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[Axiom-developer] 20080302.01.tpd.patch (add additional hyperdoc page tr
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From: |
daly |
|
Subject: |
[Axiom-developer] 20080302.01.tpd.patch (add additional hyperdoc page translations) |
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Date: |
Sun, 2 Mar 2008 16:05:53 -0600 |
This patch adds additional hyperdoc page translations -- Tim
========================================================================
diff --git a/changelog b/changelog
index d14449f..7966a8b 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080302 tpd src/hyper/bookvol11 add additional hyperdoc page translations
20080301 tpd src/hyper/bookvol11 add additional hyperdoc page translations
20080229 tpd src/hyper/bookvol11 add additional hyperdoc page translations
20080222 tpd src/Makefile move hyperdoc bitmaps location
diff --git a/src/hyper/bookvol11.pamphlet b/src/hyper/bookvol11.pamphlet
index f3d863e..4871419 100644
--- a/src/hyper/bookvol11.pamphlet
+++ b/src/hyper/bookvol11.pamphlet
@@ -473,6 +473,7 @@ PAGES=rootpage.xhtml \
dbopasech.xhtml \
dbopatan.xhtml \
dbopatanh.xhtml \
+ dbopbernoullib.xhtml \
dbopbesseli.xhtml \
dbopbesselj.xhtml \
dbopbesselk.xhtml \
@@ -480,6 +481,8 @@ PAGES=rootpage.xhtml \
dbopbeta.xhtml \
dbopbinary.xhtml \
dbopcardinalnumber.xhtml \
+ dbopchebyshevt.xhtml \
+ dbopchebyshevu.xhtml \
dbopcoefficient.xhtml \
dbopcoefficients.xhtml \
dbopcoerce.xhtml \
@@ -503,11 +506,13 @@ PAGES=rootpage.xhtml \
dbopcsc.xhtml \
dbopcsch.xhtml \
dbopcycleragits.xhtml \
+ dbopcyclotomic.xhtml \
dbopd.xhtml \
dbopdecimal.xhtml \
dbopdefiningpolynomial.xhtml \
dbopdegree.xhtml \
dbopdenom.xhtml \
+ dbopdraw.xhtml \
dbopdeterminant.xhtml \
dbopdiagonalmatrix.xhtml \
dbopdigamma.xhtml \
@@ -522,6 +527,7 @@ PAGES=rootpage.xhtml \
dbopeigenvectors.xhtml \
dbopelt.xhtml \
dbopequal.xhtml \
+ dbopeulere.xhtml \
dbopeulerphi.xhtml \
dbopeval.xhtml \
dbopevenq.xhtml \
@@ -537,6 +543,7 @@ PAGES=rootpage.xhtml \
dbopfractionpart.xhtml \
dbopgamma.xhtml \
dbopgcd.xhtml \
+ dbophermiteh.xhtml \
dbophex.xhtml \
dbophorizconcat.xhtml \
dbophtrigs.xhtml \
@@ -546,6 +553,7 @@ PAGES=rootpage.xhtml \
dbopinverse.xhtml \
dbopinvmod.xhtml \
dbopjacobi.xhtml \
+ dboplaguerrel.xhtml \
dboplaurent.xhtml \
dboplcm.xhtml \
dbopleadingcoefficient.xhtml \
@@ -8224,6 +8232,16 @@ the operations will have extra ones added at some stage.
<<page foot>>
@
+\subsection{dbopbernoullib.xhtml}
+<<dbopbernoullib.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopbernoullib not implemented
+<<page foot>>
+@
+
\subsection{dbopbesseli.xhtml}
<<dbopbesseli.xhtml>>=
<<standard head>>
@@ -8284,6 +8302,26 @@ the operations will have extra ones added at some stage.
<<page foot>>
@
+\subsection{dbopchebyshevt.xhtml}
+<<dbopchebyshevt.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopchebyshevt not implemented
+<<page foot>>
+@
+
+\subsection{dbopchebyshevu.xhtml}
+<<dbopchebyshevu.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopchebyshevu not implemented
+<<page foot>>
+@
+
\subsection{dbopcoefficient.xhtml}
<<dbopcoefficient.xhtml>>=
<<standard head>>
@@ -8514,6 +8552,16 @@ the operations will have extra ones added at some stage.
<<page foot>>
@
+\subsection{dbopcyclotomic.xhtml}
+<<dbopcyclotomic.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopcyclotomic not implemented
+<<page foot>>
+@
+
\subsection{dbopd.xhtml}
<<dbopd.xhtml>>=
<<standard head>>
@@ -8564,6 +8612,16 @@ the operations will have extra ones added at some stage.
