Change theorem counter in Springer template

Question

I used Springer template for my book, more concrete I used svmono.

Here is a MWE, that is the shortened version of my template file.

  \documentclass[graybox,envcountsec,sectrefs,vecarrow,envcountresetsect]{svmono}
  \usepackage[utf8]{inputenc}
  \usepackage[vietnam]{babel}
  \usepackage{savesym}
  \usepackage{mathptmx}
  \savesymbol{hbar}
  \usepackage{helvet}
  \usepackage{courier}
  \usepackage{type1cm}           
  \usepackage{fouriernc}
  \usepackage{esvect}   
  \let\remark\relax
  \let\endremark\relax
  \renewcommand{\thesection}{\arabic{section}.}
  \renewcommand\definitionname{Định nghĩa}
  \spnewtheorem*{remark}{Remark}{\itshape}{\rmfamily}
  \renewcommand\remarkname{Chú ý}
  \renewcommand\lemmaname{Bổ đề}
  \begin{document}
  \chapter{The direction of a segment}
  \section{Some basics definition}
  \begin{definition}
  That is definition
  \end{definition}
  \begin{theorem}
  This is theorem. 
  \end{theorem}
  \begin{remark}
  This is remark
  \end{remark}
  \begin{lemma}
  this is lemma
  \end{lemma}
  \end{document}

I want to numbering the chapter like Chapter I, not chapter 1 as in this template did. I also want to numbering the theorem, definition, remark, lemma section-wise, i.e Theorem 2.1(the first theorem in section 2), the next enviroment(definition, lemma, ..) will be Defintion 2.2,..i.e use the same counter in a section for every enviroment(except the proof enviroment) ?

But how can I change the template to get that ? Please help me.

Answer 1

Here's one possibility. Using the predefined structures from svmono.cls, there's no easy way to make the changes to the counters. You have two possibilities:

1. Define new structures with the desired numbering schema, as I illustrate below for definitions, lemmata and theorems:

   \documentclass[graybox,sectrefs,vecarrow,envcountresetsect]{svmono}
     \usepackage[utf8]{inputenc}
     \usepackage[vietnam]{babel}
     \usepackage{savesym}
     \usepackage{mathptmx}
     \savesymbol{hbar}
     \usepackage{helvet}
     \usepackage{courier}
     \usepackage{type1cm}           
     \usepackage{fouriernc}
     \usepackage{esvect}   
     \usepackage{chngcntr}   
   % chapter numbering in Roman numerals
     \renewcommand{\thechapter}{\Roman{chapter}}
   % section numbering arabic, without chapter counter
     \renewcommand{\thesection}{\arabic{section}}
     \renewcommand\definitionname{Định nghĩa}
   
     \let\remark\relax
     \let\endremark\relax
   
   \spnewtheorem*{remark}{Remark}{\itshape}{\rmfamily}
   \spnewtheorem{theo}{Theorem}[section]{\bfseries}{\itshape}
   \spnewtheorem{lemm}[theo]{Lemma}{\bfseries}{\itshape}
   \spnewtheorem{defi}[theo]{Definition}{\bfseries}{\itshape}
   
   
     \renewcommand\remarkname{Chú ý}
     \renewcommand\lemmaname{Bổ đề}
   
   \usepackage{titlesec}
   % Add a period after the section number
   \titleformat{\section}
     {\normalfont\large\bfseries}{\thesection.}{0.4em}{}
   
   % counters within section counter
     \counterwithin{definition}{section}
     \counterwithin{theorem}{section}
     \counterwithin{lemma}{section}
   
     \begin{document}
     \chapter{The direction of a segment}
     \section{Some basics definition}
     \begin{defi}
     That is definition
     \end{defi}
     \begin{theo}
     This is theorem. 
     \end{theo}
     \begin{remark}
     This is remark
     \end{remark}
     \begin{lemm}
     this is lemma
     \end{lemm}
     \end{document}
   

2. If, for some reason, new structures are not possible (perhaps you already have written a large amount of your text), then you can first annihilate the original definitions (by \letting the corresponding macros to \relax) and then make new definitions with the desired numbering schema:

   \documentclass[graybox,sectrefs,vecarrow,envcountresetsect]{svmono}
     \usepackage[utf8]{inputenc}
     \usepackage[vietnam]{babel}
     \usepackage{savesym}
     \usepackage{mathptmx}
     \savesymbol{hbar}
     \usepackage{helvet}
     \usepackage{courier}
     \usepackage{type1cm}           
     \usepackage{fouriernc}
     \usepackage{esvect}   
     \usepackage{chngcntr}   
   % chapter numbering in Roman numerals
     \renewcommand{\thechapter}{\Roman{chapter}}
   % section numbering arabic, without chapter counter
     \renewcommand{\thesection}{\arabic{section}}
     \renewcommand\definitionname{Định nghĩa}
   
     \let\remark\relax
     \let\endremark\relax
     \let\definition\relax
     \let\enddefinition\relax
     \let\lemma\relax
     \let\endlemma\relax
     \let\theorem\relax
     \let\endtheorem\relax
   
   \spnewtheorem*{remark}{Remark}{\itshape}{\rmfamily}
   \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
   \spnewtheorem{lemma}[theorem]{Lemma}{\bfseries}{\itshape}
   \spnewtheorem{definition}[theorem]{Definition}{\bfseries}{\itshape}
   
     \renewcommand\remarkname{Chú ý}
     \renewcommand\lemmaname{Bổ đề}
   
   \usepackage{titlesec}
   % Add a period after the section number
   \titleformat{\section}
     {\normalfont\large\bfseries}{\thesection.}{0.4em}{}
   
   % counters within section counter
     \counterwithin{definition}{section}
     \counterwithin{theorem}{section}
     \counterwithin{lemma}{section}
   
     \begin{document}
     \chapter{The direction of a segment}
     \section{Some basics definition}
     \begin{definition}
     That is definition
     \end{definition}
     \begin{theorem}
     This is theorem. 
     \end{theorem}
     \begin{remark}
     This is remark
     \end{remark}
     \begin{lemma}
     this is lemma
     \end{lemma}
     \end{document}
   

Answer 2

You don't need any new package. Just redefine the theorem environments:

\documentclass[
  graybox,envcountsec,sectrefs,
  vecarrow,envcountresetsect
]{svmono}

\usepackage[utf8]{inputenc}
\usepackage[vietnam]{babel}

\usepackage{fouriernc}

%%% chapters will have a Roman number
\renewcommand{\thechapter}{\Roman{chapter}}
\renewcommand{\thesection}{\arabic{section}.}

%%% remove the predefined environments
\let\remark\relax
\let\theorem\relax
\let\lemma\relax
\let\definition\relax

%%% redefine the theorem environments
\spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
\renewcommand\thetheorem{\thesection\arabic{theorem}}
\spnewtheorem{lemma}[theorem]{Lemma}{\bfseries}{\itshape}
\spnewtheorem{definition}[theorem]{Definition}{\bfseries}{\upshape}

\spnewtheorem*{remark}{Remark}{\itshape}{\rmfamily}

%\renewcommand\theoremname{???}
\renewcommand\lemmaname{Bổ đề}
\renewcommand\definitionname{Định nghĩa}
\renewcommand\remarkname{Chú ý}


\begin{document}

\chapter{The direction of a segment}
\section{Some basics definition}
\begin{definition}
That is definition
\end{definition}
\begin{theorem}
This is theorem. 
\end{theorem}
\begin{remark}
This is remark
\end{remark}
\begin{lemma}
this is lemma
\end{lemma}
\end{document}