Commit e4633419 authored by Gunter Königsmann's avatar Gunter Königsmann Committed by Raymond Toy

Manual: A bunch of many additional missing anchors.

I guess it is reasonable to commit them all in one go;
Will now trigger the Nightly Linux build in order to see if any
currently-active Ubuntu version runs into any problems with the
new anchors.
parent fa631829
Pipeline #1349 passed with stages
in 1 minute and 22 seconds
......@@ -253,6 +253,7 @@ The symbol for base vectors.
@end defvr
@anchor{sf}
@deffn {Function} sf (@var{u}, @var{v})
A symmetric scalar function that is used in commutation relations.
......
......@@ -314,6 +314,7 @@ m1pbranch:false m1pbranch:true
@end defvr
@c -----------------------------------------------------------------------------
@anchor{nonnegintegerp}
@deffn {Function} nonnegintegerp (@var{n})
Return @code{true} if and only if @code{@var{n} >= 0} and @var{n} is an integer.
......
......@@ -302,6 +302,7 @@ Examples:
@end defvr
@c -----------------------------------------------------------------------------
@anchor{combine}
@deffn {Function} combine (@var{expr})
Simplifies the sum @var{expr} by combining terms with the same
......
......@@ -6,6 +6,7 @@
@node Introduction to asympa, Functions and variables for asympa, asympa-pkg, asympa-pkg
@section Introduction to asympa
@anchor{asympa}
@deffn {Function} asympa
@code{asympa} is a package for asymptotic analysis. The package contains
simplification functions for asymptotic analysis, including the ``big O''
......
......@@ -5,6 +5,7 @@
@node Functions and Variables for augmented_lagrangian, , augmented_lagrangian-pkg, augmented_lagrangian-pkg
@section Functions and Variables for augmented_lagrangian
@anchor{augmented_lagrangian_method}
@deffn {Function} augmented_lagrangian_method @
@fname{augmented_lagrangian_method} (@var{FOM}, @var{xx}, @var{C}, @var{yy}) @
@fname{augmented_lagrangian_method} (@var{FOM}, @var{xx}, @var{C}, @var{yy}, optional_args) @
......
......@@ -5,6 +5,7 @@
@node Functions and Variables for clebsch_gordan, , clebsch_gordan-pkg, clebsch_gordan-pkg
@section Functions and Variables for clebsch_gordan
@anchor{clebsch_gordan}
@deffn {Function} clebsch_gordan (@var{j1}, @var{j2}, @var{m1}, @var{m2}, @var{j}, @var{m})
Compute the Clebsch-Gordan coefficient @verb{|<j1, j2, m1, m2 | j, m>|}.
......@@ -14,6 +15,7 @@ Compute the Clebsch-Gordan coefficient @verb{|<j1, j2, m1, m2 | j, m>|}.
@closecatbox
@end deffn
@anchor{racah_v}
@deffn {Function} racah_v (@var{a}, @var{b}, @var{c}, @var{a1}, @var{b1}, @var{c1})
Compute Racah's V coefficient (computed in terms of a related
......@@ -24,6 +26,7 @@ Clebsch-Gordan coefficient).
@closecatbox
@end deffn
@anchor{racah_w}
@deffn {Function} racah_w (@var{j1}, @var{j2}, @var{j5}, @var{j4}, @var{j3}, @var{j6})
Compute Racah's W coefficient (computed in terms of a Wigner @verb{|6j|} symbol)
......@@ -33,6 +36,7 @@ Compute Racah's W coefficient (computed in terms of a Wigner @verb{|6j|} symbol)
@closecatbox
@end deffn
@anchor{wigner_3j}
@deffn {Function} wigner_3j (@var{j1}, @var{j2}, @var{j3}, @var{m1}, @var{m2}, @var{m3})
Compute Wigner's @verb{|3j|} symbol (computed in terms of a related
......@@ -43,6 +47,7 @@ Clebsch-Gordan coefficient).
@closecatbox
@end deffn
@anchor{wigner_6j}
@deffn {Function} wigner_6j (@var{j1}, @var{j2}, @var{j3}, @var{j4}, @var{j5}, @var{j6})
Compute Wigner's @verb{|6j|} symbol.
