I've been trying to continue learning Sage. This morning I translated
another of my scripts from Maple. This computes Hodge numbers of
complete intersections in projective space using a formula of
Hirzebruch. My first goal was to make it logically correct, and I
think it is. But now I need to worry about efficiency. The problem is
that this is generating huge polynomial expressions which seem to be
overwhelming Maxima running inside Sage for moderately large examples.
(Maple seems to be OK with these examples.)
A typical error log looks like this:
---------------------------------------
Traceback (most recent call last):
File "/Applications/local/lib/python2.5/site-packages/sympy/
plotting/", line 1, in <module>
File "/Users/donu/.sage/sage_notebook/worksheets/admin/1/code/
11.py", line 104, in hodge
return hodge1(degs, n-len(degs))
File "/Users/donu/.sage/sage_notebook/worksheets/admin/1/code/
11.py", line 153, in hodge1
nexth = htemp.coeff(x,i).coeff(y,level-i)
File "/Applications/local/lib/python2.5/site-packages/sage/calculus/
calculus.py", line 2660, in coeff
return self.parent()(self._maxima_().coeff(x, n))
File "/Applications/local/lib/python2.5/site-packages/sage/calculus/
calculus.py", line 1134, in _maxima_
return RingElement._maxima_(self, maxima)
File "sage_object.pyx", line 316, in
sage.structure.sage_object.SageObject._maxima_ (sage/structure/
sage_object.c:2879)
File "sage_object.pyx", line 247, in
sage.structure.sage_object.SageObject._interface_ (sage/structure/
sage_object.c:1886)
File "/Applications/local/lib/python2.5/site-packages/sage/calculus/
calculus.py", line 5078, in _maxima_init_
return '(%s) %s (%s)' % (ops[0]._maxima_init_(),
...
File "/Applications/local/lib/python2.5/site-packages/sage/calculus/
calculus.py", line 5078, in _maxima_init_
return '(%s) %s (%s)' % (ops[0]._maxima_init_(),
RuntimeError: maximum recursion depth exceeded
--------------------------------------
I guess one solution would be explicitly call Singular which should be
able handle these kinds of calculations more gracefully that Maxima.
Another solution would be to trim the polynomials as I go along, by
throwing away high degree terms. Does anyone know a good way to do
this in Sage? In Maple I would do something like this for p(x,y)
trim := 0
for term in op(p) do
if (degree(term, x) + degree(term,y) <= N) then
trim := trim + term
end if
end do
But I'm not sure it translates.
- Donu
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