# Glossary.ml

```(* Copyright INRIA and Microsoft Corporation, 2008-2013. *)

INCLUDE "preamble.ml"

let italic s = DC.dstyle (DC.css_of_string "font-style: italic") s

let glossary =
(* Please, keep the notions alphabetically sorted. *)
[
("ansatz",
(<:text<\
An \$(italic "ansatz") is an expression for the general solutions \
of a problem, or for most of them, which typically involves \
undetermined coefficients, and is used for an educated guess.\
>>)) ;
("Chebyshev expansion",
(<:text<\
A \$(italic "Chebyshev expansion") is a series of the form \
<:imath<f(x)=\frac{c_0}{2}+\sum_{n=1}^{+\infty} c_nT_n(x)>> \
where <:imath<T_n(x)>> denotes the <:imath<n>>th Chebyshev polynomial \
of the first kind.\
>>)) ;
("formal power series",
(<:text<\
A \$(italic "formal power series") <:imath<f(x)>> is an infinite sum \
of the form <:imath<\sum_{n = 0}^\infty f_n x^n>> \
where the <:imath<f_n>> are in some common ring <:imath<R>>. \
The coefficient <:imath<f_n>> of <:imath<x^n>> in <:imath<f(x)>> \
is also denoted <:imath<[x^n] \, f(x)>>. \
The ring of formal power series is denoted <:imath<R[[x]]>>.\
>>)) ;
("formal logarithmic sum",
(<:text<\
A \$(italic "formal logarithmic sum") is a finite sum of the form \
<:imath<\sum_{\alpha,j} x^\alpha f_{\alpha,j}(x) \log(x)^j>> \
where the <:imath<\alpha>> are in some common ring <:imath<R>> \
and the <:imath<f_{\alpha,j}(x)>> are formal power series \
in <:imath<R[[x]]>>.\
>>)) ;
("indicial equation",
(<:text<\
The \$(italic "indicial equation") (or \$(italic "indicial polynomial")) \
of a linear differential equation with polynomial coefficients is the \
coefficient of the power of_<:imath<x>> with lowest exponent \
in the expression that is obtained by the substitution \
<:imath<y(x) = x^\alpha>> into the equation. \
Its roots are exactly the exponents of <:imath<x>> that can appear \
as lowest exponents in a series solution of the differential equation.\
>>)) ;
("majorant series",
(<:text<\
A series <:imath<\sum_{n\geq0} g_n z^n>> with nonnegative coefficients \
is a \$(italic "majorant series") of a series \
<:imath<\sum_{n\geq0} f_n z^n>> with complex coefficients if \
<:imath<|f_n| \leq g_n>> for all <:imath<n>>.\
>>)) ;
("ordinary point",
(<:text<\
A complex number <:imath<z_0>> is an \$(italic "ordinary point") of a \
linear ordinary differential equation with polynomial coefficients, if \
the leading coefficient of the equation does not vanish \
at <:imath<z_0>>.\
>>)) ;
("ramification index",
(<:text<\
The \$(italic "ramification index") is the smallest positive \
integer <:imath<r>> such that the exponent of an exponential factor \
can be expressed as a polynomial in <:imath<x^{-1/r}>>.
>>)) ;
("singular point",
(<:text<\
A complex number <:imath<z_0>> is a \$(italic "singular point") (or \
\$(italic "singularity") of a linear ordinary differential equation \
with polynomial coefficients, if the leading coefficient of the \
equation vanishes at <:imath<z_0>>.\
>>)) ;
("Laplace transform",
(<:text<\
The \$(italic "Laplace transform") of a function <:imath<f>> of the \
variable <:imath<z>> is the function <:imath<F>> defined by the \
integral <:imath<F(s) = \int_0^\infty e^{-sz} f(z) \,dz>>.\
>>))
]

(* A single function, named g for conciseness, as it is called Glossary.g. *)
let g ?(display = None) notion =
let body =
try List.assoc notion glossary with
| Not_found ->
<:text<(\$(italic notion) deserves a definition)>>
in

DC.definition
(match display with
| Some d -> d
| None -> notion)
body

let title _ = <:text<Glossary>>

let par = List.map (fun (_, body) -> <:par< \$(t_ent:body) >>) glossary

let_service Glossary : DC.sec_entities * unit with { title = title } =
(DC.section
(title ())
(if not (DynaMoW.Services.Renderings.is_defined ()) then
<:par<
Make sure you have selected a mathematical rendering