From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/algebra/paramete.spad.pamphlet | 218 +++++++++++++++++++++++++++++++++++++
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diff --git a/src/algebra/paramete.spad.pamphlet b/src/algebra/paramete.spad.pamphlet
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra paramete.spad}
+\author{Clifton J. Williamson}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{domain PARPCURV ParametricPlaneCurve}
+<<domain PARPCURV ParametricPlaneCurve>>=
+)abbrev domain PARPCURV ParametricPlaneCurve
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: curve, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric curve, graphics
+++ References:
+++ Description: ParametricPlaneCurve is used for plotting parametric plane 
+++ curves in the affine plane.
+ 
+ParametricPlaneCurve(ComponentFunction): Exports == Implementation where
+  ComponentFunction : Type
+  NNI             ==> NonNegativeInteger
+ 
+  Exports ==> with
+    curve: (ComponentFunction,ComponentFunction) -> %
+      ++ curve(c1,c2) creates a plane curve from 2 component functions \spad{c1}
+      ++ and \spad{c2}.
+    coordinate: (%,NNI) -> ComponentFunction
+      ++ coordinate(c,i) returns a coordinate function for c using 1-based 
+      ++ indexing according to i. This indicates what the function for the
+      ++ coordinate component i of the plane curve is.
+ 
+  Implementation ==> add
+ 
+    Rep := Record(xCoord:ComponentFunction,yCoord:ComponentFunction)
+ 
+    curve(x,y) == [x,y]
+    coordinate(c,n) ==
+      n = 1 => c.xCoord
+      n = 2 => c.yCoord
+      error "coordinate: index out of bounds"
+
+@
+\section{package PARPC2 ParametricPlaneCurveFunctions2}
+<<package PARPC2 ParametricPlaneCurveFunctions2>>=
+)abbrev package PARPC2 ParametricPlaneCurveFunctions2
+++ Description:
+++ This package \undocumented
+ParametricPlaneCurveFunctions2(CF1: Type, CF2:Type): with
+  map: (CF1 -> CF2, ParametricPlaneCurve(CF1)) -> ParametricPlaneCurve(CF2)
+	++ map(f,x) \undocumented
+ == add
+  map(f, c) == curve(f coordinate(c,1), f coordinate(c, 2))
+
+@
+\section{domain PARSCURV ParametricSpaceCurve}
+<<domain PARSCURV ParametricSpaceCurve>>=
+)abbrev domain PARSCURV ParametricSpaceCurve
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: curve, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric curve, graphics
+++ References:
+++ Description: ParametricSpaceCurve is used for plotting parametric space 
+++ curves in affine 3-space.
+ 
+ParametricSpaceCurve(ComponentFunction): Exports == Implementation where
+  ComponentFunction : Type
+  NNI             ==> NonNegativeInteger
+ 
+  Exports ==> with
+    curve: (ComponentFunction,ComponentFunction,ComponentFunction) -> %
+      ++ curve(c1,c2,c3) creates a space curve from 3 component functions 
+      ++ \spad{c1}, \spad{c2}, and \spad{c3}.
+    coordinate: (%,NNI) -> ComponentFunction
+      ++ coordinate(c,i) returns a coordinate function of c using 1-based 
+      ++ indexing according to i. This indicates what the function for the
+      ++ coordinate component, i, of the space curve is.
+ 
+  Implementation ==> add
+ 
+    Rep := Record(xCoord:ComponentFunction,_
+                  yCoord:ComponentFunction,_
+                  zCoord:ComponentFunction)
+ 
+    curve(x,y,z) == [x,y,z]
+    coordinate(c,n) ==
+      n = 1 => c.xCoord
+      n = 2 => c.yCoord
+      n = 3 => c.zCoord
+      error "coordinate: index out of bounds"
+
+@
+\section{package PARSC2 ParametricSpaceCurveFunctions2}
+<<package PARSC2 ParametricSpaceCurveFunctions2>>=
+)abbrev package PARSC2 ParametricSpaceCurveFunctions2
+++ Description:
+++ This package \undocumented
+ParametricSpaceCurveFunctions2(CF1: Type, CF2:Type): with
+  map: (CF1 -> CF2, ParametricSpaceCurve(CF1)) -> ParametricSpaceCurve(CF2)
+	++ map(f,x) \undocumented
+ == add
+  map(f, c) == curve(f coordinate(c,1), f coordinate(c,2), f coordinate(c,3))
+
+@
+\section{domain PARSURF ParametricSurface}
+<<domain PARSURF ParametricSurface>>=
+)abbrev domain PARSURF ParametricSurface
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: surface, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric surface, graphics
+++ References:
+++ Description: ParametricSurface is used for plotting parametric surfaces in 
+++ affine 3-space.
+ 
+ParametricSurface(ComponentFunction): Exports == Implementation where
+  ComponentFunction : Type
+  NNI             ==> NonNegativeInteger
+ 
+  Exports ==> with
+    surface: (ComponentFunction,ComponentFunction,ComponentFunction) -> %
+      ++ surface(c1,c2,c3) creates a surface from 3 parametric component 
+      ++ functions \spad{c1}, \spad{c2}, and \spad{c3}.
+    coordinate: (%,NNI) -> ComponentFunction
+      ++ coordinate(s,i) returns a coordinate function of s using 1-based 
+      ++ indexing according to i.  This indicates what the function for the
+      ++ coordinate component, i, of the surface is.
+ 
+  Implementation ==> add
+ 
+    Rep := Record(xCoord:ComponentFunction,_
+                  yCoord:ComponentFunction,_
+                  zCoord:ComponentFunction)
+ 
+    surface(x,y,z) == [x,y,z]
+    coordinate(c,n) ==
+      n = 1 => c.xCoord
+      n = 2 => c.yCoord
+      n = 3 => c.zCoord
+      error "coordinate: index out of bounds"
+
+@
+\section{package PARSU2 ParametricSurfaceFunctions2}
+<<package PARSU2 ParametricSurfaceFunctions2>>=
+)abbrev package PARSU2 ParametricSurfaceFunctions2
+++ Description:
+++ This package \undocumented
+ParametricSurfaceFunctions2(CF1: Type, CF2:Type): with
+  map: (CF1 -> CF2, ParametricSurface(CF1)) -> ParametricSurface(CF2)
+	++ map(f,x) \undocumented
+ == add
+  map(f, c) == surface(f coordinate(c,1), f coordinate(c,2), f coordinate(c,3))
+
+@
+\section{License}
+<<license>>=
+--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
+--All rights reserved.
+--
+--Redistribution and use in source and binary forms, with or without
+--modification, are permitted provided that the following conditions are
+--met:
+--
+--    - Redistributions of source code must retain the above copyright
+--      notice, this list of conditions and the following disclaimer.
+--
+--    - Redistributions in binary form must reproduce the above copyright
+--      notice, this list of conditions and the following disclaimer in
+--      the documentation and/or other materials provided with the
+--      distribution.
+--
+--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
+--      names of its contributors may be used to endorse or promote products
+--      derived from this software without specific prior written permission.
+--
+--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
+--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+@
+<<*>>=
+<<license>>
+
+<<domain PARPCURV ParametricPlaneCurve>>
+<<package PARPC2 ParametricPlaneCurveFunctions2>>
+<<domain PARSCURV ParametricSpaceCurve>>
+<<package PARSC2 ParametricSpaceCurveFunctions2>>
+<<domain PARSURF ParametricSurface>>
+<<package PARSU2 ParametricSurfaceFunctions2>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
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