[with patch, positive review] ode_solver __init__ method ignores many parameters

[jwmerrill]

The following example comes from the in-source documentation for ode_solver:

sage: T = ode_solver()
sage: g_1= lambda t,y: [y[1]*y[2],-y[0]*y[2],-0.51*y[0]*y[1]]
sage: T.function=g_1
sage: T.y_0=[0,1,1]
sage: T.scale_abs=[1e-4,1e-4,1e-5]
sage: T.error_rel=1e-4
sage: T.ode_solve(t_span=[0,12],num_points=100)
sage: f = T.interpolate_solution()
sage: f(pi)              # slightly random precision
0.53794725135406318

It should be possible to set these attributes using arguments to the constructor, but this fails:

sage: T = ode_solver(g_1,y_0=[0,1,1],scale_abs=[1e-4,1e-4,1e-5],error_rel=1e-4)
sage: T.ode_solve(t_span=[0,12],num_points=100)
sage: f = T.interpolate_solution()
sage: f(pi)
Traceback (click to the left for traceback)
...
TypeError: object of type 'NoneType' has no len()

[jwmerrill]

Adds a doctest and fixes the init method

[jwmerrill]

One thing I'm worried about is that the tests for ode.pyx already take a long time (more than two minutes), and this makes them take even longer.

[jason]

This seems to work and doctests pass. However, the given example is not the same as the example before (as the docs claim), since the algorithm used is different. The referee patch adds an algorithm keyword to make it the same. Apply the referee patch after the original patch and then it is positive review.

[jason]

jwmerrill, related to the docs of ode_solver, could you review #3966? Thanks.

[mabshoff]

Merged both patches in Sage 3.1.2.alpha2