CoCoA » CoCoA-5

I suspect the main problem is that creating a poly ring also creates a std::vector containing each power-product as a length 1 polynomial. This is quite slow using a dense repr for the power-products.

Perhaps the default type of power product should change to a sparse PP repr when the number of indets exceeds a given limit (what value should this limit have?)

I also note that creating the ring also consumed about 1.5Gbytes of RAM. :-(

I was forgetting that the use command in CoCoA-5 also assigns all the CoCoA-5 variables whose names coincide with those of the indets. It must be this which is causing CoCoA-5 to be so slow compared to CoCoALib!

More profiling to find out what is so costly, and how (if possible) this can be avoided or mitigated.

Functions involved include:
RING::injectIndeterminates in Interpreter.C:456 which calls
allSymbolValues in Interpreter.C:434 which calls
createAllSymbolValues in Interpreter.C:440 which calls
ctor for RingElem from a symbol which calls
RingBase::myNew (from a symbol) which calls
AreDistinct as a "cheat" way of testing whether the symbol is in the ring.

AreDistinct sorts the vector then checks whether two adjacent symbols are equal, via op= which calls cmp for symbol.
op= computes its answer by calling symbol::myCmp.
symbol::myCmp is called about 6*10^9 times!! 8-0

This is unacceptable!

In PolyRing.H there is a fn called IndetSymbol which apparently gives the symbol of the k-th indet. Presumably createAllSymbolValues could iterate over integer indices, rather than iterate over the symbols.

But how to descend into subrings?

One possible approach is to devise a hash for symbol then just comparing hashes will probably show quickly that they are different. I wonder how much it would cost to compute a hash of a symbol?

Nevertheless I do feel that the interpreter should create the values by using indet rather than constructing an RingElem from a symbol; this should avoid doing many comparisons between symbol values.

NOTE: on the new Kassel machine I confirmed the cause of slowness:

t0 := CpuTime();
P ::= QQ[x[1..10000]];
TimeFrom(t0);  --> 0.73s
t1 := CpuTime();
use P;
TimeFrom(t1);  --> 126s

A further comparison: with 20000 indets instead of 10000 -- complexity is quadratic :-(

t0 := CpuTime();
P ::= QQ[x[1..20000]];
TimeFrom(t0);  --> 2.6s
t1 := CpuTime();
use P;
TimeFrom(t1);  --> 515s