[with patch, needs work] Additional functions for Indefinite Binary Quadratic Forms

[aliashamieh]

I added functions to check for the reducibility of an indefinite binary quadratic form and reduce it.

[aliashamieh]

added missing doctests

[davidloeffler]

Am changing this from "need review" to "needs review" so it shows up in the standard queries

[cremona]

Review

The patch applied fine to 4.0.1, and it provides some functions which look useful.

I think that not all new new functions have doctests. Why are the new functions not implemented as member functions of the BinaryQF class? That would be much better; as it is anyone using them has to import them explicitly. So I suggest that they are converted to be member functions (which is trivial to do).

Secondly, the use of the python math functions sqrt and floor is not a good idea, since the coefficients of the form will be Sage integers. For example:

sage: from sage.quadratic_forms.binary_qf import normalized_indefinite_form
sage: f = BinaryQF([10^100,10^500,10^200])
sage: f.discriminant()>0
True
sage: normalized_indefinite_form(f)
---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)

/home/john/.sage/temp/ubuntu/9768/_home_john__sage_init_sage_0.py in <module>()

/home/john/sage-4.0.1/local/lib/python2.5/site-packages/sage/quadratic_forms/binary_qf.pyc in normalized_indefinite_form(f)
    486         raise ValueError, "This only works for indefinite forms"
    487     
--> 488     if sqrt(delta) <= abs(a):
    489         s=(a/abs(a))*floor(-1*b/(2*abs(a)))
    490     else:

OverflowError: math range error

For example, the line if sqrt(delta) <= abs(a): could be replaced by if delta <= a2: .

The docstring for this function should also say what the definition of "normalised" is.

I also slightly amended the ticket's title to give a better description.

[ncalexan]

Alia and I are going to work on this in the next few days.

[aliashamieh]

[with patch, needs review] Additional functions for Indefinite Binary Quadratic Forms