isCommutative(ComplexMap) doesn't cache if debugLevel != 0

[mahrud]

I suspect this was added so that for a map that doesn't commute the printed messages tell the user which differential doesn't commute, but it has the result that if debugLevel is positive, for a commutative complex map the cached result is ignored.

M2/M2/Macaulay2/packages/Complexes/ChainComplexMap.m2

Lines 437 to 439 in 2cb101f

	isCommutative ComplexMap := Boolean => f -> (
	if debugLevel == 0 and f.cache.?isCommutative then
	return f.cache.isCommutative;

cc: @mikestillman @ggsmith

[mikestillman]

The intent of this code is that if debugLevel > 0, then we want the code to check that it really is commutative. The motivation for this had nothing to do with the printing of messages. Basically, we wanted a method that could check whether the logic setting this isCommutative flag in a number of other functions was in fact correct.

[mahrud]

Okay, I think this has a few problems:

1. it makes sense to make sure isCommutative is run at least once on any given map, but you might end up running isCommutative over and over on the same map because the cache is always ignored!
2. you only call isCommutative once and mostly isCommutativeCached, which doesn't use this logic, so you end up not really testing most maps that have the isCommutative flag set.
3. you should use something less generic, like assertLevel (see Add assertLevel and automatic timer #3211) or at least a specific number like debugLevel == 123 or whatever. The documentation only says:

If the debugLevel is greater than zero, then the location of the first failure of commutativity is displayed.