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## [Axiom-developer] Re: FW: [book] more verbatim #

 From: root Subject: [Axiom-developer] Re: FW: [book] more verbatim # Date: Mon, 6 Nov 2006 01:30:49 -0500

patched in axiom--silver--1

--- book.pamphlet       Sun Nov  5 23:19:25 2006
+++ book.pamphlet.new   Mon Nov  6 01:23:12 2006
@@ -14174,7 +14174,7 @@

\begin{verbatim}
greatGrandParents == [x for x in people |
-  reduce(\_or,
+  reduce(_or,
[not empty? children(y) for y in grandchildren(x)],false)]
\end{verbatim}
\returnType{Type: Void}
@@ -54462,7 +54462,7 @@
outlineRender(vp, "on")                      Show polygon outlines.
showRegion(vp,"on")                          Enclose in a box.
-  n := \# flist                                The number of ribbons
+  n := # flist                                 The number of ribbons
zoom(vp,n,1,n)                               Zoom in x- and z-directions.
rotate(vp,0,75)                              Change the angle of view.
vp                                           Return the viewport.
@@ -54725,7 +54725,7 @@
Here is a program to draw a bouquet of $n$ arrows.

\begin{verbatim}
-drawBouquet(n,title) ==}{}
+drawBouquet(n,title) ==
angle := address@hidden                          The initial angle
sp := createThreeSpace()                     Create empty space $sp$
for i in 0..n-1 repeat                       For each index i, create:
@@ -54961,7 +54961,7 @@
real := lo(realRange)                            The initial real value
for i in 1..realSteps+1 repeat                   Begin real iteration
imag := lo(imagRange)                          initial imaginary value
-    lp := []\$(List Point DFLOAT) initial list of points$lp$+ lp := []$(List Point DFLOAT)                   initial list of points $lp$
for j in 1..imagSteps+1 repeat                 Begin imaginary iteration
z := f complex(real,imag)                    value of $f$ at the point
pt := point [real,imag, clipFun sqrt norm z, Create a point
@@ -55101,7 +55101,7 @@

complexNumericFunction f ==                    Turn an expression $f$ into a
v := theVariableIn f                         function
-  compiledFunction(f, v)\$complexFunPack + compiledFunction(f, v)$complexFunPack

complexDerivativeFunction(f,n) ==              Create an nth derivative
v := theVariableIn f                         function
@@ -55110,7 +55110,7 @@

theVariableIn f ==                             Returns the variable in $f$
vl := variables f                            The list of variables
-  nv := \# vl                                  The number of variables
+  nv := # vl                                   The number of variables
nv > 1 => error "Expression is not univariate."
nv = 0 => 'x                                 Return a dummy variable
first vl
@@ -55276,8 +55276,8 @@
Implementation == add                           Implementation part begins
arrowScale : DFLOAT := (0.2)::DFLOAT --relative size Local variable 1
arrowAngle : DFLOAT := pi()-pi()/(20::DFLOAT)        Local variable 2
-    realSteps  : INT := 11 --\# real steps               Local variable 3
-    imagSteps  : INT := 11 --\# imaginary steps          Local variable 4
+    realSteps  : INT := 11 --# real steps                Local variable 3
+    imagSteps  : INT := 11 --# imaginary steps           Local variable 4
clipValue  : DFLOAT  := 10::DFLOAT --maximum vector length
Local variable 5

@@ -55705,13 +55705,13 @@

bubbleSort!(m,f) ==
-      n := \#m
+      n := #m
for i in 1..(n-1) repeat
for j in n..(i+1) by -1 repeat
if f(m.j,m.(j-1)) then swap!(m,j,j-1)
m
insertionSort!(m,f) ==
-      for i in 2..\#m repeat
+      for i in 2..#m repeat
j := i
while j > 1 and f(m.j,m.(j-1)) repeat
swap!(m,j,j-1)
@@ -55755,8 +55755,8 @@
...
if S has OrderedSet then
-      bubbleSort!(m) == bubbleSort!(m,<\$S) - insertionSort!(m) == insertionSort!(m,<\$S)
+      bubbleSort!(m) == bubbleSort!(m,<$S) + insertionSort!(m) == insertionSort!(m,<$S)
\end{verbatim}

