From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001 From: dos-reis Date: Tue, 14 Aug 2007 05:14:52 +0000 Subject: Initial population. --- src/input/equation.input.pamphlet | 148 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 148 insertions(+) create mode 100644 src/input/equation.input.pamphlet (limited to 'src/input/equation.input.pamphlet') diff --git a/src/input/equation.input.pamphlet b/src/input/equation.input.pamphlet new file mode 100644 index 00000000..30b5cbb4 --- /dev/null +++ b/src/input/equation.input.pamphlet @@ -0,0 +1,148 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input equation.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<>= +--Copyright The Numerical Algorithms Group Limited 1996. +@ +<<*>>= +<> +-- +--To ease the use of equation (more user friendly applications) +--I have enhanced the datatype Equation to have more +--mathematical richness. +-- +--First of all now you can embed s from S to Equation S +--as s = s. +--This allows to easily manipulate equations bring terms +--from one side to the other by simply adding or multiplying +--or ... provided, that the equation domain inherits the +--structure of the underlying S. +-- +--So I went through the code saying +-- +--If S has BlaBla then BlaBla +-- +--for the most important structures, please suggest others +--if necessary, Steve, do we have a more general method in +--the new compiler rather than repeating all these +--definitions as +-- +--inv(eq) == inv lhs eq = inv rhs eq +-- +--?? +-- +-- +--Furthermore, we have function to put 0 or 1 on one side +--and factor the left hand side, after the right hand side +--is 0 and we have an IntegralDomain. +-- +--Please comment and test. +-- +--Johannes + + +eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x) +-- +-- +-- 3 2 4 +-- (1) - 6x + 13x + 4= - x + 12x +-- Type: Equation Polynomial Integer +-- Time: 1.61 (IN) + 1.47 (OT) = 3.08 sec +eq2 := x**4+13*x**2-12*x = 6*x**3-4 +-- +-- +-- 4 2 3 +-- (2) x + 13x - 12x= 6x - 4 +-- Type: Equation Polynomial Integer +-- Time: 0.16 (IN) + 0.11 (OT) = 0.27 sec +eq := eq1*y**2+eq2 +-- +-- +-- 3 2 2 4 2 4 2 3 +-- (3) (- 6x + 13x + 4)y + x + 13x - 12x= (- x + 12x)y + 6x - 4 +-- Type: Equation Polynomial Integer +-- Time: 0.26 (IN) + 0.01 (EV) + 0.01 (OT) + 1.54 (GC) = 1.82 sec +swap % +-- +-- +-- 4 2 3 3 2 2 4 2 +-- (4) (- x + 12x)y + 6x - 4= (- 6x + 13x + 4)y + x + 13x - 12x +-- Type: Equation Polynomial Integer +-- Time: 0.07 (OT) = 0.07 sec +% + 4 +-- +-- +-- 4 2 3 3 2 2 4 2 +-- (5) (- x + 12x)y + 6x = (- 6x + 13x + 4)y + x + 13x - 12x + 4 +-- Type: Equation Polynomial Integer +-- Time: 0.69 (IN) + 0.01 (OT) = 0.70 sec +%-6*x**3 +-- +-- +-- 4 2 3 2 2 4 3 2 +-- (6) (- x + 12x)y = (- 6x + 13x + 4)y + x - 6x + 13x - 12x + 4 +-- Type: Equation Polynomial Integer +-- Time: 0.19 (IN) + 0.01 (OT) = 0.20 sec +leftZero % +-- +-- +-- 4 3 2 2 4 3 2 +-- (7) 0= (x - 6x + 13x - 12x + 4)y + x - 6x + 13x - 12x + 4 +-- Type: Equation Polynomial Integer +-- Time: 0.01 (IN) + 0.05 (OT) = 0.06 sec +swap % +-- +-- +-- 4 3 2 2 4 3 2 +-- (8) (x - 6x + 13x - 12x + 4)y + x - 6x + 13x - 12x + 4= 0 +-- Type: Equation Polynomial Integer +-- Time: 0.01 (IN) = 0.01 sec +factor lhs % +-- +-- +-- 2 2 2 +-- (9) (x - 2) (x - 1) (y + 1) +-- Type: Factored Polynomial Integer +-- Time: 0.50 (IN) + 0.09 (EV) + 0.30 (OT) = 0.89 sec +factorAndSplit eq +-- +-- +-- 2 +-- (10) [x - 2= 0,x - 1= 0,y + 1= 0] +-- Type: List Equation Polynomial Integer +-- Time: 0.09 (EV) + 0.21 (OT) = 0.30 sec +inv (eq :: EQ FRAC POLY INT) +-- +-- +-- 1 1 +-- (11) - ------------------------------------= - ---------------------- +-- 3 2 2 4 2 4 2 3 +-- (6x - 13x - 4)y - x - 13x + 12x (x - 12x)y - 6x + 4 +-- Type: Equation Fraction Polynomial Integer +-- Time: 0.03 (IN) = 0.03 sec +- % +-- +-- +-- 1 1 +-- (12) ------------------------------------= ---------------------- +-- 3 2 2 4 2 4 2 3 +-- (6x - 13x - 4)y - x - 13x + 12x (x - 12x)y - 6x + 4 +-- Type: Equation Fraction Polynomial Integer +-- Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec +-- +-- +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} -- cgit v1.2.3