#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
---------------------------------+------------------------------------------
Reporter: mhansen | Owner: mhansen
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.2
Component: commutative algebra | Keywords:
---------------------------------+------------------------------------------
Comment(by SimonKing):
Recall that the starting point of my implementation was that the stretch
method of the dense implementation requires too many resources in some
cases.
However, my stretch implementation is ''slower'' than yours, as long as
the stretch factor is small and as long as one uses {{{timeit}}} and not
{{{time}}}.
The reason is: The critical part of the dense stretch method is the
creation of a large polynomial ring. Once this is done, the ring is re-
used, and it is very fast. In contrast, the sparse stretch method only
creates a small ring (faster), but this has to be repeated over and over
again.
Therefore one has:
{{{
sage: X.<x,y> = SymmetricPolynomialRing(QQ)
sage: Y.<a,b> = InfinitePolynomialRing(QQ)
sage: timeit('t=x[10].stretch(10)')
625 loops, best of 3: 194 µs per loop
sage: timeit('t=a[10].stretch(10)')
625 loops, best of 3: 92.8 µs per loop
sage: timeit('t=(x[10]*y[5]+x[100]*y[83]).stretch(500)')
125 loops, best of 3: 2.29 ms per loop
sage: time t=(a[10]*b[5]+a[100]*b[83]).stretch(500) # fails after 2:30
minutes:
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occured in SAGE.
This probably occured because a *compiled* component
of SAGE has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run SAGE under gdb with 'sage -gdb' to debug this.
SAGE will now terminate (sorry).
------------------------------------------------------------
}}}
So again, this is an argument to include ''both'' implementation into
Sage. That way, one can pick the method that is better for the respective
application.
But who will review our patches? I guess neither of us. Should we ping
malb?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:18>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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