Как установить ширину уравнения, чтобы оно помещалось в один столбец

Question

Я использую двухколоночный макет в исходном файле latex, и у меня есть ряд уравнений (неравенств), которые нужно показать, и я хотел бы сохранить их внутри левого столбца. Однако с окружением \begin{align*} уравнения выходят за пределы столбца и занимают дополнительное место в правом столбце. Вы можете обратиться к картинкам, которые я прикрепил здесь, чтобы увидеть, что происходит. Как мне ограничить уравнения, чтобы они находились только в пределах первого столбца?

Вот мой исходный код латекса. А вот MWE, который вы можете примерить..

% \documentclass[conference]{IEEEtran}
\documentclass[10pt,conference,letterpaper]{IEEEtran}

\usepackage{amsmath}
\begin{document}

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
    \begin{align*}
        & \sum\nolimits_{e \in E^*} COST(g(e))\\
    &= \sum\nolimits_{e \in S_1} COST(g(e))
                                            + \sum\nolimits_{e \in S_2} COST(g(e))
                                            + \sum\nolimits_{e \in S_3} COST(g(e))\\
                        &\le 
                            2(1+\epsilon) COST(T^* \setminus T) 
                            +  COST(T^* \cap T)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                            &\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 2(1+\epsilon)COST(T^*)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4(1+\epsilon)OPT_n
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4+10\epsilon OPT_n
    \end{align*}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj




\end{document}

Answer 1

Это одно из возможных решений. Использование пакета resizeboxfrom graphicxи parboxcombo, как показано ниже.

 \resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{ math envrionment}}

или

 {\tiny \begin{align*} ... \end{align*} environment} 

Код

\documentclass[10pt,conference,letterpaper]{IEEEtran}

\usepackage{amsmath,graphicx}
\begin{document}

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
\resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{
    \begin{align*}
        & \sum\nolimits_{e \in E^*} COST(g(e))\\
    &= \sum\nolimits_{e \in S_1} COST(g(e))
                                            + \sum\nolimits_{e \in S_2} COST(g(e))
                                            + \sum\nolimits_{e \in S_3} COST(g(e))\\
                        &\le 
                            2(1+\epsilon) COST(T^* \setminus T) 
                            +  COST(T^* \cap T)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                            &\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 2(1+\epsilon)COST(T^*)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4(1+\epsilon)OPT_n
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4+10\epsilon OPT_n
    \end{align*}
}}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs 
\end{document}

Answer 2

Я предлагаю вам не предпринимать никаких шагов, которые в конечном итоге приведут к уменьшению размера шрифта, используемого в математическом выражении, относительно того, который используется для окружающего текста. Вместо этого вы можете использовать следующий подход:

• Не используйте \nolimitsмодификатор после каждого \sumмакроса. Вместо этого заключите \sum{...}выражения в \smashoperatorдирективы; это уменьшит количество пробелов до и после знаков суммирования. (Макрос \smashoperatorпредоставляется пакетом mathtools, который является расширением (и загружает) amsmathпакет.)

• Вставьте дополнительные переносы строк в строки 3 и 4.

• Необязательно: Отобразите "COST" и "OPT" прямым шрифтом. В настоящее время TeX интерпретирует COST и OPT как группы переменных из четырех и трех букв, т. е. как C O S Tи как O P T, что приводит к свободному и неоптимальному межбуквенному интервалу. (Если вы хотите отобразить имена переменных курсивом, а не прямым шрифтом, используйте \textitвместо \textupв макросах, которые определяют \COSTи \OPT.)

\begin{align*}
& \smashoperator{\sum_{e \in E^*}} \COST(g(e))\\
&= \smashoperator{\sum_{e \in S_1}} \COST(g(e)) + 
   \smashoperator{\sum_{e \in S_2}} \COST(g(e)) + 
   \smashoperator{\sum_{e \in S_3}} \COST(g(e))\\
&\le 2(1+\epsilon) \COST(T^* \setminus T) + \COST(T^* \cap T)\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)(\COST(T^* \setminus T) + \COST(T^* \cap T))\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)\COST(T^*) + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4(1+\epsilon)\OPT_n + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4+10\eps

илон \OPT_n \end{align*}