数学の常識・非常識 - 由緒正しい TeX 入力法

Size: px

Start display at page:

Download "数学の常識・非常識 - 由緒正しい TeX 入力法"

かずしおいもり
5 years ago
Views:

1 , 4 1, , pp TEX,.,, (copy editor),., TEX, TEX.,, TEX,., ( ).,,,.,,., TEX 1, TEX 2.,, 3., Tohoku Mathematical Journal,., ,,, 4.,. 1 TEX, [1], [2], [3], [4]., TEX, TEX, \., L A TEX 2ε, plain TEX AMS-TEX., TEX, control sequence,...tex,, % commented out,,., TEX,. 1

2 1.1,, (, TEX upright shape, roman family ), (, TEX mathitalic ).., f(x) a S, f (x) a S. TEX, $,.,, mathroman,.,., dim, lim, log, sin, min. dimv, logx, sinx, dim V, log x, sin x. dimv, d, i, m, V.,. GL(n, R), S L(n, C), O(n), S p(n),. K3, $K3$, ( 1.3 )., d,,, ISO., (H1) (A)., ( 1.3 ). 1.2 math operators log x log x., (in text), lim n a n, display lim a n. TEX control sequence n,. $\log x$, $\lim_{n\rightarrow\infty}a_n$., TEX control sequence. conv{v 1, v 2,..., v n } Hom R (M, N), conv{v 1, v 2,..., v n } Hom R (M, N)., \log control sequence, math operator. ${\mathop{\mathrm{hom}}\nolimits}_r(m,n)$ Hom R (M, N). AMS-TEX AMS-L A TEX, $\operatorname{hom}_r(m,n)$., L A TEX 2ε, \newcommand{\hom}{\mathop{\mathrm{hom}}\nolimits} control sequence \Hom preamble, $\Hom_R(M,N)$. TEX control sequence math operators ( Log-like functions ) arccos, arcsin, arctan, arg, cos, cosh, cot, coth, csc, deg, det, dim, exp, gcd, hom, inf, ker, lg, lim, lim inf, lim sup, ln, log, max, min, Pr, sec, sin, sinh, sup, tan, tanh 2

3 . math operators ad, Ad, Ass, Aut, BMO, ch, Char, Chow, Cl, codim, conv, dir lim, div, Div, Dom, End, Ext, Flag, Gal, gr, grad, Grass, Hilb, Hol, Hom, Im, ind lim, init, int, Ker, length, lcm, Lie, NS, ord, Pic, proj lim, Proj, Re, rel int, res, Res, Ric, sign, sgn, Sing, span, Spec, supp, Td, Todd, Tor, Tr, Trace, Vol, vol, weight, wt. math operator mod. TEX $\bmod$ $\pmod$ 2 control sequence, x a mod p x a (mod p). $x\equiv a\bmod p$ $x\equiv a\pmod p$. math operator ess, Id, id, ns, pt, red, reg, top, ur, a.e. I, II, III,..., i, ii, iii, , slant. control sequence, projective (resp. quasi-projective), Mumford [3], K3 surface, 2, (1), (ii), the hypothesis (H1). projective (resp. quasi-projective), Mumford [3], K3 surface, 2, (1), (ii), the hypothesis (H1). L A TEX 2ε.,, Mumford $[3]$, $K3$ surface, \S $2$, $(1)$, $(\mathrm{ii})$, $\cite{ega}$, \S $\ref{sec_notation}$. 1.4 suffix TEX,., TEX,,., 2 3, d f dx, a 1 2, 1 2 S, 2/3, d f /dx, a1/2, 2 1 S, (1/2)S (solidus). {\displaystyle } 2 3,. 3

4 1.5,,,,,. ( )., TEX. ( cf. [ 10] ), the following : (cf. [10]), the following:.,,,,, i.e. e.g. a.e.,. P.A.Griffiths Indeed,we have..., P. A. Griffiths Indeed, we have....,.,. TEX,,., J. Math. Soc. Japan J. Math. Soc. Japan.,. J. Math.\ Soc.\ Japan.,, A, B, etc.. Thus we have C..... (\ldots) (\cdots). x 1, x 2,..., x n, x a := x a 1 1 xa 2 2 xa n n, x 1 + x x n. 1.6 TEX 1.6.1, en, em quasi-projective, p en, em. -. en p em ,. P 1 -fibration P 1 fibration., $\mathbf{p}ˆ1$-fibration $\mathbf{p}ˆ1-$fibration., n-points in general position n points in general position. (n + 1) points n + 1 points, n + 1-dimensional (n + 1)-dimensional. 4