......@@ -52,6 +57,7 @@ Compute Wigner's @verb{|6j|} symbol.
@closecatbox
@end deffn
@anchor{wigner_9j}
@deffn {Function} wigner_9j (@var{a}, @var{b}, @var{c}, @var{d}, @var{e}, @var{f}, @var{g}, @var{h}, @var{i}, @var{j},)
Compute Wigner's @verb{|9j|} symbol.
......
......@@ -239,6 +239,7 @@ Extensive debugging traces and messages are displayed if the command
@node Functions and Variables for contrib_ode, Possible improvements to contrib_ode, Introduction to contrib_ode, contrib_ode-pkg
@section Functions and Variables for contrib_ode
@anchor{contrib_ode}
@deffn {Function} contrib_ode (@var{eqn}, @var{y}, @var{x})
Returns a list of solutions of the ODE @var{eqn} with
......@@ -250,6 +251,7 @@ independent variable @var{x} and dependent variable @var{y}.
@end deffn
@anchor{odelin}
@deffn {Function} odelin (@var{eqn}, @var{y}, @var{x})
@code{odelin} solves linear homogeneous ODEs of first and
......@@ -282,6 +284,7 @@ special functions.
@end deffn
@anchor{ode_check}
@deffn {Function} ode_check (@var{eqn}, @var{soln})
Returns the value of ODE @var{eqn} after substituting a
......@@ -408,6 +411,7 @@ The derivative with respect to @var{x} of @code{gauss_a(@var{a}, @var{b}, @var{c
@end deffn
@anchor{dgauss_b}
@deffn {Function} dgauss_b (@var{a}, @var{b}, @var{c}, @var{x})
The derivative with respect to @var{x} of @code{gauss_b(@var{a}, @var{b}, @var{c}, @var{x})}.
......@@ -470,6 +474,7 @@ The derivative with respect to @var{x} of @code{kummer_u(@var{a}, @var{b}, @var{
@end deffn
@anchor{bessel_simplify}
@deffn {Function} bessel_simplify (@var{expr})
Simplifies expressions containing Bessel functions bessel_j, bessel_y,
bessel_i, bessel_k, hankel_1, hankel_2, strauve_h and strauve_l.
......@@ -518,6 +523,7 @@ differ by less than 2.
@end deffn
@anchor{expintegral_e_simplify}
@deffn {Function} expintegral_e_simplify (@var{expr})
Simplify expressions containing exponential integral expintegral_e
using the recurrence (A&S 5.1.14).
......
......@@ -74,6 +74,7 @@ equation into a system of two autonomous equations.
@subsection Functions
@anchor{drawdf}
@deffn {Function} drawdf @
@fname{drawdf} (@var{dydx}, ...options and objects...) @
@fname{drawdf} (@var{dvdu}, [@var{u},@var{v}], ...options and objects...) @
......
......@@ -47,6 +47,7 @@ with the contraction ratio.
You can change the transformations and find another fractal
@anchor{sierpinskiale}
@deffn {Function} sierpinskiale (@var{n})
Sierpinski Triangle: 3 contractive maps; .5 contraction constant and translations;
......@@ -66,6 +67,7 @@ Example:
@end deffn
@anchor{treefale}
@deffn {Function} treefale (@var{n})
3 contractive maps all with the same contraction ratio.
......@@ -85,6 +87,7 @@ Example:
@end deffn
@anchor{fernfale}
@deffn {Function} fernfale (@var{n})
4 contractive maps, the probability to choice a transformation must be related
......@@ -107,6 +110,7 @@ Example:
@node Definitions for complex fractals, Definitions for Koch snowflakes, Definitions for IFS fractals, Top
@section Definitions for complex fractals
@anchor{mandelbrot_set}
@deffn {Function} mandelbrot_set (@var{x}, @var{y})
Mandelbrot set.
......@@ -132,7 +136,7 @@ the computing time is also related with the number of grid points.
@anchor{julia_set}
@deffn {Function} julia_set (@var{x}, @var{y})
Julia sets.
