Tests are useful in your package for these reasons:

• If somebody changes something in the future which breaks your code, they will know and will be able to adjust the code so it doesn't.
• Tests compatibility with various versions of other packages (e.g. if you test against output of another package).
• It makes sure that your code is right (if you test with a known example from a textbook, for example).
• The code complains adequately if functions are fed wrong input.
• Recording errors in code so they do not happen again.

• Regression tests: when there's an error, and you fix it, you put in a test to ensure it doesn't happen again in the future.

 assert(det(M)!=0)

• Type test: does this function give the correct type.

 assert(instance(foo(x),List))

• Run test: does the code run at all?

 foo(x)

• Error test: if an error SHOULD occur on foo(x), you can make sure that happens with:

 assert(try (foo(x); false) else true)

• Unit test: just check that the output of something is something else.

 assert(foo(x)==2)

• Property test: checks a property of a function on an example.

 QQ[x,y]
 I = ideal(x^2, x*y)
 assert(isSubset(I, radical I))

--This is a comment, write what you'd like here, like "testing dimension and degree"
TEST ///
R = QQ[x,y,z]
assert(dim(ideal(x,y))==1)
assert(degree(ideal(x,y))==1)
///
--This is a second test now.
TEST ///
R = QQ[x,y,z]
assert(dim(ideal(x,y))==1)
///
--repeat these so that at least each exported function gets tested

• A test block will fail if there is any error in the block.
• Tests are implicitly numbered in the order in which they are read, starting at mypackage.m2.

check "SumsOfSquares" -- runs all tests in the package SumsOfSquares
check_3 "SumsOfSquares" -- checks the third test in the SumsOfSquares package
 -- capturing check(3, "SumsOfSquares") -- .197867s elapsed
tests("SumsOfSquares") -- gives each test, and where it is in the code base
 {0 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1221:5-1230:3] }
 {1 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1233:5-1247:3] }
 {2 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1250:5-1261:3] }
 {3 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1264:5-1271:3] }
 {4 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1274:5-1292:3] }
 {5 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1295:5-1302:3] }
 {6 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1305:5-1347:3] }
 {7 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1350:5-1374:3] }
 {8 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1377:5-1390:3] }
 {9 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1393:5-1427:3] }
 {10 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1430:5-1434:3]}
 {11 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1437:5-1442:3]}
 {12 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1445:5-1449:3]}
 {13 => TestInput[/usr/share/Macaulay2/SumsOfSquares.m2:1452:5-1456:3]}

Here are common places people choose to put tests:

• In the main package file mypackage.m2, either right after a function is defined, or all together at the end.
• A common choice is putting them all at the end of the top package file.
• The recommended choice (especially for new contributors) is in a directory:

 /packages/mypackage/tests.m2

and load this file in mypackage.m2. Don't forget to set AuxiliaryFiles=>true in the preamble.

• Each exported function should be tested with all options if options are available.
• Always test the trivial cases and boundary cases (what if you give the empty list? the zero ideal <0>? <1>?).
• Do not repeatedly construct the exact same object in one test block. You can use it more than once!
• Try to keep each test to a minimal time requirement (over 5s will be flagged and only allowed if necessary).
• Crucial core functions, give several tests, possibly right after defining the function.
• Sometimes toString is useful (or value(toString(x)) if you are concerned about printing breaking things).
• Note: = means assignment, == checks that two things are mathematically the same, === are these the literal same object in the computer science sense:

 i8 : R = QQ[x,y];
 i9 : ideal(x,y) === ideal(x+y,y)
 o9 = false
 i10 : ideal(x,y) == ideal(x+y,y)
 o10 = true

• Test properties, not just examples! e.g.:

 I = ideal(x^2, x*y)
 assert(isSubset(I, radical I))

• Test bad input deliberately.
• Document why non-obvious tests exist (i.e. regression tests).
• In general, it's good to have comments on why you are testing certain things.