5 1.6.2,,, 2, 2. ". Quotation Quotation, "Quotation" Quotation. P s, P s. $P$ s $P s$. (1 ), (ii ) (1 ), (ii ) $(1 )$, $(\mathrm{ii} )$ < x, y >, x, y. $<x,y>$ $\langle x,y\rangle$. \langle, \rangle. <, > 2, , φ. X Y = φ, X Y =. $X\cap Y=\phi$ $X\cap Y=\emptyset$ $\backslash$ $\setminus$. G\X, Y \ X. \ 2,. $G\backslash X$ $Y\setminus X$ G\X Y \ X. AMS-TEX AMS-L A TEX (amssymb package), \smallsetminus l, 1. TEX, l. 1. l-adic l-adic. rank ( A l ), l(m), l l. l $\ell$, l $l$. 5

6 1.6.7, X Y X Y $\cup$ $\cap$, i I X i i I X i, $\bigcup$ $\bigcap$. i I X i i I X i. $\bigcup$ $\bigcap$, display X i, i I i I. big.,,,.,, big. Λ. X i 1.7 TEX, TEX,.,.,,. FEP IME,,. (,,,.),, TEX.,,. TEX,,.., theorem. \begin{theorem} \upshape. 1.8 OHP TEX (OHP) TEX (, OHP 91, 3 3, p. 42),.,,. OHP 1. A4 2/3.,. OHP.. L A TEX 2ε, \begin{document} preamble. \renewcommand{\baselinestretch}{1.2}., L A TEX 2ε,, \begin{document} \huge \bfseries \mathversion{bold}.. 6

7 OHP. f(x) C (X), lim f(x) = f(a). x a 2 TEX,. [1], [2], [4, 3, 6 8 ],. 2.1 full spelling,, full spelling. Math. Reviews Zentralblatt für Math. 2.,.,,..,, full spelling. Thanks are due to Professor A. Bcd for... Thanks are due to Professor Akio Bcd for....., middle name, J. William Fulbright middle name full spelling., first name middle name ( vich ).,,, full spelling., first name middle name. Math. Reviews,.,,. Science Citation Index. 2.2,. ASCII Introduction.,.,.. 7

8 2.4,,.. 1,,., Kasumigaseki. 2-3 Kasumigaseki 1-chome. 2.5,.,,.... as in the following figure.... as in the table above.,.... as in Figure as in Table 2. (cf. Figure 3). 2.6, credit,., [3, Theorem 2]., [3, 4], [3], [4]., (proceedings symposium,, )., Math. Reviews. ( 2.7 C-vector space, C-, C. Griffiths-Harris Shimura-Taniyama, -,. -,,. 2, =,.,, Griffiths Harris en ( ),. (, Commun. Math. Physics en.), Griffiths - Harris., Swinnerton-Dyer Birch Swinnerton-Dyer. ([3, 5.94].),,.., 8

9 Since A B, A C., Since A B, we have A C. A C, since A B... for all, for any there exists, for some. display.,. display. display. paragraph.,, paragraph indent paragraph., paragraph indent, 1. lim sup lim inf.. exp,. X Y, x f (x). $\rightarrow$, $\mapsto$. def =, :=. [x],. the greatest integer [x] not greater than x.,,, Γ(X), Γ(X), Γ(X), (Γ(X)), (Γ(X)), (Γ(X)),. x, x 2 x 2 (x ) 2. 3,. [5]. [6] [4, 4 ]., Theorem 1, Proposition 2, Lemma 3, Corollary 4, Figure 5, Table 6, Section 7. theorem 1, the theorem 1, the Theorem 1.,, Theorems 1 and 2 Propositions 2 through 10. the. the Hölder s inequality, the Hölder inequality Hölder s inequality. the referee s comment, the referee comment. Green s function,. the Green function. 9

10 by definition, by assumption, by induction on n, a circle with center at the origin, by the definition of X, by the assumption in Theorem 2.. a an, a unique, an L 2 -estimate, an S -module, a one-to-one map, a Euclidean space, an unique, a L 2 -estimate, a S -module, an one-to-one map, an Euclidean space., (n + 1)-th, (n + 2)-th, (n + 3)-th, (n + 1)-st, (n + 2)-nd, (n + 3)-rd. n plus first. Riemannian metric, Hilbert space, Banach space, Hermitian symmetric space, Jacobian, Hessian, Archimedean, Euclidean. riemannian metric. abelian, Abelian variety abelian variety. abelian group. glueing gluing, glued.. ing ( ed ).. the concept C introduced in the previous section introduce, the concept C., the concept D introduced in the next section. the concept C appeared in the previous section, (1) the concept C which appeared in the previous section (2) the concept C appearing in the previous section 10

