gh-38966: Clean up Cygwin remnants

We dropped support for Cygwin a while ago, but there is some stuff left
over in the tree. Let's finally remove it.

URL: #38966
Reported by: Michael Orlitzky
Reviewer(s): Kwankyu Lee

Author: Release Manager

build/bin/sage-guess-package-system

@@ -32,12 +32,5 @@ elif xbps-install --version > /dev/null 2>&1; then
 elif pkg -v > /dev/null 2>&1; then
     echo freebsd
 else
-    case `uname -s` in
-        CYGWIN*)
-            echo cygwin
-            ;;
-        *)
-            echo unknown
-            ;;
-    esac
+    echo unknown
 fi

build/bin/sage-print-system-package-command

@@ -182,12 +182,6 @@ case $system:$command in
     slackware*:install)
         [ -n "$system_packages" ] && print_shell_command ${SUDO}slackpkg install $system_packages
         ;;
-    cygwin*:update)
-        print_comment "first install apt-cyg from https://github.com/transcode-open/apt-cyg"
-        ;;
-    cygwin*:install)
-        [ -n "$system_packages" ] && print_shell_command apt-cyg install $system_packages
-        ;;
     freebsd*:install)
         [ -n "$system_packages" ] && print_shell_command ${SUDO}pkg install $system_packages
         ;;

build/bin/sage-spkg-info

@@ -85,7 +85,6 @@ for system in $systems; do
             alpine)     tab "Alpine";;
             arch)       tab "Arch Linux";;
             conda)      tab "conda-forge";;
-            cygwin)     tab "Cygwin";;
             debian)     tab "Debian/Ubuntu";;
             fedora)     tab "Fedora/Redhat/CentOS";;
             freebsd)    tab "FreeBSD";;