aptitude are convenient front-ends for the underlying
dpkg command, the Debian package system. They (pre-)handle stuff like dependency and conflict resolution and package download, before they invoke
dpkg with explicit instructions to install downloaded *.deb files, or to remove packages and their dependency, or to automatically (un)configure them, or what not...
You presumably asked
aptitude to force-install a certain package. Its conflict resolution kicked in and force-fully removed conflicting packages, breaking other packages. Presumably, the dependency resolution found certain dependencies having to be installed in a specific version or architecture, which cannot co-exist with the ones already installed. Certain things simply won't work, but since you asked to force the installation... well, you got what you asked for.
Here's where you may find useful information about the package-history and state of your system. Use
less <log-file> (or
zless <compressed-log-file>) to read these files.
/var/log/apt/history.log* you can see the command history of
apt-get and the resolutions it came up with for your requests/commands.
/var/log/apt/term.log* you can see the output of said requests/commands.
/var/log/aptitude* you will see some of aptitudes activities.
/var/log/dpkg.log* you can see what happened to individual packages status-vise.
dpkg -l will list all packages on your system and their status, including the status of packages previously installed (i.e. "removed" packages). The list header (or
man dpkg) will tell you the meaning of the letters in the first column. The 1st letter will tell you what status you/apt-get/aptitude requested for a package. The second will tell the status a package is currently in. If there is a third letter
R, that package needs reinstall.
dpkg -l | grep -v "^ii" will list the same packages excluding those "currently installed as requested", which may help to narrow down on your "removed" or "half-configured" or "half-installed" packages.
If you add
| less to either command pipeline, you can scroll the output.
What you want to do now is to find out which packages have been removed and why. The "why" part is presumably as mentioned above and cannot easily be worked around. So, you probably want to remove/purge your imagemagick first (do
apt-get remove <the-offending-package>, then continue with
apt-get autoremove or
apt-get remove <other-packages> to remove its dependencies, which are no longer required; CAREFULLY append
--purge to either command if you want to remove configuration files as well).
Then you may reinstall the lost packages. Or rather, you want to force-reinstall the main broken packages you're interested in, and have apt-get/aptitude automatically install the old dependencies on the way, as usual. That way trivial lib* dependencies won't get marked "manually installed", which would prevent auto-removal in the future if necessary.
To reinstall a package:
apt-get install <package>, optionally append
--reinstall to explicitly re-unpack packages, if necessary.
Also, you may have a look at
man apt-get and
man aptitude to get an idea about their options.