#5627: [with new patch, needs review] Trivial typo in quadratic_nonresidue
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Reporter: kcrisman | Owner: justin
Type: defect | Status: new
Priority: trivial | Milestone: sage-3.4.2
Component: quadratic forms | Keywords:
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Comment(by cremona):
I have added another 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.
All tests in sage/quadratic_forms pass, as do those in arith.py and
rational.py which were also touched.
If one of the origianl posters can ok my patch then the whole lot can be
merged, I hope.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5627#comment:5>
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