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>> @
_______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer