Speed up diff; extend interface

[jverzani]

This implements suggestion in #225 to have a step for early termination in diff if possible.
This passes on #225; the additional allocations to check for early termination would be paid in every instance; whereas the suggestion of #225 only pays off in certain situations. (The allocation could be avoided by some call to basic_has_symbol, but even that had a performance cost)

• Avoids use of BasicType to check that x is a symbol; as this is more performant
• adds a diff(ex) method for case where ex has just 0 or 1 symbol
• extends diff interface closer to SymPy by allowing expressions like diff(ex, x, 2, y).
• does not cover diff(ex, (x,2)) interface of SymPy, as that method is used otherwise. (would fix were it not breaking)
• adds tests
• clean up one verbose test by using repr

[jverzani]

There are two things here: one extends the interface, the other closes #225. The latter adds a check for whether the expression is zero. As such, it may be a performance concern. I didn't benchmark, But if there is a concern, I can modify this PR.

[jverzani]

This last commit to this PR has a noticeable speed up for basic differentation:

Before

julia> @btime diff(sin(x),x)
  1.243 μs (5 allocations: 88 bytes)

After

julia> @btime diff(sin(x), x)
  833.444 ns (3 allocations: 48 bytes)

This is gained by avoiding the use of BasicType for dispatch, which is slower than desired, as it needs to allocate a string to check if x is a symbol.

[jverzani]

Hi @isuruf any objections to my merging this?

[jverzani]

Hi @isuruf, can I merge this?

[isuruf]

Looks good. One question. Wouldn't it be better to have an inplace diff and call it multiple times to reduce the number of allocations?

[jverzani]

Great idea! (I always forget Basic is mutable). I'll try and investigate soon

[isuruf]

This should probably use a mutating diff as well, but not necessary for this PR

[isuruf]

Minor comment