How Does Homebrew Add Things to My Environment?

OS X 10.11.5. I'm new to OS X and Ruby. I used homebrew to install chruby and ruby-install, then used these to install Ruby and Rails. Later I installed RubyMine. I like it, but it does not support chruby. I want to uninstall chruby and ruby-install and use RVM. On a different iMac I installed rvm and RubyMine and everything works fine. Now I want to clean up my iMac to install rvm.

The main thing I don't understand is how my set output has things like these:

GEM_PATH=/Users/mark/.gem/ruby/2.3.1:/Users/mark/.rubies/ruby-2.3.1/lib/ruby/gems/2.3.0
GEM_ROOT=/Users/mark/.rubies/ruby-2.3.1/lib/ruby/gems/2.3.0
...
RUBY_ROOT=/Users/mark/.rubies/ruby-2.3.1
RUBY_VERSION=2.3.1
...
chruby_reset () 
{ 
    [[ -z "$RUBY_ROOT" ]] && retu;  
    PATH=":$PATH:";
PATH="${PATH//:$RUBY_ROOT/bin:/:}";
if (( $UID != 0 )); then
    [[ -n "$GEM_HOME" ]] && PATH="${PATH//:$GEM_HOME/bin:/:}";
    [[ -n "$GEM_ROOT" ]] && PATH="${PATH//:$GEM_ROOT/bin:/:}";
    GEM_PATH=":$GEM_PATH:";
    [[ -n "$GEM_HOME" ]] && GEM_PATH="${GEM_PATH//:$GEM_HOME:/:}";
    [[ -n "$GEM_ROOT" ]] && GEM_PATH="${GEM_PATH//:$GEM_ROOT:/:}";
    GEM_PATH="${GEM_PATH#:}";
    GEM_PATH="${GEM_PATH%:}";
    unset GEM_ROOT GEM_HOME;
    [[ -z "$GEM_PATH" ]] && unset GEM_PATH;
fi;
PATH="${PATH#:}";
PATH="${PATH%:}";
unset RUBY_ROOT RUBY_ENGINE RUBY_VERSION RUBYOPT;
hash -r
}
...

I've looked in the places man bash says to look, /etc/bashrc, /etc/profile, ~/.bash_profile and ~/.bashrc, but I have not figured out how GEM_PATH gets put in my bash shell.

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