<<page foot>>
@
+\subsection{dbopdraw.xhtml}
+<<dbopdraw.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopdraw not implemented
+<<page foot>>
+@
+
\subsection{dbopdeterminant.xhtml}
<<dbopdeterminant.xhtml>>=
<<standard head>>
@@ -8704,6 +8762,16 @@ the operations will have extra ones added at some stage.
<<page foot>>
@
+\subsection{dbopeulere.xhtml}
+<<dbopeulere.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbopeulere not implemented
+<<page foot>>
+@
+
\subsection{dbopeulerphi.xhtml}
<<dbopeulerphi.xhtml>>=
<<standard head>>
@@ -8854,6 +8922,16 @@ dbopfractionpart not implemented
<<page foot>>
@
+\subsection{dbophermiteh.xhtml}
+<<dbophermiteh.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dbophermiteh not implemented
+<<page foot>>
+@
+
\subsection{dbophex.xhtml}
<<dbophex.xhtml>>=
<<standard head>>
@@ -8945,6 +9023,16 @@ dbopfractionpart not implemented
<<page foot>>
@
+\subsection{dboplaguerrel.xhtml}
+<<dboplaguerrel.xhtml>>=
+<<standard head>>
+ </head>
+ <body>
+<<page head>>
+dboplaguerrel not implemented
+<<page foot>>
+@
+
\subsection{dboplaurent.xhtml}
<<dboplaurent.xhtml>>=
<<standard head>>
@@ -38490,6 +38578,10 @@ Although they have somewhat limited utility, Axiom
provides Roman numerals.
\subsection{numnumericfunctions.xhtml}
<<numnumericfunctions.xhtml>>=
<<standard head>>
+ <script type="text/javascript">
+<<handlefreevars>>
+<<axiom talker>>
+ </script>
</head>
<body onload="resetvars();">
<<page head>>
@@ -38687,6 +38779,318 @@ of the functions yield an error if the result is not
real.
<div id="ansp6"><div></div></div>
</li>
</ul>
+A number of additional operations may be used to compute numerical
+values. These are special polynomial functions that can be evaluated
+for values in any commutative ring R, and in particular for values in
+any floating-point type. The following operations are provided by the
+package <a href="db.html?OrthogonalPolynomialFunctions">
+OrthogonalPolynomialFunctions</a>:
+<ul>
+ <li> <a href="dbopchebyshevt.xhtml">chebyshevT</a>:
+ (nonNegativeInteger,R) -> R
+ <br/>
+ chebyshevT(n,z) is the nth Chebyshev polynomial of the first kind,
+ T[n](z). These are defined by
+ <br/>
+ (1-t*z)/(1-2*t*z*t**2)=sum(T[n](z)*t**n,n=0..)
+ </li>
+ <li> <a href="dbopchebyshevu.xhtml">chebyshevU</a>:
+ (nonNegativeInteger,R) -> R
+ <br/>
+ chebyshevU(n,z) is the nth Chebyshev polynomial of the second kind,
+ U[n](z). These are defined by
+ <br/>
+ 1/(1-2*t*z+t**2)=sum(U[n](z)*t**n,n=0..)
+ </li>
+ <li> <a href="dbophermiteh.xhtml">hermiteH</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ hermiteH(n,z) is the nth Hermite polynomial, H[n](z). These are
+ defined by
+ <br/>
+ exp(2*t*z-t**2)=sum(H[n](z)*t**n/n!,n=0..)
+ </li>
+ <li> <a href="dboplaguerrel.xhtml">laguerreL</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ laguerreL(n,z) is the nth Laguerre polynomial, L[n](z). These are
+ defined by
+ <br/>
+ (exp(-t*z/(1-t))/(1-t)=sum(L[n](z)*t**n/n!,n=0..)
+ </li>
+ <li> <a href="dboplaguerrel.xhtml">laguerreL</a>:
+ (NonNegativeInteger,NonNegativeInteger,R) -> R
+ <br/>
+ labuerreL(m,n,2) is the associated Laguerre polynomial, L<m>[n](z).
+ This is the nth derivative of L[n](z).
+ </li>
+ <li> <a href="dboplegendrep.xhtml">legendreP</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ legendreP(n,z) is the nth Legendre polynomial, P[n](z). These are
+ defined by
+ <br/>
+ 1/sqrt(1-2*z*t+t**2)=sum(P[n](z)*t**n,n=0..)
+ </li>
+</ul>
+<br/>
+<br/>
+These operations require non-negative integers for the indices,
+but otherwise the argument can be given as desired.
+<ul>
+ <li>
+ <input type="submit" id="p7" class="subbut"
+ onclick="makeRequest('p7');"
+ value="[chebyshevT(i,z) for i in 0..5]" />
+ <div id="ansp7"><div></div></div>
+ </li>
+</ul>
+The expression chebyshevT(n,z) evaluates to the nth Chebyshev polynomial
+of the first kind.
