[Axiom-developer] 20080127.01.tpd.patch (refcard)

[daly]

This patch create a one-page, 2-sided reference card for Axiom.

Tim

=========================================================================
diff --git a/changelog b/changelog
index 052e649..d486296 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080127 tpd src/doc/Makefile add refcard
+20080127 tpd src/doc/refcard added
 20080125 tpd --patch-55 (January 2008) release
 20080125 tpd src/input/Makefile add En regression test 
 20080125 tpd src/input/en.input regression test En
diff --git a/src/doc/Makefile.pamphlet b/src/doc/Makefile.pamphlet
index cd17c11..6cbc985 100644
--- a/src/doc/Makefile.pamphlet
+++ b/src/doc/Makefile.pamphlet
@@ -81,6 +81,17 @@ ${DVI}/bookvol1.dvi: ${IN}/bookvol1.pamphlet
        cp ${IN}/ps/*ps* ${DVI}/ps )
 
 @
+\section{The Reference Card}
+This is the one-page, 2 sided reference card
+<<refcard>>=
+${DVI}/refcard.dvi: ${IN}/refcard.pamphlet
+       @echo 4 making ${DVI}/refcard.dvi from ${IN}/refcard.pamphlet
+       @(cd ${MID} ; \
+       cp ${IN}/refcard.pamphlet ${MID} ;\
+       ${DOCUMENT} ${NOISE} refcard ; \
+       cp refcard.dvi ${DVI} )
+
+@
 \section{The End Papers}
 This document reproduces the diagrams on the inside covers of the
 original Jenks Axiom book but adds hyperlinks.
@@ -164,8 +175,8 @@ DVI=${MNT}/${SYS}/doc
 DOC=${INT}/doc
 
 FILES= ${MID}/axiom.bib ${STY}/axiom.sty ${DVI}/bookvol4.dvi \
-       ${DVI}/book.dvi ${DVI}/bookvol1.dvi ${DVI}/endpaper.dvi \
-       ${DVI}/rosetta.dvi ${DVI}/spadhelp/spadhelp.files
+       ${DVI}/book.dvi ${DVI}/bookvol1.dvi ${DVI}/refcard.dvi \
+       ${DVI}/endpaper.dvi ${DVI}/rosetta.dvi ${DVI}/spadhelp/spadhelp.files
 
 CMDS=${OUT}/booklet
 
@@ -180,6 +191,7 @@ all: ${FILES} ${CMDS}
 <<bookvol4>>
 <<Book>>
 <<bookvol1>>
+<<refcard>>
 <<Endpapers>>
 <<rosetta>>
 <<spadhelp.files>>
diff --git a/src/doc/refcard.pamphlet b/src/doc/refcard.pamphlet
new file mode 100644
index 0000000..ef6afbe
--- /dev/null
+++ b/src/doc/refcard.pamphlet
@@ -0,0 +1,514 @@
+\documentclass{article}
+\usepackage[landscape]{geometry}
+\usepackage{multicol}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\advance\topmargin-.8in
+\advance\textheight2in
+\advance\textwidth3in
+\advance\oddsidemargin-1.5in
+\advance\evensidemargin-1.5in
+\parindent0pt
+\parskip2pt
+\newcommand{\hr}{\centerline{\rule{3.5in}{1pt}}}
+\begin{document}
+\begin{multicols*}{3}
+\begin{center}
+\textbf{Axiom Quick Reference (January 2008)}\\
+\end{center}
+
+\textbf{Command Line}
+
+)cd $\langle$pathname$\rangle$
+
+)clear all -- clear workspace
+
+)display op $\langle$function$\rangle$ -- function arguments
+
+)set message autoload off -- quietly load algebra
+
+)set message bottom on -- show selection process
+
+)set stream calculate 20 -- number of terms to calculate
+
+)show $\langle$domain$\rangle$ -- list all functions
+
+)spool $\langle${\sl filename}$\rangle$ -- start save session