11 (3) the concept C having appeared in the previous section. (, (3)., (3).) appear, (3). appearing,. the concept C. dangling participle ( ). Expanding the right hand side of (1) in terms of q, the theorem follows.. expand the theorem. Let If Let Assume, If. Let G be a group, then..., Let G be a group. Then.... And But,,. However, But. for this reason the reason for. by this reason the reason of., an explanation for, an estimate for, a motivation for, a criterion for, an abbreviation for. in a similar way, in the same way, by induction on n. on the left hand side, on the right hand side. to equivalent to be reduced to be devoted to to,., equivalent to giving..., equivalent to give.... Section 3 is devoted to proving... Section 3 is devoted to the proof of... We are reduced to checking...., The key to proving the theorem is... to, proving, key to prove the theorem. 11

12 intersect. A intersects with C, A intersects C. the intersection with C., contradict, this contradicts to the hypothesis. a contradiction to the hypothesis. thank, we thank to Professor X we thank Professor X. thanks to Professor X. equal, x equals y, equal x is equal to y. contain include contain. X is contained in Y Y contains X, X is included in Y Y includes X., X Y inclusion opposite inclusion. similar by an argument similar to that in 1, to as,. by a similar argument as in 1. same the same argument as that in 1,. 2, two, twenty-three., 0 1, genus zero, one-dimensional, one-parameter. 1-parameter., 1 1 in one-to-one correspondence. in 1-1 correspondence. the following, the followings. the. as follows: as follows:. as follows;. We prove the following:. notation notation s. data datum. genera genus. formula lemma, formulas lemmas, formulae lemmata. notes 1 lecture notes. A, the notes taken by Mr. A. These notes are meant for graduate students

13 another another an other,. each, every each every. 2 every two years, every second year. 2 3 between 2, 3 among., each other 2, 3 one another. X the number of X the cardinality of X the number of elements in X. Indeed, In fact,,., In fact, we can say more.,. first at first at first., first. At first, we prove Propositon 1 We first prove Proposition 1. composite composition,,. the composite g f of f and g, by the composition of f and g we get g f. translate translation, transform transformation. analog analogy analog ( analogue), analogy., if and only if, if. A subgroup H of G is said to be normal, if x 1 Hx = H holds for all x G., call. H is called normal H is said to be normal. H is called a normal subgroup.. that is XX XX, for short. the case where. that is. A and B are equivalent, that is, there exists a...., That is, Namely,. a = 0.. Without loss of generality, we may assume a = 0. 13

14 iff, it isn t, we don t, w. r. t.. if and only if, it is not, we do not, with respect to., it its it s. it s it is. of course,,. naturally needless to say, It goes without saying that.... by the way. We would like to add... Here is an additional remark.... anyway, in any case at any rate. want to would like to. there is, there are, there exists, there exist.. In this section, we prepare some lemmas. In this section, we prove lemmas needed later.. The author expresses hearty thanks to Professor.... Thanks are due to Professor... Deep appreciation goes to Professor... The author expresses gratitude to Professor...,., fibre, fiber. fibre,., neighborhood neighbourhood, program programme., polarise, polarisation, generalise, generalisation, z s. and etc., etc. et cetera (and so forth, and so on ). et and. et al. et alii (and others ). i.e. id est (that is ). e.g. exempli gratia (for example ). viz. videlicet (namely ). q.e.d. quod erat demonstrandum (which was to be demonstrated). 14

15 [1] A Manual for Authors of Mathematical Papers, Bull. Amer. Math. Soc. 68 (1962), (.) [2] E. Swanson, Mathematics into Type, Amer. Math. Soc [3] The Chicago Manual of Style (14th edition), Chicago Univ. Press, [4] N. J. Higham, Handbook of Writing for the Mathematical Sciences, siam (Soc. for Industrial and Applied Mathematics), 1993; (, ),, [5], (How to Write Mathematics in English),, [6],,, 1216, (, ) 15

oda_tex.dvi

oda_tex.dvi , 4 1, 1999 5, pp.95 112. TEX,.,, (copy editor),., TEX, TEX.,, TEX,., 1.1 1.2 ( ).,,,.,,., TEX 1, TEX 2.,, 3., Tohoku Mathematical Journal,.,. 1996 1,,, 4.,. 1 TEX, [1], [2], [3], [4]., TEX, TEX, \., L