Option to render elementary differentials using summation notation #103
Description
There is one thing that's in the TOMS paper that BSeries.jl actually still doesn't do, which is to write the elementary differentials for an unspecified RHS function
I would like to add this option. Here's some simple code that generates this as a LaTeX string:
function elementary_differential_string(t)
indices = ["i","j","k","l","m","n"];
labels = copy(indices[1:length(t.level_sequence)]);
edstring = ""
for i in 1:order(t)
edstring *= "f^{"
edstring *= labels[i]
edstring *= "}_{"
for j in i+1:order(t)
if t.level_sequence[j] == t.level_sequence[i]
break
elseif t.level_sequence[j]-t.level_sequence[i] == 1
edstring *= labels[j]
end
end
edstring *= "} "
end
edstring = replace(edstring,"_{}"=>"")
return edstring
end
Before going ahead, I wanted to get your opinion (@ranocha).
- Is direct string generation the best approach? In principle we could generate the products of partial derivatives symbolically first and then render those. This is more elegant but otherwise I don't see an advantage to it.
- How should the user specify that they want the elementary differentials in this form? My plan is to implement a global option like the one in
RootedTrees.jlfor how to render trees. - There is a minor issue of needing enough distinct index labels for a given tree. My plan is to just start with "i" and go through the end of the alphabet. In practice it seems unlikely that someone would work with a tree that exhausts this.