+
+)spool -- close spool file
+
+)trace $\langle$domain$\rangle$ )math -- trace execution
+
+)quit -- exit Axiom
+
+)read $\langle$filename$\rangle$[.input] -- evaluate a file
+
+)sys $\langle$command line$\rangle$ -- execute command
+
+\_ continues input lines or escapes chars \verb|a_ b| = ``a b''
+
+\% is last value
+
+\%\%(n) is $n$th value
+
+-- and ++ start comment lines
+
+%*********************************************
+\hr\textbf{Programming}
+
+assignment: var := value\\
+\hbox{\hskip 2cm}x:=3
+
+conditional: if $\langle$pred$\rangle$ then $\langle$truecase$\rangle$
+else $\langle$falsecase$\rangle$\\
+\hbox{\hskip 2cm}\verb|if (2 > 4) then 4 else 5|
+
+loop: for $\langle$pred$\rangle$ repeat $\langle$block$\rangle$\\
+\hbox{\hskip 2cm}\verb|for i in 1..5 repeat print i|
+\hbox{\hskip 2cm}\verb|while i < 3 repeat (print i ; i:=i+1)|
+
+function: $f(x)=x^2$ \\
+\hbox{\hskip 2cm}\verb|f(x)==x^2|
+
+anon. function: \verb|g:=x +-> x+1| \quad g(3) $\rightarrow$ 4
+
+Indentation is significant:\\
+\hbox{\hskip 2cm}\verb|f(x)==(x > 3 => x ; 0)|\\
+\hbox{\hskip 2cm}\verb|f(x)==|\\
+\hbox{\hskip 2.4cm}\verb|x > 3 => x|\\
+\hbox{\hskip 2.4cm}\verb|0|
+
+%*********************************************
+\hr\textbf{Basic constants and functions}
+
+$\pi=$ \verb|%pi| \quad $e=$ \verb|%e| \quad $i=$ \verb|%i| 
+\quad $\infty=$ \verb|%infinity|
+
+$+\infty$=\verb|%plusInfinity|\quad $-\infty$=\verb|%minusInfinity|
+
+\verb|numeric(%pi)| $=3.1415926535\ 897932385$
+
+%Binary operations: \verb|+  -  *  /  ^|
+
+Functions: \verb|sin cos tan sec csc cot sinh cosh tanh| \verb|sech csch coth 
log ln exp|
+
+$ab=$ \verb|a*b| \quad $\frac a b=$ \verb|a/b| 
+\quad 
+$a^b=$ \verb|a^b| \quad $\sqrt{x}=$ \verb|sqrt(x)|
+
+$\sqrt[n]{x}=$\verb|x^(1/n)|
+$|x|=$\verb|abs(x)|
+$\log_b(x)=$\verb|log(x)/log(b)|
+
+%*********************************************
+\hr\textbf{Operations on expressions}
+
+\verb|factor(...)|\qquad \verb|expand(...)|\qquad \verb|simplify(...)|
+
+Symbolic equations: \verb|f(x)=g(x)|
+
+Solve $f(x)=g(x)$: \verb| solve(f(x)=g(x),x)|
+
+\verb|solve([x^2*y-1,x*y^2-2],.01)|\\
+\hbox{\hskip 2.0cm} $\rightarrow$ $[[y=1.5859375,x=0.79296875]]$
+
+\verb|complexSolve([x^2*y-1,x*y^2-2],1/1000)|
+
+\verb|radicalSolve([x^2/a+a+y^3-1,a*y+a+1],[x,y])|
+
+$\displaystyle\sum_{i=k}^n f(i)=$ \verb|reduce(+,[f(i) for i in k..n])|
+
+$\displaystyle\prod_{i=k}^n f(i)=$ \verb|reduce(*,[f(i) for i in k..n])|
+
+%*********************************************
+\hr\textbf{Pattern Matching}
+
+logrule:=rule log(x)+log(y) == log(x*y) $\rightarrow$\\
+\hbox{\hskip 2.1cm}\verb|log(y)+log(x)+%B==log(x y)+%B|
+
+f:=log sin x + log x $\rightarrow$ log(sin(x))+log(x)
+
+logrule f $\rightarrow$ log(x sin(x))
+
+%*********************************************
+\hr\textbf{Calculus}
+
+$\displaystyle\lim_{x\to a} f(x)=$ \verb|limit(f(x), x=a)|
+