......@@ -178,7 +182,7 @@ Its default value is @mref{%i}; we suggest the values @code{-.745+%i*.113002},
@anchor{julia_sin}
@deffn {Function} julia_sin (@var{x}, @var{y})
While function @code{julia_set} implements the transformation @code{julia_parameter+z^2},
......@@ -214,6 +218,7 @@ See also @mref{julia_parameter}.
@anchor{snowmap}
@deffn {Function} snowmap (@var{ent}, @var{nn})
Koch snowflake sets. Function @code{snowmap} plots the snow Koch map
......@@ -245,6 +250,7 @@ Examples:
Continuous curves that cover an area. Warning:
the number of points exponentially grows with @var{n}.
@anchor{hilbertmap}
@deffn {Function} hilbertmap (@var{nn})
Hilbert map. Argument @var{nn} must be small (5, for example).
......@@ -263,6 +269,7 @@ Example:
@end deffn
@anchor{sierpinskimap}
@deffn {Function} sierpinskimap (@var{nn})
Sierpinski map. Argument @var{nn} must be small (5, for example).
......
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......@@ -1115,6 +1115,7 @@ row operation @code{R_i <- R_i - theta * R_j}. If @var{M} doesn't have a row
@end deffn
@anchor{linalg_rank}
@deffn {Function} linalg_rank (@var{M})
Return the rank of the matrix @var{M}. This function is equivalent to
......
......@@ -689,6 +689,7 @@ the half-integer Bessel functions are evaluated using the SLATEC code.
@node Functions and Variables for orthogonal polynomials, , Introduction to orthogonal polynomials, orthopoly-pkg
@section Functions and Variables for orthogonal polynomials
@anchor{assoc_legendre_p}
@deffn {Function} assoc_legendre_p (@var{n}, @var{m}, @var{x})
The associated Legendre function of the first kind of degree @var{n} and
order @var{m}.
......@@ -702,6 +703,7 @@ Reference: Abramowitz and Stegun, equations 22.5.37, page 779, 8.6.6
@end deffn
@anchor{assoc_legendre_q}
@deffn {Function} assoc_legendre_q (@var{n}, @var{m}, @var{x})
The associated Legendre function of the second kind of degree @var{n}
and order @var{m}.
......@@ -714,6 +716,7 @@ Reference: Abramowitz and Stegun, equation 8.5.3 and 8.1.8.
@end deffn
@anchor{chebyshev_t}
@deffn {Function} chebyshev_t (@var{n}, @var{x})
The Chebyshev polynomial of the first kind of degree @var{n}.
......@@ -725,6 +728,7 @@ Reference: Abramowitz and Stegun, equation 22.5.47, page 779.
@end deffn
@anchor{chebyshev_u}
@deffn {Function} chebyshev_u (@var{n}, @var{x})
The Chebyshev polynomial of the second kind of degree @var{n}.
......@@ -736,6 +740,7 @@ Reference: Abramowitz and Stegun, equation 22.5.48, page 779.
@end deffn
@anchor{gen_laguerre}
@deffn {Function} gen_laguerre (@var{n}, @var{a}, @var{x})
The generalized Laguerre polynomial of degree @var{n}.
......@@ -747,6 +752,7 @@ Reference: Abramowitz and Stegun, equation 22.5.54, page 780.
@end deffn
@anchor{hermite}
@deffn {Function} hermite (@var{n}, @var{x})
The Hermite polynomial of degree @var{n}.
......@@ -758,6 +764,7 @@ Reference: Abramowitz and Stegun, equation 22.5.55, page 780.
@end deffn
@anchor{intervalp}
@deffn {Function} intervalp (@var{e})
Return @code{true} if the input is an interval and return false if it isn't.
......@@ -768,6 +775,7 @@ Return @code{true} if the input is an interval and return false if it isn't.
@end deffn
@anchor{jacobi_p}
@deffn {Function} jacobi_p (@var{n}, @var{a}, @var{b}, @var{x})
The Jacobi polynomial.
