%
% Only the most commonly-used macros. Needed by everything else.
%
+\ifx\havemjocommon\undefined
+\def\havemjocommon{1}
-% Needed for \mathbb.
-\usepackage{amsfonts}
+\ifx\mathbb\undefined
+ \usepackage{amsfonts}
+\fi
-% Needed for \bigtimes.
-\usepackage{mathtools}
+\ifx\restriction\undefined
+ \usepackage{amssymb}
+\fi
% Place the argument in matching left/right parentheses.
-\providecommand*{\of}[1]{ \left({#1}\right) }
+\newcommand*{\of}[1]{ \left({#1}\right) }
% Group terms using parentheses.
-\providecommand*{\qty}[1]{ \left({#1}\right) }
+\newcommand*{\qty}[1]{ \left({#1}\right) }
% Group terms using square brackets.
-\providecommand*{\sqty}[1]{ \left[{#1}\right] }
-
-% Create a set from the given elements
-\providecommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
-
-% A set comprehension, where the ``such that...'' bar is added
-% automatically. The bar was chosen over a colon to avoid ambiguity
-% with the L : V -> V notation. We can't leverage \set here because \middle
-% needs \left and \right present.
-\providecommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
+\newcommand*{\sqty}[1]{ \left[{#1}\right] }
% A pair of things.
-\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
% A triple of things.
-\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
-
-% The Cartesian product of two things.
-\providecommand*{\cartprod}[2]{ {#1}\times{#2} }
-
-% The Cartesian product of three things.
-\providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
-
-% The direct sum of two things.
-\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
-
-% The direct sum of three things.
-\providecommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+\newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
+
+% A four-tuple of things.
+\newcommand*{\quadruple}[4]{ \left({#1},{#2},{#3},{#4}\right) }
+
+% A five-tuple of things.
+\newcommand*{\quintuple}[5]{ \left({#1},{#2},{#3},{#4},{#5}\right) }
+
+% A six-tuple of things.
+\newcommand*{\sextuple}[6]{ \left({#1},{#2},{#3},{#4},{#5},{#6}\right) }
+
+% A seven-tuple of things.
+\newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
+
+% A free-form tuple of things. Useful for when the exact number is not
+% known, such as when \ldots will be stuck in the middle of the list,
+% and when you don't want to think in column-vector terms, e.g. with
+% elements of an abstract Cartesian product space.
+\newcommand*{\tuple}[1]{ \left({#1}\right) }
+
+% The "least common multiple of" function. Takes a nonempty set of
+% things that can be multiplied and ordered as its argument. Name
+% chosen for synergy with \gcd, which *does* exist already.
+\newcommand*{\lcm}[1]{ \operatorname{lcm}\of{{#1}} }
+\ifdefined\newglossaryentry
+ \newglossaryentry{lcm}{
+ name={\ensuremath{\lcm{X}}},
+ description={the least common multiple of the elements of $X$},
+ sort=l
+ }
+\fi
% The factorial operator.
-\providecommand*{\factorial}[1]{ {#1}! }
+\newcommand*{\factorial}[1]{ {#1}! }
+
+% Restrict the first argument (a function) to the second argument (a
+% subset of that functions domain). Abused for polynomials to specify
+% an associated function with a particular domain (also its codomain,
+% in the case of univariate polynomials).
+\newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
+\ifdefined\newglossaryentry
+ \newglossaryentry{restriction}{
+ name={\ensuremath{\restrict{f}{X}}},
+ description={the restriction of $f$ to $X$},
+ sort=r
+ }
+\fi
%
% Product spaces
%
% The natural n-space, N x N x N x ... x N.
-\providecommand*{\Nn}[1][n]{
+\newcommand*{\Nn}[1][n]{
\mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{N}{
+ name={\ensuremath{\Nn[1]}},
+ description={the set of natural numbers},
+ sort=N
+ }
+\fi
+
% The integral n-space, Z x Z x Z x ... x Z.
-\providecommand*{\Zn}[1][n]{
+\newcommand*{\Zn}[1][n]{
\mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Z}{
+ name={\ensuremath{\Zn[1]}},
+ description={the ring of integers},
+ sort=Z
+ }
+\fi
+
% The rational n-space, Q x Q x Q x ... x Q.
-\providecommand*{\Qn}[1][n]{
+\newcommand*{\Qn}[1][n]{
\mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Q}{
+ name={\ensuremath{\Qn[1]}},
+ description={the field of rational numbers},
+ sort=Q
+ }
+\fi
+
% The real n-space, R x R x R x ... x R.
-\providecommand*{\Rn}[1][n]{
+\newcommand*{\Rn}[1][n]{
\mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{R}{
+ name={\ensuremath{\Rn[1]}},
+ description={the field of real numbers},
+ sort=R
+ }
+\fi
+
+
% The complex n-space, C x C x C x ... x C.
-\providecommand*{\Cn}[1][n]{
+\newcommand*{\Cn}[1][n]{
\mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
-% The space of real symmetric n-by-n matrices.
-\providecommand*{\Sn}[1][n]{
- \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+\ifdefined\newglossaryentry
+ \newglossaryentry{C}{
+ name={\ensuremath{\Cn[1]}},
+ description={the field of complex numbers},
+ sort=C
+ }
+\fi
+
+% The n-dimensional product space of a generic field F.
+\newcommand*{\Fn}[1][n]{
+ \mathbb{F}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
-% The space of complex Hermitian n-by-n matrices.
-\providecommand*{\Hn}[1][n]{
- \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
-%
-% Basic set operations
-%
-
-% The union of its two arguments.
-\providecommand*{\union}[2]{ {#1}\cup{#2} }
+\ifdefined\newglossaryentry
+ \newglossaryentry{F}{
+ name={\ensuremath{\Fn[1]}},
+ description={a generic field},
+ sort=F
+ }
+\fi
-% A three-argument union.
-\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
-
-% The intersection of its two arguments.
-\providecommand*{\intersect}[2]{ {#1}\cap{#2} }
-
-% A three-argument intersection.
-\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
% An indexed arbitrary binary operation such as the union or
% intersection of an infinite number of sets. The first argument is
% argument is the lower index, for example k=1. The third argument is
% the upper index, such as \infty. Finally the fourth argument should
% contain the things (e.g. indexed sets) to be operated on.
-\providecommand*{\binopmany}[4]{
+\newcommand*{\binopmany}[4]{
\mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
{ {#1}_{#2}^{#3}{#4} }
{ {#1}_{#2}^{#3}{#4} }
{ {#1}_{#2}^{#3}{#4} }
}
-\providecommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
-\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
-\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
-\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
-
% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
% the real line.
-\providecommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
-\providecommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
-\providecommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
-\providecommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+\newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+
+
+\fi
projects / mjotex.git / blobdiff