+$\displaystyle\lim_{x\to a^-} f(x)=$ \verb|limit(f(x), x=a, "left")|
+
+$\displaystyle\lim_{x\to a^+} f(x)=$ \verb|limit(f(x), x=a, "right")|
+
+$\displaystyle\lim_{x\to \infty} f(x)=$ \verb|limit(f(x), x=%plusInfinity)|
+
+\verb|limit(sin(x)/x,x=%plusInfinity)| $\rightarrow$ 0
+
+\verb|complexLimit(sin(x)/x,x=%infinity)| $\rightarrow$ "failed"
+
+$\frac{d}{dx}(f(x))=$ \verb|D(f(x),x)|
+
+$\frac{\partial}{\partial x}(f(x,y))=$ \verb|D(f(x,y),x)|
+
+$\int f(x)dx=$ \verb|integrate(f(x),x)|
+
+$\int_a^b f(x)dx=$ \verb|integrate(f(x),x=a..b)|
+
+%*********************************************
+\hr\textbf{Series}
+
+x:=series 'x
+
+y:=sin(x) $\rightarrow$ 
+$x-\frac{1}{6}x^3+\frac{1}{120}x^5-\frac{1}{5040}x^7+O(x^9)$
+
+coefficient(y,3) $\rightarrow$ $-\frac{1}{6}$
+
+taylor(f(x),x=a)
+
+laurent(x/log(x),x=1)
+
+\verb|puiseux(sqrt(sec(x)),x=3*%pi/2)|
+
+%*********************************************
+\hr\textbf{2D graphics}
+
+\verb|draw(cos(5*t/8),t=0..16*%pi,coordinates==polar)|
+
+\verb|f(t:SF):SF == sin(3*t/5)|
+
+\verb|g(t:SF):SF == sin(t)|
+
+\verb|draw(curve(f,g),0..%pi)|
+
+\verb|draw(x^2+y^3-1=0,x,y,range==[-1..1,-1..1])|
+
+v1:=draw(Gamma(i),i=-4.2..4,adaptive==true)
+
+v2:=draw(1/Gamma(i),i=-4.2..4,adaptive==true)
+
+putGraph(v2,getGraph(v1,1),2)
+
+makeViewport2D(v2)
+
+options: adaptive clip toScale curveColor pointColor\\
+unit range coordinates
+
+%*********************************************
+\hr\textbf{3D graphics}
+
+m(u:SF,v:SF):SF == 1
+
+\verb|draw(m,0..2*%pi,0..%pi,coordinates==spherical)|
+
+options: title style colorFunction coordinates tubeRadius
+tubePoints var1Steps var2Steps space
+
+%*********************************************
+\hr\textbf{Discrete math}
+
+$\lfloor x\rfloor=$ \verb|floor(x)| 
+\quad 
+$\lceil x\rceil=$ \verb|ceiling(x)|
+
+Remainder of $n$ divided by $k=$ \verb|rem(n,k) |, $k|n$ iff \verb| n%k==0|
+
+$n!=$ \verb|factorial(n)| \qquad
+${x\choose m}=$ \verb|binomial(x,m)|
+
+$\phi(n)=$ \texttt{eulerPhi($n$)}\quad Tuples: \ \verb|(1,'Hello,x)| 
+
+%*********************************************
+\hr\textbf{Type Conversions}
+
+\verb|r:=(2/3)*x^2-y+4/5| $\rightarrow$ $-y+\frac{2}{3}x^2+\frac{4}{5}$\\
+\hbox{\hskip 2.0cm} Type: Polynomial Fraction Integer
+
+r::FRAC POLY INT $\rightarrow$ $\frac{-15y+10x^2+12}{15}$\\
+\hbox{\hskip 2.0cm} Type: Fraction Polynomial Integer
+
+\verb|s:=(3+4*%i)/(7+3*%i)| $\rightarrow$ $\frac{33}{58}+\frac{19}{58}\%i$
+
+s::FRAC COMPLEX INT $\rightarrow$ $\frac{3+4\%i}{7+3\%i}$
+
+%*********************************************
+\hr\textbf{Equation}
+
+eq1:=3*x+4*y=5 $\rightarrow$ $4y+3x=5$
+
+eq2:=2*x+2*y=3 $\rightarrow$ $2y+2x=3$
+
+lhs eq1 $\rightarrow$ $4y+3x$
+
+rhs eq1 $\rightarrow$ 5
+
+eq1+eq2 $\rightarrow$ $6y+5x=8$
+
+%*********************************************
+\hr\textbf{Factored}
+
+g:=factor(4312) $\rightarrow$ $2^3 7^2 11$
+
+unit g $\rightarrow$ 1
+
+numberOfFactors g $\rightarrow$ 3
+
