Commit 023d5433 authored by Xin's avatar Xin

add 9, validated

parent f718108b
\begin{mhmodnl}[creators=Xin]{monicpolynomial}{zhs}
\begin{definition}[id=monicpolynomial.def]
当一个\mtrefi[polynomial?polynomial]{多项式}\mtrefi[leadingcoefficient?leading-coefficient]{首项系数}$1$时,称其为\defi[name=monic]{首一的}
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=Xin]{monoid-power}{zhs}
\begin{definition}
$\mvstructure{\magmaset,\magmaopOp,\unitalunit}$为一个\mtrefi[monoid?monoid]{幺半群},且有$\inset{a}\magmaset$$\inset{n}\NaturalNumbers$,则称$\monpow{a}n$$a$$n$\defi[name=power]{}并且通过$\fundefeq{a}{\monpow{a}0}e$$\fundefeq{a,n}{\monpow{a}{\natplus{n,1}}}{\magmaop{a}{\monpow{a}n}}$定义。
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=zhs]{monoid}{zhs}
\begin{definition}
称一个\mtrefi[unital?unital]{有单位元的}\mtrefi[semigroup?semigroup]{半群}\defi[name=monoid]{幺半群}
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
% LocalWords: gle circ defi circ tref
\begin{mhmodnl}[creators=jusche]{monstergroup}{de}
\begin{definition}
\defi[name=monster-group]{魔群}$\monster$$\monster[monstervar]$(也被称为\defi[name=monster-group]{费雪-格里斯怪兽}\defi[name=monster-group]{友善巨人})是一个有限单\mtrefi[group?group]{},是26个散在的群中之一,其阶为:
\begin{eqnarray*}
\card{M} & = & \atimes{\power2{46},\power3{20},\power59,\power76,\power{11}2,\power{13}3,17,19,23,29,31,41,47,59,71}\\
& = & 808017\,424794\,512875\,886459\,904961\,710757\,005754\,368000\,000000\\
& \approxeqOp & \atimes[cdot]{8,\power{10}{53}}
\end{eqnarray*}
\end{definition}
\end{mhmodnl}
\begin{mhmodnl}[creators=Xin]{normal-subgroup}{zhs}
\begin{definition}[id=name.def]
\mtrefi[group?group]{}的一个\mtrefi[subgroup?subgroup]{子群} $N$ $\mvstructure{\magmaset,\magmaopOp,\unitalunit,\groupinvOp}$\defi[name=normal-subgroup]{正规的},当对于所有$\inset{n}{N}$$\inset{g}\magmaset$满足$\inset{\nsgop{g,n,\groupinv{g}}}{N}$,并且$N$\mtrefi[conjugation?conjugation]{共轭}时不变。
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=Xin]{period}{zhs}
\begin{definition}
一个带有\mtrefi[unital?unit]{单位元}$e$的群的元素的\defi[name=order]{}(或\defi[name=order]{周期})是满足$\monpow{a}m=e$的最小\mtrefi[naturalnumbers?natural-number]{自然数}$m$。若$m$不存在,则称$a$\defi[name=infinite-order]{无穷阶}
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=Xin]{permutation-group}{zhs}
\begin{definition}
称一个\mtrefi[symmetric-group?symmetric-group]{对称群}\mtrefi[subgroup?subgroup]{子群}\defi[name=permutation-group]{置换群}
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=Xin]{polynomial-function}{zhs}
\begin{definition}[functions=p]
$R$为一个\mtrefi[ring?ring]{}$p$为一个$R$上变量为$\naseqli{x}1n$\mtrefi[polynomial?polynomial]{多项式},则称$p(\naseqli{r}1n)$$p$$\ntupli{r}1n$上的估计的函数$\funsuchthat{f}{\ndim{R}n}R{\ntupli{r}1n}{p(\naseqli{r}1n)}$为关于$p$\defi[name=polynomial-function]{多项式函数}
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\begin{mhmodnl}[creators=Xin]{polynomial}{zhs}
\begin{definition}[id=polynomial.def]
一个\mtrefi[ring?ring]{}$R$上的\defi[name=polynomial]{多项式}是一个由$R$上的一个\mtrefi[variable?variable]{变量}以及$R$上的\defi[name=coefficient]{系数}所组成且只包含$R$中的\mtrefi[magma?operation]{运算}的表达式。
$p$的第$i$项为$i$\defi[name=monomial-degree]{}
\end{definition}
\begin{definition}
一个\mtrefi[?polynomial]{多项式}\defi[name=degree]{次数}$\degree{p}$是使得\mtrefi[?coefficient]{系数}$\livar{a}k$不为零的最大$k$。称其为\defi[name=leading-coefficient]{首项系数}
\end{definition}
\begin{definition}
称一个\mtrefi[?leading-coefficient]{首项系数}\mtrefi[ring?multiplicative-unit]{乘法单元}\mtrefi[?polynomial]{多项式}\defi[name=monic]{首一的}
\end{definition}
\begin{definition}
称一个$d$\mtrefi[?degree]{}\mtrefi[?polynomial]{多项式}\defi[name=constant]{常数},若$d=0$\defi[name=constant]{线性},若$d=1$\defi[name=quadratic]{二次},若$d=2$\defi[name=cubic]{三次},若$d=3$
\end{definition}
\end{mhmodnl}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
\ No newline at end of file
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment