Survival: open, look, exit

Goal

Launch gap, evaluate an expression, read what the prompt is telling you, recover from a mistake, and quit... all without feeling stranded.

Concept

GAP is a read-eval-print loop. You type an expression terminated by ;, it evaluates and shows the result. The whole session is one long conversation with a live interpreter that remembers everything you've defined until you quit. Two things trip people up on day one: the statement terminator (; vs ;;) and the break loop (brk>), which looks like a crash but isn't.

Commands to try

Launch it from your own terminal:

gap

You'll get a banner (version, loaded packages, memory) and then the gap> prompt. The banner is worth one glance: note the version number and which packages auto-loaded. We'll care later when something needs LoadPackage.

Now type these one at a time. After each, look at the result before moving on.

2 + 2;

Expect 4. The ; ends the statement; GAP prints the value.

2 + 2;;

Nothing prints. The double semicolon ;; evaluates but suppresses output. You'll want this later when a computation returns a 50,000-element list you don't want scrolling past. Mentally file it; don't dwell.

Factorial(20);

A big integer, exact. GAP has arbitrary-precision integers natively - no overflow, no floats sneaking in. This matters: group orders and other counts get large and stay exact.

last;

last is the previous result. GAP also keeps last2 and last3. Cheap way to reuse a value you forgot to name.

x := 7;

Assignment is :=, not =. (= is for comparison - it tests equality and returns true/false.) This is the single most common day-one error. Try the wrong one deliberately so you recognize the message:

x = 8;

Returns false. It compared; it did not assign. x is still 7. You can check this for yourself:

x;

The break loop - meet it on purpose

Type something genuinely broken:

1/0;

You'll drop into a brk> prompt with an error about division. This is not a crash. GAP has paused inside an error handler so you could inspect state. You get out with:

quit;

That leaves the break loop and returns you to the normal gap> prompt. (Inside the break loop quit; means "leave the break loop"; at the top level it means "leave GAP." Same word, level-dependent. So get that straight now so the next part doesn't surprise you.)

Getting help

?Factorial

Opens the manual entry. ? followed by a topic searches the help system; ??topic does a broader full-text search. Arrow keys scroll, q quits the pager back to the prompt.

Predict-then-check

Before you type the next line, commit to an answer out loud (or in this chat):

Order(SymmetricGroup(5));

What integer do you expect? Write it down first, then evaluate. (Hint: it's a factorial you already computed a smaller cousin of above.) Write down your prediction and what GAP returned:

Exit

quit;

At the top-level gap> prompt this ends the session and returns you to your shell. If GAP ever asks you to confirm or seems stuck in a pager, q then quit;.

Exercise

1. Open a fresh gap.
2. Without using Factorial, get GAP to tell you the order of the symmetric group on 7 points.
3. Define a variable g holding that group, then ask for its Size. Notice Order and Size both work here. When we hit large groups we'll see why GAP distinguishes them.
4. Trigger the break loop on purpose with any error, then escape it cleanly.
5. Quit.

Report back: the order of S₇, and one thing that behaved differently from what you expected.

Pitfalls

• := assigns, = compares. Burn this in now.
• ; prints, ;; is silent. Forgetting ; entirely makes GAP wait for more input (you'll see a > continuation prompt). Just type ; and Enter.
• quit; is context-dependent: it leaves the break loop or leaves GAP depending on which prompt you're at (brk> vs gap>).
• The banner's package list is information, not noise. Glance at it.