#5834: Improvements to quadratic_forms/extras/py
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Reporter: cremona | Owner: justin
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.2
Component: quadratic forms | Keywords: quadratic forms
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As first raised in #5627, concerning quadratic_forms/extras.py (which
contains various utilities written for use in various places in thw
quadratic_forms module):
I have added a patch after looking carefully at this, which does the
following:
1. I removed hilbert_symbol_rational(), making a trivial change to
hilbert_symbol() so that it already works on rationals. I think this will
useful outside the quadratic forms module.
2. I moved {{{IsPadicSquare()}}} to a member function for rationals, so
you now say r.is_padic_square(p) instead of {{{IsPadicSquare(r,p)}}},
while at the same time making the function simpler and cleaner. I think
this will also be useful outside the quadratic forms module.
3. I removed random_int_upto(n) since it does the same as
ZZ.random_element(n).
4. I simplified quadratic_nonresidue() (and changed its name to
least_quadratic_nonresidue()) -- by putting in three simple tests for when
the answer is 2, 3 or 5 the loop is avoided in 7/8 of the cases. I also
changed the loop to "for r in xsrange(7,p)", in response to the discussion
earlier on this ticket: adding the x gives an iterator instead of making
the whole list and iterating through it (bad for large p!), and adding the
s makes the iterator yield Sage integers (so it works for p too large to
fit into a python int). I also added an is_prime() test on p, since
otherwise if you give it a huge composite number there seemed to be a
danger that it would run through a loop of length p before realising that
the input was invalid.
5. I simplified sgn().
All tests in sage/quadratic_forms pass, as do those in arith.py and
rational.py which were also touched.
The patch needs to be applied to (at least) 3.4.1.rc3 + the two patches at
#5627.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5834>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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