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I have been struggling with a couple of things concerning the following system of equations, this is the best I could achieve so far:

\documentclass[11pt,a4paper,oneside]{report}
\usepackage[pdftex]{graphicx} % to work PDFLaTex
\usepackage[T1]{fontenc} 
\usepackage{fouriernc}
\usepackage{amsfonts,amsmath,amssymb,amsthm} 
\usepackage[a4paper, hmargin={3.5cm,3cm}, vmargin={2.5cm,2.5cm}]{geometry} 
\usepackage{multicol}
\usepackage{fancyhdr} 
\usepackage{enumerate}
\usepackage{wasysym} % symbols
\usepackage[pdftex]{hyperref}
\newcommand\abs[1]{\left|#1\right|}
\newcommand{\ndiv}{\hspace{-4pt}\not|\hspace{2pt}}
\def\quotient#1#2{%
\raise1ex\hbox{$#1$}\Big/\lower1ex\hbox{$#2$}%
}
\DeclareMathOperator{\z}{\mathbf{Z}} 
\DeclareMathOperator{\q}{\mathbf{Q}} 
\begin{document}
\begin{align}
e_{v} & \colon \q[x]\longrightarrow \Lambda\otimes_{\z}\q  \\
e_{v} & \colon f(x) \longmapsto f(\omega_{1})\\
\intertext{where $ker\;e_{v}=\bigl<(x^3-bx^2+acx-a^2d)\bigr>$. The evaluation map is clearly surjective hence by the First Isomorphism Theorem for rings it induces an isomorpism}
\lambda & \colon  \q[x]\xrightarrow{\hspace*{1.6cm}} \Lambda\otimes_{\z}\q\\
\lambda & \colon  \quotient{\q[x]}{\text{ker}\;e_{v}} \longmapsto f(\omega_{1})
\end{align} 
\end{document}

and the result enter image description here

I would like possibly to improve the following:

1) only one numbering that is centered between each two equations

2) the arrows in the first and the second system of equations to be vertically aligned (the length of the second arrow in the second system has been adjusted manually...)

3) and in the second system I would like Q[x] and Q[x]/ker e_v to be also vertically aligned with one another

I would really appreciate if someone could help me with this. Thanks in advance.

share|improve this question

2 Answers 2

up vote 1 down vote accepted

With aligned inside a gather environment. Note there already exists a faktor package that uses \diagup from amssymb and typesets nicely quotient structures; you'll compare in the proposed code. Your definition of \abs does not introduce correct spacing and has fixed height, whatever the content; it's better to use \DeclarePairedDelimiter from the mathtools package (which loads amsmath). This you can use \abs* which adds a pair of \left and \right; or you can use optional arguments: \big, \Big, &c. Also, note there exists a \ker operator command, with correct spacing.

Last remark: unless I misunderstood, there is a mathematical error in your last group of equations, that I corrected. \documentclass[11pt,a4paper,oneside]{report} \usepackage[pdftex]{graphicx} % to work PDFLaTex \usepackage[T1]{fontenc} \usepackage{fourier} \usepackage{mathtools} \usepackage{faktor} \usepackage{amsthm,amssymb}% \usepackage[ hmargin={3.5cm,3cm}, vmargin=2.5cm]{geometry} \usepackage[pdftex]{hyperref} \newcommand{\ndiv}{\hspace{-4pt}\not|\hspace{2pt}} \def\quotient#1#2{% \raise1ex\hbox{$#1$}\Big/\lower1ex\hbox{$#2$}% } \DeclareMathOperator{\z}{\mathbf{Z}} \DeclareMathOperator{\q}{\mathbf{Q}}

\DeclarePairedDelimiter{\Span}{\langle}{\rangle}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}

\begin{gather}
\begin{alignedat}{2}
e_{v} & \colon & \q[x]&\longrightarrow \Lambda\otimes_{\z}\q \\
e_{v} & \colon& f(x) & \longmapsto f(\omega_{1})
\end{alignedat}
\\
\intertext{where\, $\ker e_{v}=\Span*{x^3-bx^2+acx-a^2d}$. The evaluation map is clearly surjective hence by the First Isomorphism Theorem for rings it induces an isomorphism}
\begin{alignedat}{2}
\lambda & \colon & \quotient{\q[x]}{\ker e_{v}} &\longrightarrow{} \Lambda\otimes_{\z}\q\\
\lambda & \colon & f(x) + \ker e_{v} &\longmapsto f(\omega_{1})
\end{alignedat}\\
\shortintertext{Variant: }
\begin{alignedat}{2}
\lambda & \colon & \faktor{\q[x]}{\ker e_{v}} &\longrightarrow{} \Lambda\otimes_{\z}\q\\
\lambda & \colon & f(x) + \ker e_{v} &\longmapsto f(\omega_{1})
\end{alignedat}
\end{gather}
\vskip 1cm
Personally, I would not repeat the map name on the second line of a group of equations, and write only this, which is simpler to type:
\begin{gather}
\begin{aligned}
e_{v} \colon \q[x]&\longrightarrow \Lambda\otimes_{\z}\q \\
 f(x) & \longmapsto f(\omega_{1})
\end{aligned}
\\
\intertext{where\, $\ker e_{v}=\Span*{x^3-bx^2+acx-a^2d}$. The evaluation map is clearly surjective hence by the First Isomorphism Theorem for rings it induces an isomorphism}
\begin{aligned}
\lambda \colon \quotient{\q[x]}{\ker e_{v}} &\longrightarrow{} \Lambda\otimes_{\z}\q\\
  f(x) + \ker e_{v} &\longmapsto f(\omega_{1})
\end{aligned}\\
\shortintertext{Variant: }
\begin{aligned}
\lambda \colon \faktor{\q[x]}{\ker e_{v}} &\longrightarrow{} \Lambda\otimes_{\z}\q\\
 f(x) + \ker e_{v} &\longmapsto f(\omega_{1})
\end{aligned}
\end{gather}
\end{document} 

