100x slowdown in matrix multiplication over coefficient ring

[mahrud]

What is i3 doing that it takes so long?!

i1 : R = QQ[x];

i2 : elapsedTime id_(R^1000) * random(R^1000, R^1);
 -- .0252717s elapsed

i3 : elapsedTime id_(R^1000) * random(ZZ^1000, ZZ^1);
 -- 13.0427s elapsed

i4 : elapsedTime id_(R^1000) * promote(random(ZZ^1000, ZZ^1), R);
 -- .0474103s elapsed

cc: @Devlin-Mallory

[mikestillman]

While tracking this down, I have came across something that is pretty annoying. I don't recall this being so bad in the past, so maybe it was introduced relatively recently? Not sure...

In any case, try this:

R = QQ[x];
elapsedTime m1 = id_(R^1000);
elapsedTime m1 + y

The third line, on my machine, takes more than 4 seconds, as it is trying to determine what error message to give, and probably creating the entire string of m1, which is pretty long...! We should have a easier way to get a shorter version of the display. @pzinn You have such a version already? Or am I mistaken? Maybe we could use that instead. We don't need or want to display the entire thing.

[mikestillman]

In fact, I am currently thinking that is the entire slowdown here. From inside the code for code(symbol*, Matrix, Matrix), we see (switching m to m1, S to ZZ):

elapsedTime promote(m1, ZZ)

There is no method for this call to promote, but trying to display the first argument takes a large amount of time.

[mikestillman]

I think that fixing issue #3661 should fix this.