+<ul>
+ <li>
+ <input type="submit" id="p8" class="subbut"
+ onclick="makeRequest('p8');"
+ value="chebyshevT(3,5.0+6.0*%i)" />
+ <div id="ansp8"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p9" class="subbut"
+ onclick="makeRequest('p9');"
+ value="chebyshevT(3,5.0::DoubleFloat)" />
+ <div id="ansp9"><div></div></div>
+ </li>
+</ul>
+The expression chebyshevU(n,z) evaluates to the nth Chebyshev polynomial
+of the second kind.
+<ul>
+ <li>
+ <input type="submit" id="p10" class="subbut"
+ onclick="makeRequest('p10');"
+ value="[chebyshevU(i,z) for i in 0..5]" />
+ <div id="ansp10"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p11" class="subbut"
+ onclick="makeRequest('p11');"
+ value="chebyshevU(3,0.2)" />
+ <div id="ansp11"><div></div></div>
+ </li>
+</ul>
+The expression hermiteH(n,z) evaluates to the nth Hermite polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p12" class="subbut"
+ onclick="makeRequest('p12');"
+ value="[hermiteH(i,z) for i in 0..5]" />
+ <div id="ansp12"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p13" class="subbut"
+ onclick="makeRequest('p13');"
+ value="hermiteH(100,1.0)" />
+ <div id="ansp13"><div></div></div>
+ </li>
+</ul>
+The expression laguerreL(n,z) evaluates to the nth Laguerre polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p14" class="subbut"
+ onclick="makeRequest('p14');"
+ value="[laguerreL(i,z) for i in 0..4]" />
+ <div id="ansp14"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p15" class="subbut"
+ onclick="makeRequest('p15');"
+ value="laguerreL(4,1.2)" />
+ <div id="ansp15"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p16" class="subbut"
+ onclick="makeRequest('p16');"
+ value="[laguerreL(j,3,z) for j in 0..4]" />
+ <div id="ansp16"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p17" class="subbut"
+ onclick="makeRequest('p17');"
+ value="laguerreL(1,3,2.1)" />
+ <div id="ansp17"><div></div></div>
+ </li>
+</ul>
+The expression legendreP(n,z) evaluates to the nth Legendre polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p18" class="subbut"
+ onclick="makeRequest('p18');"
+ value="[legendreP(i,z) for i in 0..5]" />
+ <div id="ansp18"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p19" class="subbut"
+ onclick="makeRequest('p19');"
+ value="legendreP(3,3.0*%i)" />
+ <div id="ansp19"><div></div></div>
+ </li>
+</ul>
+<br/>
+<br/>
+Finally, three number-theoretic polynomial operations may be evaluated.
+The following operations are provided by the package
+<a href="db.xhtml?NumberTheoreticPolynomialFunctions">
+NumberTheoreticPolynomialFunctions</a>.
+<ul>
+ <li> <a href="dbopbernoullib.xhtml">bernoulliB</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ bernoulliB(n,z) is the nth Bernoulli polynomial, B[n](z). These are
+ defined by
+ <br/>
+ t*exp(z*t)/(exp t - 1)=sum(B[n](z)*t**n/n! for n=0..)
+ </li>
+ <li> <a href="dbopeulere.xhtml">eulerE</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ eulerE(n,z) is the nth Euler polynomial, E[n](z). These are defined by
+ <br/>
+ 2*exp(z*t)/(exp t + 1)=sum(E[n](z)*t**n/n! for n=0..)
+ </li>
+ <li> <a href="dbopcyclotomic.xhtml">cyclotomic</a>:
+ (NonNegativeInteger,R) -> R
+ <br/>
+ cyclotomic(n,z) is the nth cyclotomic polynomial φ(n,z).
+ This is the polynomial whose roots are precisely the primitive nth
+ roots of unity. This polynomial has degree given by the Euler
+ totient function φ(n).
+ </li>
+</ul>
+
+The expression bernoulliB(n,z) evaluates to the nth Bernoulli polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p20" class="subbut"
+ onclick="makeRequest('p20');"
+ value="bernoulliB(3,z)" />
+ <div id="ansp20"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p21" class="subbut"
+ onclick="makeRequest('p21');"
+ value="bernoulliB(3,0.7+0.4*%i)" />
+ <div id="ansp21"><div></div></div>
+ </li>
+</ul>
+The expression eulerE(n,z) evaluates to the nth Euler polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p22" class="subbut"
+ onclick="makeRequest('p22');"
+ value="eulerE(3,z)" />
+ <div id="ansp22"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p23" class="subbut"
+ onclick="makeRequest('p23');"
+ value="eulerE(3,0.7+0.4*%i)" />
+ <div id="ansp23"><div></div></div>
+ </li>
+</ul>
+The expression cyclotomic(n,z) evaluates to the nth cyclotomic polynomial.
