\sum in text mode when inserted in math mode

Question

I have the following line of code :

$$
\operatorname{aff}(\mathcal{C})
\coloneqq
\{
\lambda_{1}x_{1}+\lambda_{2}x_{2}+\cdots+\lambda_{k}x_{k}
\mid 
x_{1},x_{2},\ldots,x_{k}\in\mathcal{C},\sum_{i}\lambda_{i}=1
\}
$$

which should generate the following expression :

I wish to know if there is a way to replace the summation notation above and replace it with the smaller summation notation used in text mode i.e. the one below :

$\sum_{i}\lambda_{i}$ 

I attempted to use \text{$\sum_{i}$} in math mode but it did not work because it gave me the large summation notation.

Answer 1

For a one-off case you can use Zarko's method.

If you need it several times, you can define a command that forces text style when the symbol is to be used in display style. However, I'd also use \big size for the braces.

\documentclass{article}
\usepackage{amsmath,mathtools}
\DeclareMathOperator{\aff}{aff}
\makeatletter
\newcommand{\tsum}{\DOTSB\mathop{\tsum@}\nolimits}
\newcommand{\tsum@}{\mathchoice{\textstyle\sum}{\sum}{\sum}{\sum}}
\makeatother
\begin{document}
[
\aff{\mathcal{C}}\coloneqq
\bigr{
  \lambda_{1}x_{1}+\lambda_{2}x_{2}+\cdots+\lambda_{k}x_{k}
  \mid
  x_{1},x_{2},\ldots,x_{k}\in\mathcal{C},\tsum_{i}\lambda_{i}=1
\bigr}
]
\end{document}

Answer 2

Use \textstyle.

And use \[\] instead of $$ $$ for display style math.

Improved Answer (modification according to Zarko's and egreg's comments):

\documentclass{article}
\usepackage{mathtools}
\begin{document}
[
\operatorname{aff}(\mathcal{C})
\coloneqq
{
\lambda_{1}x_{1}+\lambda_{2}x_{2}+\cdots+\lambda_{k}x_{k}
\mid
x_{1},x_{2},\ldots,x_{k}\in\mathcal{C},{\textstyle\sum_{i}\lambda_{i}}=1
}
]
\end{document}

• Removed the amsmath package as it is loaded by the mathtools package (mentioned by zarko).
• Grouped the part that is to be displayed by \textstyle in the text style mode as \textstyle is not a macro (mentioned by egreg).

Original Problametic answer:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
[
\operatorname{aff}(\mathcal{C})
\coloneqq
{
\lambda_{1}x_{1}+\lambda_{2}x_{2}+\cdots+\lambda_{k}x_{k}
\mid
x_{1},x_{2},\ldots,x_{k}\in\mathcal{C},\textstyle{\sum_{i}\lambda_{i}}=1
}
]
\end{document}

Answer 3

A wee bit modified @Imran answer:

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator{\aff}{aff} % <---
\begin{document}
[
\aff(\mathcal{C})\coloneqq
\bigl{  % <---
\lambda_{1}x_{1}+\lambda_{2}x_{2}+\cdots+\lambda_{k}x_{k}
\mid
x_{1},x_{2},\ldots,x_{k}\in\mathcal{C},{\textstyle\sum_{i}}\lambda_{i}=1 % <---
\bigr}   % <---
]
\end{document}