Scalar Field Arithmetics: Trivial Cases

[gh-mjungmath]

Setup:

sage: M = Manifold(2, 'M', structure='topological') # the 2-dimensional sphere S^2
sage: U = M.open_subset('U') # complement of the North pole
sage: c_xy.<x,y> = U.chart() # stereographic coordinates from the North pole
sage: V = M.open_subset('V') # complement of the South pole
sage: c_uv.<u,v> = V.chart() # stereographic coordinates from the South pole
sage: M.declare_union(U,V)   # S^2 is the union of U and V
sage: xy_to_uv = c_xy.transition_map(c_uv, (x/(x^2+y^2), y/(x^2+y^2)),
....:                                intersection_name='W',
....:                                restrictions1= x^2+y^2!=0,
....:                                restrictions2= u^2+v^2!=0)
sage: uv_to_xy = xy_to_uv.inverse()
sage: f = M.scalar_field({c_xy: 1/(1+x^2+y^2), c_uv: (u^2+v^2)/(1+u^2+v^2)},
....:                    name='f')

Current state:

sage: %timeit M.one_scalar_field()*f
10 loops, best of 5: 47.5 ms per loop
sage: %timeit f*M.one_scalar_field()
10 loops, best of 5: 48 ms per loop

This ticket:

sage: %timeit M.one_scalar_field()*f
The slowest run took 4.05 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 5: 21.1 µs per loop
sage: %timeit f*M.one_scalar_field()
10000 loops, best of 5: 26.5 µs per loop

But the generic multiplication seems not affected:

Current state:

sage: %timeit f*f
10 loops, best of 5: 77.8 ms per loop

This ticket:

sage: %timeit f*f
10 loops, best of 5: 77.4 ms per loop

The output is improved, too:

Current state:

sage: M.one_scalar_field()*M.one_scalar_field()
Scalar field 1*1 on the 2-dimensional topological manifold M

This ticket:

sage: M.one_scalar_field()*M.one_scalar_field()
Scalar field 1 on the 2-dimensional topological manifold M

[gh-mjungmath]

New commits:

​2446f7e

Trac 30291: simple checks for trivial cases in _mul_, _add_ and _div_

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​4bd82e4

Trac #30291: patchbot doctest fixed

[gh-mjungmath]

Apparently, I mixed some things up with #30239. I'll rebase; same for #30239.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​4f3b69f

Trac 30291: simple checks for trivial cases in _mul_, _add_ and _div_

[gh-mjungmath]

I am also curious about your opinion on my very last comment, Matthias.

[gh-mjungmath]

Wrong ticket, sorry Matthias...I was referring to #30239. But you're already in the cc there.

[tscrim]

Note that (self - 1) will involve a coercion call. How difficult would it be to instead add a method is_trivial_one that just pushes the x - self.base_ring().one() (or maybe x - SR.one()) computation to the essential code to avoid creating fewer temporary (heavy) objects?

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​339781a

Trac #30291: add is_trivial_one() method

[gh-mjungmath]

You mean something like this?

[tscrim]

Yep, exactly. This seems like it should be faster than using (self - 1).is_trivial_zero(). If the the patchbot comes back green, then you can set a positive review.

[gh-mjungmath]

I will do a short performance check tomorrow and post it here.

[gh-mjungmath]

Thanks Travis.

Performance check follows...