+<ul>
+ <li>
+ <input type="submit" id="p24" class="subbut"
+ onclick="makeRequest('p24');"
+ value="cyclotomic(3,z)" />
+ <div id="ansp24"><div></div></div>
+ </li>
+ <li>
+ <input type="submit" id="p25" class="subbut"
+ onclick="makeRequest('p25');"
+ value="cyclotomic(3,(-1.0+0.0*%i)**(2/3))" />
+ <div id="ansp25"><div></div></div>
+ </li>
+</ul>
+<br/>
+<br/>
+Drawing complex functions in Axiom is presently somewhat awkward compared
+to drawing real functions. It is necessary to use the
+<a href="dbopdraw.xhtml">draw</a> operations that operate on functions
+rather than expressions.
+
+This is the complex exponential function. When this is displayed in color,
+the height is the value of the real part of the function and the color is
+the imaginary part. Red indicates large negative imaginary values, green
+indicates imaginary values near zero and blue/violet indicates large
+positive imaginary values.
+<ul>
+ <li>
+ <input type="submit" id="p26" class="subbut"
+ onclick="makeRequest('p26');"
+ value='draw((x,y)+->real exp
complex(x,y),-2..2,-2*%pi..2*%pi,colorFunction==(x,y)+->imag exp
complex(x,y),title=="exp(x+%i*y)",style=="smooth")' />
+ <div id="ansp26"><div></div></div>
+ </li>
+</ul>
+This is the complex arctangent function. Again, the height is the real part
+of the function value but here the color indicates the function value's phase.
+The position of the branch cuts are clearly visible and one can see that the
+function is real only for a real argument.
+<ul>
+ <li>
+ <input type="submit" id="p27" class="subbut"
+ onclick="makeRequest('p27');"
+ value='vp:=draw((x,y)+->real atan
complex(x,y),-%pi..%pi,-%pi..%pi,colorFunction==(x,y)+->argument atan
complex(x,y),title=="atan(x+%i*y)",style=="shade"); rotate(vp,-160,-45); vp' />
+ <div id="ansp27"><div></div></div>
+ </li>
+</ul>
+This is the complex Gamma function.
+<ul>
+ <li>
+ <input type="submit" id="p28" class="subbut"
+ onclick="makeRequest('p28');"
+ value='draw((x,y)+->max(min(real Gamma
complex(x,y),4),-4),-%pi..%pi,-%pi..%pi,style=="shade",colorFunction==(x,y)+->argument
Gamma complex(x,y),title=="Gamma(x+%i*y)",var1Steps==50,var2Steps==50)' />
+ <div id="ansp28"><div></div></div>
+ </li>
+</ul>
+This shows the real Beta function near the origin.
+<ul>
+ <li>
+ <input type="submit" id="p29" class="subbut"
+ onclick="makeRequest('p29');"
+
value='draw(Beta(x,y)/100,x=-1.6..1.7,y=-1.6..1.7,style=="shade",title=="Beta(x,y)",var1Steps==40,var2Steps==40)'
/>
+ <div id="ansp29"><div></div></div>
+ </li>
+</ul>
+This is the Bessel function J(alpha,x) for index alpha in the range -6..4 and
+argument x in the range 2..14.
+<ul>
+ <li>
+ <input type="submit" id="p30" class="subbut"
+ onclick="makeRequest('p30');"
+ value='draw((alpha,x)+->min(max(besselJ(alpha,x+8),-6),
6),-6..4,-6..6,title=="besselJ(alpha,x)",style=="shade",var1Steps==40,var2Steps==40)'
/>
+ <div id="ansp30"><div></div></div>
+ </li>
+</ul>
+This is the modified Bessel function I(alpha,x) evaluated for various real
+values of the index alpha and fixed argument x=5.
+<ul>
+ <li>
+ <input type="submit" id="p31" class="subbut"
+ onclick="makeRequest('p31');"
+ value="draw(besselI(alpha,5),alpha=-12..12,unit==[5,20])" />
+ <div id="ansp31"><div></div></div>
+ </li>
+</ul>
+This is similar to the last example except the index alpha takes on complex
+values in a 6x6 rectangle centered on the origin.
+<ul>
+ <li>
+ <input type="submit" id="p32" class="subbut"
+ onclick="makeRequest('p32');"
+ value='draw((x,y)+->real
besselI(complex(x/20,y/20),5),-60..60,-60..60,colorFunction==(x,y)+->argument
besselI(complex(x/20,y/20),5),title=="besselI(x+i*y,5)",style=="shade")' />
+ <div id="ansp32"><div></div></div>
+ </li>
+</ul>
<<page foot>>
@
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