......@@ -784,6 +792,7 @@ Reference: Abramowitz and Stegun, equation 22.5.42, page 779.
@end deffn
@anchor{laguerre}
@deffn {Function} laguerre (@var{n}, @var{x})
The Laguerre polynomial of degree @var{n}.
......@@ -795,6 +804,7 @@ Reference: Abramowitz and Stegun, equations 22.5.16 and 22.5.54, page 780.
@end deffn
@anchor{legendre_p}
@deffn {Function} legendre_p (@var{n}, @var{x})
The Legendre polynomial of the first kind of degree @var{n}.
......@@ -806,6 +816,7 @@ Reference: Abramowitz and Stegun, equations 22.5.50 and 22.5.51, page 779.
@end deffn
@anchor{legendre_q}
@deffn {Function} legendre_q (@var{n}, @var{x})
The Legendre function of the second kind of degree @var{n}.
......@@ -817,6 +828,7 @@ Reference: Abramowitz and Stegun, equations 8.5.3 and 8.1.8.
@end deffn
@anchor{orthopoly_recur}
@deffn {Function} orthopoly_recur (@var{f}, @var{args})
Returns a recursion relation for the orthogonal function family
@var{f} with arguments @var{args}. The recursion is with
......@@ -880,6 +892,7 @@ case, the interval is a disk in the complex plane.
@end defvr
@anchor{orthopoly_weight}
@deffn {Function} orthopoly_weight (@var{f}, @var{args})
Returns a three element list; the first element is
......@@ -910,6 +923,7 @@ signals an error.
@end deffn
@anchor{pochhammer}
@deffn {Function} pochhammer (@var{x}, @var{n})
The Pochhammer symbol. For nonnegative integers @var{n} with
@code{@var{n} <= pochhammer_max_index}, the expression @code{pochhammer (@var{x}, @var{n})}
......@@ -993,6 +1007,7 @@ Reference: Abramowitz and Stegun, equation 6.1.16, page 256.
@end defvr
@anchor{spherical_bessel_j}
@deffn {Function} spherical_bessel_j (@var{n}, @var{x})
The spherical Bessel function of the first kind.
......@@ -1005,6 +1020,7 @@ Reference: Abramowitz and Stegun, equations 10.1.8, page 437 and 10.1.15, page 4
@end deffn
@anchor{spherical_bessel_y}
@deffn {Function} spherical_bessel_y (@var{n}, @var{x})
The spherical Bessel function of the second kind.
......@@ -1017,6 +1033,7 @@ Reference: Abramowitz and Stegun, equations 10.1.9, page 437 and 10.1.15, page 4
@end deffn
@anchor{spherical_hankel1}
@deffn {Function} spherical_hankel1 (@var{n}, @var{x})
The spherical Hankel function of the
first kind.
......@@ -1030,6 +1047,7 @@ Reference: Abramowitz and Stegun, equation 10.1.36, page 439.
@end deffn
@anchor{spherical_hankel2}
@deffn {Function} spherical_hankel2 (@var{n}, @var{x})
The spherical Hankel function of the second kind.
......@@ -1042,6 +1060,7 @@ Reference: Abramowitz and Stegun, equation 10.1.17, page 439.
@end deffn
@anchor{spherical_harmonic}
@deffn {Function} spherical_harmonic (@var{n}, @var{m}, @var{x}, @var{y})
The spherical harmonic function.
......@@ -1069,6 +1088,7 @@ takes on the value 1/2 at zero, use @code{(1 + signum (@var{x}))/2}.
@end deffn
@anchor{ultraspherical}
@deffn {Function} ultraspherical (@var{n}, @var{a}, @var{x})
The ultraspherical polynomial (also known as the Gegenbauer polynomial).
......
......@@ -281,6 +281,7 @@ Example:
@category{Package functs}
@closecatbox
@anchor{rempart}
@deffn {Function} rempart (@var{expr}, @var{n})
Removes part @var{n} from the expression @var{expr}.
......@@ -296,6 +297,7 @@ To use this function write first @code{load(functs)}.
