Computing minimal Weierstrass equations of hyperelliptic curves

We describe an algorithm for determining a minimal Weierstrass equation for hyperelliptic curves over principal ideal domains. When the curve has a rational Weierstrass point w0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_0$$\end{document}, we also give a similar algorithm for determining the minimal Weierstrass equation with respect to w0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_0$$\end{document}.