enter image description here

share|improve this answer
    
Two quibbles: the colons don't line up in the first group, and the term after the first \lambda: in the second group should simply be \q[x], right? –  Mico Aug 16 at 10:33
    
@Mico: for the colons, I don't think we can do anything — unless the spacing betweene_v and the colon is increased. Actually, I wouldn't write the map name again in the second line. As for the\q[q[x] –  Bernard Aug 16 at 11:21
    
Thank you Bernard. Your solution looks way better! I have just discovered that the equation for $\lambda$ is wrong, the function should be defined as $\lambda \colon \ker e_{v}+f(x) &\longmapsto f(\omega_{1})$ but then colons are again not lined up. Could you please tell me how to fix it? P.S great tips, I will try to apply them. –  user124471 Aug 16 at 13:07
    
The probem is fixed, but unless it's your university convention, one does not have to repeat λ, &c., on the second line that defines a map. See my updated answer. –  Bernard Aug 16 at 13:29
    
This looks great. I think you are probably right, I will use the second variant. Many thanks!!! –  user124471 Aug 16 at 13:59

Some suggestions:

  • You could use \parbox macros to typeset the shorter pieces in each of the two groups of statements. The widths of the parboxes would be those of the corresponding longer pieces.

  • Use two separate, nested equation and split environments instead of one large align environment. This will give you the equation number placement and numbering you want. It's not clear to me why the colons in the e_v group should be aligned vertically with the colons in the \lambda group.

  • Two minor points: First, use \langle and \rangle instead of \bigl< and \bigr>, and use \ker instead of \text{ker}\;. Second, is it necessary to define \q and \z as math operators? It may be better to define them as ordinary macros, using \newcommand.

Finally, you'll see that I've simplified your preamble quite a bit in an effort to make it easier to understand which packages are actually needed to get the MWE to compile.

enter image description here

\documentclass{report}
\usepackage{fouriernc}
\usepackage{amsmath} 

\def\quotient#1#2{%
  \raise1ex\hbox{$#1$}\Big/\lower1ex\hbox{$#2$}%
}
\newcommand*{\z}{\mathbf{Z}} %why define them as operators?
\newcommand*{\q}{\mathbf{Q}} 
\usepackage{calc} % provides \widthof macro
\newlength\leni
\setlength\leni{\widthof{$\q[x]$}}
\newlength\lenii
\setlength\lenii{\widthof{$\quotient{\q[x]}{\ker e_{v}}$}}

\begin{document}
\begin{equation}\begin{split}
e_{v} & \colon \q[x] \longrightarrow \Lambda\otimes_{\z} \q  \\
e_{v} & \colon \parbox{\leni}{$f(x)$} \longmapsto f(\omega_{1})
\end{split}\end{equation}
where $\ker e_{v}=\langle (x^3-bx^2+acx-a^2d)\rangle$. The evaluation map is clearly surjective, hence by the First Isomorphism Theorem for rings it induces an isomorpism.
\begin{equation}\begin{split}
\lambda & \colon  \parbox{\lenii}{$\q[x]$}\longrightarrow \Lambda\otimes_{\z}\q\\
\lambda & \colon  \quotient{\q[x]}{\ker e_{v}} \longmapsto f(\omega_{1})
\end{split}\end{equation}
\end{document}
share|improve this answer
    
Thank you Mico. I did not know about the existence of \ker. I defined \q, \z as math operators because they appear in my text very often, and it is much faster to write them this way instead of writing \mathbf{Q} and so on. Thank you also for simplifying the preamble. –  user124471 Aug 16 at 13:10
    
@user124471 - I wasn't questioning your desire to create the two shortcut macros \q and \z; instead, I was wondering if they're better defined, e.g., as \newcommand*{\q}{\mathbf{Q}} than as \DeclareMathOperator{\z}{\mathbf{Z}}. In TeX, math operators getting extra amounts of space inserted before and after them, which is probably not what you want for the two symbols, right? –  Mico Aug 16 at 13:14
    
I didn't know you could define these number sets this way. I'll look into it. Thanks –  user124471 Aug 16 at 13:23

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