@end deffn
@anchor{wronskian}
@deffn {Function} wronskian ([@var{f_1}, ..., @var{f_n}], @var{x})
Returns the Wronskian matrix of the list of expressions [@var{f_1}, ..., @var{f_n}] in the variable @var{x}.
The determinant of the Wronskian matrix is the Wronskian determinant of the list of expressions.
......@@ -327,6 +329,7 @@ To use @code{wronskian}, first @code{load(functs)}. Example:
@c adjoint already described in doc/info/Matrices.texi
@anchor{tracematrix}
@deffn {Function} tracematrix (@var{M})
Returns the trace (sum of the diagonal elements) of matrix @var{M}.
......@@ -357,6 +360,7 @@ To use this function write first @code{load(functs)}.
@c kronecker superseded by kron_delta in src/nset.lisp
@anchor{nonzeroandfreeof}
@deffn {Function} nonzeroandfreeof (@var{x}, @var{expr})
Returns @code{true} if @var{expr} is nonzero and @code{freeof (@var{x}, @var{expr})} returns @code{true}.
Returns @code{false} otherwise.
......
......@@ -5,6 +5,7 @@
@node Functions and Variables for stirling, , stirling-pkg, stirling-pkg
@section Functions and Variables for stirling
@anchor{stirling}o
@deffn {Function} stirling @
@fname{stirling} (@var{z},@var{n}) @
@fname{stirling} (@var{z},@var{n},@var{pred})
......
......@@ -294,6 +294,7 @@ See also @mref{setunits}. To use this function write first @code{load("unit")}.
@end deffn
@anchor{convert}
@deffn {Function} convert (@var{expr}, @var{list})
When resetting the global environment is overkill, there is the @code{convert}
command, which allows one time conversions. It can accept either a single
......@@ -690,6 +691,7 @@ control over their working environment.
@end defvr
@anchor{metricexpandall}
@deffn {Function} metricexpandall (@var{x})
Rebuilds global unit lists automatically creating all desired metric units.
@var{x} is a numerical argument which is used to specify how many metric
......
......@@ -118,6 +118,7 @@ Otherwise @code{AntiDifference} returns @code{no_hyp_antidifference}.
@end deffn
@anchor{Gosper}
@deffn {Function} Gosper (@math{F_k}, @var{k})
Returns the rational certificate @math{R(k)} for @math{F_k}, that is,
a rational function such that
......@@ -136,6 +137,7 @@ Otherwise, @code{Gosper} returns @code{no_hyp_sol}.
@end deffn
@anchor{GosperSum}
@deffn {Function} GosperSum (@math{F_k}, @var{k}, @var{a}, @var{b})
Returns the summmation of @math{F_k} from @math{@var{k} = @var{a}} to @math{@var{k} = @var{b}}
......@@ -213,6 +215,7 @@ Dependent equations eliminated: (1)
@end deffn
@iftex
@anchor{parGosper}
@deffn {Function} parGosper (@math{F_{n,k}}, @var{k}, @var{n}, @var{d})
Attempts to find a @var{d}-th order recurrence for
......@@ -237,6 +240,7 @@ $$\left[R\left(n, k\right), \left[a_0, a_1, \ldots, a_d\right]\right].$$
@end iftex
@ifnottex
@anchor{parGosper}
@deffn {Function} parGosper (@math{F_(n,k)}, @var{k}, @var{n}, @var{d})
Attempts to find a @var{d}-th order recurrence for @math{F_(n,k)}.
......@@ -256,6 +260,7 @@ Each solution has the form
@end ifnottex
@iftex
@anchor{Zeilberger}
@deffn {Function} Zeilberger (@math{F_{n,k}}, @var{k}, @var{n})
Attempts to compute the indefinite hypergeometric summation of
......@@ -287,6 +292,7 @@ $$\left[R\left(n, k\right), \left[a_0, a_1, \ldots, a_d\right]\right].$$
@end iftex
@ifnottex
@anchor{Zeilberger}
@deffn {Function} Zeilberger (@math{F_(n,k)}, @var{k}, @var{n})
Attempts to compute the indefinite hypergeometric summation of @math{F_(n,k)}.
......
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