+nthFactor(g,2) $\rightarrow$ 7
+
+nthExponent(g,2) $\rightarrow$ 2
+
+nthFlag(g,2) $\rightarrow$ "prime"
+
+map(factor,55739/2520) $\rightarrow$ $\frac{139\ 401}{2^3\ 3^2\ 5\ 7}$
+
+%*********************************************
+\hr\textbf{List}
+
+a:=[1,2,3,4] $\rightarrow$ $[1,2,3,4]$
+
+b:=[3,4,5,6] $\rightarrow$ $[3,4,5,6]$
+
+append(a,b) $\rightarrow$ $[1,2,3,4,3,4,5,6]$
+
+cons(10,a) $\rightarrow$ $[10,1,2,3,4]$
+
+empty? a $\rightarrow$ false
+
+a.2 $\rightarrow$ 2
+
+a.2 := 99 $\rightarrow$ $[1,99,3,4]$
+
+reverse b $\rightarrow$ $[6,5,4,3]$
+
+%*********************************************
+\hr\textbf{MakeFunction}
+
+\verb|expr:=(x+a)^3| $\rightarrow$ $x^3+ 3ax^2 + 3a^2x + a^3$
+
+function(expr,f,x) $\rightarrow$ f
+
+f(2) $\rightarrow$ $a^3 + 6a^2 + 12a + 8$
+
+function(expr,g,a) $\rightarrow$ g
+
+g(2) $\rightarrow$ $x^3 + 6x^2 + 12x + 8$
+
+%*********************************************
+\hr\textbf{Matrix}
+
+A:=matrix([[1,2],[3,4]]) $\rightarrow$
+$
+\left[
+\begin{array}{cc}
+1 & 2\\
+3 & 4\\
+\end{array}
+\right]
+$
+
+determinant A $\rightarrow$ -2
+
+v:=vector([1,2]) $\rightarrow$ $[1,2]$
+
+A*v $\rightarrow$ $[5,11]$
+
+\verb|A^-1| $\rightarrow$
+$
+\left[
+\begin{array}{cc}
+2 & 1\\
+\frac{3}{2} & \frac{1}{2}\\
+\end{array}
+\right]
+$
+
+transpose(A) $\rightarrow$ 
+$
+\left[
+\begin{array}{cc}
+1 & 3\\
+2 & 4\\
+\end{array}
+\right]
+$
+
+nrows A $\rightarrow$ 2
+
+ncols A $\rightarrow$ 2
+
+nullity A $\rightarrow$ 0
+
+rank A $\rightarrow$ 2
+
+trace A $\rightarrow$ 5
+
+%*********************************************
+\hr\textbf{Polynomial}
+
+x+1 yields Type {\bf Polynomial Integer}
+
+z-2.3 yields Type {\bf Polynomial Float}
+
+\verb|y^2-z+3/4| yields Type {\bf Polynomial Fraction Integer}
+
+\verb|p:=(y-1)^2*x*z| $\rightarrow$ $(xy^2-2xy+x)z$
+
+\verb|q:=(y-1)*x*(z+5)| $\rightarrow$ $(xy - x)z + 5xy - 5x$
+
+gcd(p,q) $\rightarrow$ $x y - x$
+
+mainVariable p $\rightarrow$ $z$
+
+variables p $\rightarrow$ $[z,y,x]$
+
+degree(p,y) $\rightarrow$ 2
+
+totaldegree p $\rightarrow$ 4
+
+eval(p,x,w) $\rightarrow$ $(wy^2  - 2wy + w)z$
+
+D(p,x) $\rightarrow$  $(y^2- 2y + 1)z$
+
+integrate(p,x) $\rightarrow$ $(\frac{1}{2}x^2y^2-x^2y+\frac{1}{2}x^2)z$
+
+%*********************************************
+\hr\textbf{PrimeField}
+
+x:PrimeField(7):=5 $\rightarrow$ 5
+
+\verb|x^3| $\rightarrow$ 6
+
+1/x $\rightarrow$ 3
+
+%*********************************************
+\hr\textbf{Set}
+
+\verb|s:=brace([1,2,3,4,5])| $\rightarrow$ $\{1,2,3,4,5\}$
+
+\verb;t:=brace([2,3,5,7]); $\rightarrow$ $\{2,3,5,7\}$
+
+intersect(s,t) $\rightarrow$ $\{2,3,5\}$
+
+union(s,t) $\rightarrow$ $\{1,2,3,4,5,7\}$
+
+difference(s,t) $\rightarrow$ $\{1,4\}$
+
+insert!(7,s) $\rightarrow$ $\{1,2,3,4,5,7\}$
+
+remove!(7,s) $\rightarrow$ $\{1,2,3,4,5\}$
+
+$\{1,2,1,a\}=$ \verb|brace([1,2,1,'a])| \ ($=\{1,2,a\}$)
+
+$\{f(x):x\in X,x>0\}\approx$\verb?brace([f(x) for x in X | x>0])?
+
+%*********************************************
+\hr\textbf{Special Functions}
+
+[fibonacci(k) for k in 0..] $\rightarrow$ [0,1,1,2,3,5,...]
+
+[legendre(i,11) for i in 0..5] $\rightarrow$ [0,1,- 1,1,1,1]
+
+[jacobi(i,15) for i in 0..5] $\rightarrow$ [0,1,1,0,1,0]
+
+[eulerPhi i for i in 1..] $\rightarrow$ [1,1,2,2,4,2,...]
+
+[moebiusMu i for i in 1..] $\rightarrow$ [1,- 1,- 1,0,- 1,1,...]
+
+E1(0.01) $\rightarrow$ 4.0379295765381134
+
+Gamma(0.01) $\rightarrow$ 99.432585119150588
+
+%*********************************************
+\hr\textbf{Stream}
+
+)set streams calculate 6
+
+\verb|ints := [i for i in 1..]| $\rightarrow$ \verb|[1,2,3,4,5,6,...]|
+
+ints.20 $\rightarrow$ 20
+
+\verb;[i for i in ints | odd? i]; $\rightarrow$ \verb|[1,3,5,7,9,11,...]|
+
+%*********************************************
+\hr\textbf{String}
+
+creation: \ s:= \verb|"Hello"| 
+
+concatenate \verb|"He" "llo"| $\rightarrow$ \verb|"Hello"| 
+
+\texttt{s(1)='H' \quad s.1='H' \quad s(2..3)='el' \quad s(4..)='lo'}
+
+split("hi there",char " ") $\rightarrow$ \verb|["hi","there"]|
+
+prefix?("He","Hello") $\rightarrow$ true
+
+substring?("ll","Hello",3) $\rightarrow$ true
+
+%*********************************************
+\hr\textbf{TwoDimensionalArray}
+
+creation: \verb|arr:ARRAY2 INT:=new(2,3,0)| $\rightarrow$ 
+$
+\left[
+\begin{array}{ccc}
+0 & 0 & 0\\
+0 & 0 & 0\\
+\end{array}
+\right]
+$
+
+nrows arr $\rightarrow$ 2
+
+ncols arr $\rightarrow$ 3
+
+setelt(arr,1,1,17) $\rightarrow$
+$
+\left[
+\begin{array}{ccc}
+17 & 0 & 0\\
+0 & 0 & 0\\
+\end{array}
+\right]
+$
+
+arr(1,1) $\rightarrow$ 17
+
+%*********************************************
+\hr\textbf{Univariate Polynomial}
+
+creation: \verb|p:UP(x,INT):=(3*x-1)^2*(2*x+8)|\\
+\hbox{\hskip 1.5cm}\verb|q:UP(x,INT):=(1-6*x+9*x^2)^2|
+
+leadingCoefficient p $\rightarrow$ 18
+
+degree p $\rightarrow$ 3
+
+reductum p $\rightarrow$ $60x^2-46x+8$
+
+gcd(p,q) $\rightarrow$ $9x^2-6x+1$
+
+lcm(p,q) $\rightarrow$ $162x^5+432x^4-756x^3+408x^2-94x+8$
+
+resultant(p,q) $\rightarrow$ 0
+
+p(2) $\rightarrow$ 300 (used as function)
+
+D(p) $\rightarrow$ $54x^2+120x-46$ (derivative)
+
+%*********************************************
+\hr\textbf{Vector}
+
+creation: \verb|v := vector([1,2,3,4,5])| $\rightarrow$ $[1,2,3,4,5]$
+
+length: \verb|#v| $\rightarrow$ 5
+
+access: v.2 $\rightarrow$ 2
+
+add: v+v $\rightarrow$ $[2,4,6,8,10]$
+
+multiply: 5*v $\rightarrow$ $[5,10,15,20,25]$
+
+assign: v.2 := 7 $\rightarrow$ $[1,7,3,4,5]$
+
+\end{multicols*}
+
+\end{document}
\ No newline at end of file