In \ref{ugUserBlocks} on page~\pageref{ugUserBlocks},
@@ -56047,7 +56047,7 @@
\begin{verbatim}
SetCategory(): Category ==
Join(Type,CoercibleTo OutputForm) with
-      "=" : (\$, \$) -> Boolean
+      "=" : ($,$) -> Boolean
\end{verbatim}

The definition starts off with the name of the
@@ -56166,7 +56166,7 @@

SetCategory(): Category ==
Join(Type, CoercibleTo OutputForm) with
-    "=": (\$, \$) -> Boolean
+    "=": ($,$) -> Boolean
++ \bs{}axiom\{x = y\} tests if \bs{}axiom\{x\} and
++ \bs{}axiom\{y\} are equal.
\end{verbatim}
@@ -56229,8 +56229,8 @@

\begin{verbatim}
SemiGroup(): Category == SetCategory with
-      "*":  (\$,\$) -> \$- "**": (\$, PositiveInteger) -> \$+ "*": ($,$) ->$
+      "**": ($, PositiveInteger) ->$
\end{verbatim}

This definition is as simple as that for {\tt SetCategory},
@@ -56316,11 +56316,11 @@

\begin{verbatim}
SemiGroup(): Category == SetCategory with
-      "*": (\$, \$) -> \$- "**": (\$, PositiveInteger) -> \$+ "*": ($, $) ->$
+      "**": ($, PositiveInteger) ->$
-      import RepeatedSquaring(\$) - x: \$ ** n: PositiveInteger == expt(x,n)
+      import RepeatedSquaring($) + x:$ ** n: PositiveInteger == expt(x,n)
\end{verbatim}

The $add$ part at the end is used to give default definitions'' for
@@ -56375,13 +56375,13 @@
{\tt SemiGroup}.

\begin{verbatim}
-SemiGroup\_\&(\$): Exports == Implementation where - \$: SemiGroup
+SemiGroup_&($): Exports == Implementation where +$: SemiGroup
Exports == with
-    "**": (\$, PositiveInteger) -> \$
+    "**": ($, PositiveInteger) ->$
-    import RepeatedSquaring(\$) - x:\$ ** n:PositiveInteger == expt(x,n)
+    import RepeatedSquaring($) + x:$ ** n:PositiveInteger == expt(x,n)
\end{verbatim}

\section{Axioms}
@@ -56526,13 +56526,13 @@

\begin{verbatim}
Ring(): Category ==
-  Join(Rng,Monoid,LeftModule(\$: Rng)) with + Join(Rng,Monoid,LeftModule($: Rng)) with
characteristic: -> NonNegativeInteger
-      coerce: Integer -> \$+ coerce: Integer ->$
unitsKnown
n:Integer
-      coerce(n) == n * 1\$\$
+      coerce(n) == n * 1
\end{verbatim}

There are only two new things here.
@@ -56632,7 +56632,7 @@
QuotientFieldCategory(R) : Category == ... with ...
if R has OrderedSet then OrderedSet
if R has IntegerNumberSystem then
-       ceiling: \$-> R + ceiling:$ -> R
...
\end{verbatim}

@@ -56807,10 +56807,10 @@
++ quadratic form from a symmetric,
++ square matrix \bs{}axiom\{m\}.
-      matrix: \$-> SquareMatrix(n,K) -- export matrix + matrix:$ -> SquareMatrix(n,K)       -- export matrix
++ \bs{}axiom\{matrix(qf)\} creates a square matrix
++ from the quadratic form \bs{}axiom\{qf\}.
-      elt: (\$, DirectProduct(n,K)) -> K -- export elt + elt: ($, DirectProduct(n,K)) -> K    -- export elt
++ \bs{}axiom\{qf(v)\} evaluates the quadratic form
++ \bs{}axiom\{qf\} on the vector \bs{}axiom\{v\},
++ producing a scalar.
@@ -57507,19 +57507,19 @@
PI ==> PositiveInteger
Database(S): Exports == Implementation where
S: Object with
-    elt: (\$, Symbol) -> String - display: \$ -> Void
-    fullDisplay: \$-> Void + elt: ($, Symbol) -> String
+    display: $-> Void + fullDisplay:$ -> Void

