定义函数

Question

如下定义函数是否正确？

 \documentclass[12pt,a4paper]{report}
 \usepackage{mathtools, nccmath}
  \usepackage{amssymb, amsthm, mathrsfs}

   \begin{document}

   \begin{align*}
    \psi\colon&\mathbf{G}(p+q,d)\longrightarrow\mathbf{G}(q,d)\times \mathbf{G}(p,d)\\
    &\phantom{+++++}g\mapsto\left(\psi_1(g),\psi_2(g)\right),
     \end{align*}
    with $\psi_1(g)(j)=g(j)$ for all $1\leq j\leq q$ and $\psi_2(g) (j)=g(j+q)$ 
    for all $1\leq j\leq p$.
      \end{document}

我得到

Answer 1

您应该将对齐点设置在箭头处并使用\longmapsto。

\rightarrow不过，我发现使用和更好\mapsto。

\documentclass[12pt,a4paper]{report}
\usepackage{mathtools, nccmath}
\usepackage{amssymb, amsthm, mathrsfs}

\begin{document}

\begin{align*}
\psi\colon \mathbf{G}(p+q,d) & \longrightarrow\mathbf{G}(q,d)\times \mathbf{G}(p,d)\\
g&\longmapsto (\psi_1(g),\psi_2(g)),
\end{align*}
with $\psi_1(g)(j)=g(j)$ for all $1\leq j\leq q$ and $\psi_2(g) (j)=g(j+q)$
for all $1\leq j\leq p$.

\begin{align*}
\psi\colon \mathbf{G}(p+q,d) & \rightarrow\mathbf{G}(q,d)\times \mathbf{G}(p,d)\\
g&\mapsto (\psi_1(g),\psi_2(g)),
\end{align*}
with $\psi_1(g)(j)=g(j)$ for all $1\leq j\leq q$ and $\psi_2(g) (j)=g(j+q)$
for all $1\leq j\leq p$.

\end{document}