%\usepackage{my_base}

\newcommand {\seq}[2]{#1_1,#1_2,\ldots,#1_{#2}}
\newcommand {\seqi}[1]{#1_1,#1_2,\ldots}
\newcommand {\pseq}[3]{#1_{#2},\ldots,#1_{#3}}
\newcommand {\seqomit}[3]{#1_1,\ldots,#1_{#3-1},#1_{#3+1},\ldots,#1_{#2}}
\newcommand {\seqz}[2]{#1_0,#1_1,\ldots,#1_{#2}}
\newcommand {\seqzi}[1]{#1_0,#1_1,\ldots}
\newcommand {\seqzomit}[3]{#1_0,\ldots,#1_{#3-1},#1_{#3+1},\ldots,#1_{#2}}
\newcommand {\seqinter}[3]{#1_{1}{#2},#1_{2}{#2},\ldots,#1_{#3}{#2},}
\newcommand {\seqm}[2]{#1{1},#1{2},\ldots,#1{#2}}

\newcommand {\useq}[2]{#1^{(1)},#1^{(2)},\ldots,#1^{(#2)}}
\newcommand {\useqi}[1]{#1^{(1)},#1^{(2)},\ldots}
\newcommand {\upseq}[3]{#1^{(#2)},\ldots,#1^{(#3)}}
\newcommand {\useqomit}[3]{#1^{(1)},\ldots,#1^{(#3-1)},#1^{(#3+1)},\ldots,#1^{(#2)}}

\newcommand {\fseq}[2]{#1{1},#1{2},\ldots,#1{#2}}
\newcommand {\fseqi}[1]{#1{1},#1{2},\ldots}
\newcommand {\fpseq}[3]{#1{#2},\ldots,#1{#3}}
\newcommand {\fseqomit}[3]{#1{1},\ldots,#1{#3-1},#1{#3+1},\ldots,#1{#2}}

\newcommand {\ssum}[2]{#1_1+#1_2+\ldots+#1_#2}
\newcommand {\ssumi}[1]{#1_1+#1_2+\ldots}

\newcommand {\sprod}[2]{#1_1\, #1_2\, \ldots\, #1_{#2}}
\newcommand {\sprodi}[1]{#1_1\, #1_2\, \ldots}
\newcommand {\sprodinter}[3]{#1_{1}{#2},#1_{2}{#2},\ldots,#1_{#3}{#2},}

\newcommand {\soper}[3]{#1_1 #3 #1_2 #3 \ldots #3 #1_{#2}}
\newcommand {\soperi}[2]{#1_1 #2 #1_2 #2 \ldots}
\newcommand {\seqomitoper}[4]{#1_1 #4 \ldots #4 #1_{#3-1} #4 #1_{#3+1} #4 \ldots #4 #1_{#2}}

\newcommand {\fsoper}[3]{#1{1} #3 #1{2} #3 \ldots #3 #1{#2}}
\newcommand {\fsoperi}[2]{#1{1} #2 #1{2} #2 \ldots}

\newcommand {\Sum}[2]{\sum_{#1=1}^{#2}}
\newcommand {\tSum}[2]{{\textstyle \sum_{#1=1}^{#2}}}
\newcommand {\Prod}[2]{\prod_{#1=1}^{#2}}
\newcommand {\tProd}[2]{{\textstyle \prod_{#1=1}^{#2}}}
\newcommand {\Seq}[3]{\br{#1_{#2}}_{#2=1}^{#3}}

\newcommand {\sumim}[0]{\sum_{i=1}^{m}}
\newcommand {\sumin}[0]{\sum_{i=1}^{n}}
\newcommand {\sumjm}[0]{\sum_{j=1}^{m}}
\newcommand {\sumjn}[0]{\sum_{j=1}^{n}}

\newcommand {\dseq}[3]{\left({#1}_1,{#2}_1\right),\left({#1}_2,{#2}_2\right),\ldots,\left({#1}_{#3},{#2}_{#3}\right) }
