#7580: bugs in infinite polynomial ring
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Reporter: was | Owner: SimonKing
Type: defect | Status: new
Priority: major | Milestone: sage-4.3
Component: algebra | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by SimonKing):
Here is one example why I chose to use regular expressions.
Often I have to find out what variables (i.e., generator and shift) occur
in what power in the leading monomial of a polynomial. So:
{{{
# Create a polynomial ring
# (the typical underlying finite polynomial ring of a densely
# implemented InfinitePolynomialRing)
sage: Vars = ['x_'+str(n) for n in range(50)]+['y'+str(n) for n in
range(50)]
sage: R = PolynomialRing(QQ,Vars)
# Create a big random element
sage: p = R.random_element()
sage: p *= R.random_element()
sage: p *= R.random_element()
sage: p *= R.random_element()
sage: p *= R.random_element()
}}}
The generic approach to get the exponents of the variables in the leading
monomial is, of course, the method {{{exponents()}}}. We need to associate
the exponent with the variable, so, let's zip two lists:
{{{
sage: zip(Vars,p.lm().exponents()[0])
[('x_0', 0),
('x_1', 2),
('x_2', 0),
('x_3', 0),
('x_4', 0),
('x_5', 0),
('x_6', 0),
...
}}}
It is a long list, and we still did not separate the generator name from
the shift.
Now, do essentially the same with regular expressions:
{{{
sage: import re
sage: RE = re.compile('([a-zA-Z0-9]+)_([0-9]+)\^?([0-9]*)')
sage: RE.findall(str(p.lm()))
[('x', '1', '2'),
('x', '13', '2'),
('x', '16', ''),
('x', '23', ''),
('x', '45', '')]
}}}
The list is much shorter, and moreover generator names and shifts are
already told apart. This is actually the typical situation for elements of
Infinite Polynomial Rings in dense implementation: Only few variables from
the underlying finite polynomial ring appear in the leading monomial.
And I guess this is why the regular expression is faster:
{{{
sage: timeit('L = RE.findall(str(p.lm()))')
625 loops, best of 3: 23.8 µs per loop
sage: timeit('L = zip(Vars,p.lm().exponents()[0])')
625 loops, best of 3: 40.5 µs per loop
}}}
IIRC, in a very early stage of my implementation, I did use
{{{exponents()}}}. But it soon turned out that it was too slow for Gröbner
basis computations.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7580#comment:3>
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