Exports == with
-    elt: (\$,QueryEquation) -> \$                   Select by an equation
-    elt: (\$, Symbol) -> DataList String Select by a field name - "+": (\$,\$) -> \$                              Combine two databases
-    "-": (\$,\$) -> \$Subtract one from another - display: \$ -> Void                             A brief database display
-    fullDisplay: \$-> Void A full database display - fullDisplay: (\$,PI,PI) -> Void                 A selective display
-    coerce: \$-> OutputForm Display a database + elt: ($,QueryEquation) -> $Select by an equation + elt: ($, Symbol) -> DataList String             Select by a field name
+    "+": ($,$) -> $Combine two databases + "-": ($,$) ->$                                 Subtract one from another
+    display: $-> Void A brief database display + fullDisplay:$ -> Void                          A full database display
+    fullDisplay: ($,PI,PI) -> Void A selective display + coerce:$ -> OutputForm                         Display a database
...
\end{verbatim}
@@ -57621,15 +57621,15 @@
\begin{verbatim}
QueryEquation(): Exports == Implementation where
Exports == with
-    equation: (Symbol, String) -> \$- variable: \$ -> Symbol
-    value:\ \ \ \ \$-> String + equation: (Symbol, String) ->$
+    variable: $-> Symbol + value:$ -> String

Rep := Record(var:Symbol, val:String)
equation(x, s) == [x, s]
variable q == q.var
-    value\ \ \ \ q == q.val
+    value q == q.val
\end{verbatim}

Axiom converts an input expression of the form
@@ -65031,8 +65031,8 @@
sx2 := sin(x/2)
cx2 := cos(x/2)
-  point [cx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), \_
-         sx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), \_
+  point [cx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
+         sx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
-sx2 * (sq2 + cy) + cx2 * sy * cy]

draw(klein, 0..4*\%pi, 0..2*\%pi, var1Steps==50,       Figure-8 Klein bottle
@@ -65081,7 +65081,7 @@
respectively.

draw(gam, -\%pi..\%pi, -\%pi..\%pi,                The Gamma Function
-     title == "Gamma(x + \%i*y)", \_
+     title == "Gamma(x + \%i*y)", _
var1Steps == 100, var2Steps == 100)

b(x,y) == Beta(x,y)
@@ -65376,8 +65376,8 @@
\begin{verbatim}
ntubeDraw: (ThreeCurve,TwoCurve,S,S) -> VIEW3D
ntubeDraw(spaceCurve,planeCurve,uRange,tRange) ==
-  ntubeDrawOpt(spaceCurve, planeCurve, uRange, \_
-               tRange, []\$List DROPT) + ntubeDrawOpt(spaceCurve, planeCurve, uRange, _ + tRange, []$List DROPT)

ntubeDrawOpt: (ThreeCurve,TwoCurve,S,S,List DROPT)
-> VIEW3D
@@ -65410,7 +65410,7 @@
error "Frenet Frame not well defined"
n := (1/ln)*n                              Make into unit length vectors
b := (1/lb)*b
-  [f0, t0, n, b]\$FrenetFrame + [f0, t0, n, b]$FrenetFrame
\end{verbatim}

{\bf ngeneralTube}{\it (spaceCurve, planeCurve,}{\it  delT, oltT)}
@@ -65456,7 +65456,7 @@
m2 * inverse(m1)                              in 3-space

makeColumnMatrix(t) ==                          Put the vertices of a tetra-
-  m := new(4,4,0)\$DHMATRIX(DFLOAT) hedron into matrix form + m := new(4,4,0)$DHMATRIX(DFLOAT)              hedron into matrix form
for x in t for i in 1..repeat
for j in 1..3 repeat
m(j,i) := x.j