin x,x) +D(sin(log(x/tan(x))),x) +D(tan x,x,2) +D(tan x,x,3) +D(sin(x*y),x) +D(sin(x*y),[y,x,x]) +dalembert := operator _[_] +dalembert u +J0 := operator script(J,[[0]]::List List OutputForm) +symbol[sub1,sub2] +f := operator 'f; g := operator 'g; +D(f(x)*g(x),x) +D(f(x)/g(x),x) +D(f(g(x)),x) +r := operator 'r; theta := operator 'theta ; +x(t) == r(t)*cos theta t +y(t) == r(t)*sin theta t +D(x(t),t) +D(y(t),t) +)clear all +r := operator 'r; theta := operator 'theta; +r := r(t); theta := theta(t); +x == r*cos theta; y == r*sin theta; +ax := D(x,t,2); ay := D(y,t,2); +eval(ax,theta=0) +eval(ay,theta=0) +f := operator 'f +D(f(r,theta),t) +D(f(r,theta),t,2) +)clear p x -- since x has a value +integrate(x^2,x) +integrate(%e^x,x) +integrate(1/x,x) +integrate(sin x,x) +I ==> integrate +I(x^3,x) +I(sin sin x,x) +I(x^n,x) +% - 1/(n + 1) +limit(%,n=-1) +In := %% 17 +limit(%,n=-1) +)set stream calculate 5 +series(In,n=-1) -- expand In in powers of (n+1) +In2 := In - x*%e^(-log(x))*(n+1)^(-1) +limit(In2,n=-1) +limit(x^(n+1)/(n+1),n=-1) +limit(x^(n+1)/(n+1)-1/(n+1),n=-1) +I(1/(a+x^2),x) +series(second %, a=0) +second %% 27 +(rule atan A == acot(1/A)) % +I(atan x - acot(1/x),x) +atanRule := rule atan(A) == acot(1/A) +atanRule atan x +rSimp := rule(sqrt(x^(2*(n|even? n))) == x^n) +rSimp(sqrt(x^4)) +rSimp(sqrt(x^6)) +f := operator 'f; g := operator 'g; dprod := D(f(x)*g(x),x) +(rule f x == sin x)% +(rule g x == exp x)% +(rule (f x == sin x; g x == cos x))dprod +substitutions := (rule (f x == sec x; g x == csc x)) +substitutions dprod +I(cot x, x) +normalize % +simplify % +(rule N*log A + M*log B == log(A^N*B^M)) % +(rule log(A^N) == N*log A)% +ii:=I(1/(x^3 + x + 1),x) +T0:= (tower ii).2 ::EXPR INT +f:=definingPolynomial T0 +outputGeneral 5 +solve((numerator f) :: POLY INT,0.00001) +eval(ii :: EXPR COMPLEX FLOAT,T0= rhs first %) +solve((numerator f) :: POLY INT,1/100000) +eval(ii,T0=rhs first %) :: EXPR Complex Integer +complexForm % +% :: EXPR Float +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |