A macro for pretty geometric algebra equations?

General Usage
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12

The following macro to give the option of writing geometric algebra equations using “standard” math syntax operators instead of “standard” programming syntax operators is good enough for me for now:

# convert GA math syntax to GA programming syntax
macro ga_str(str)
	C = collect(str)
	n = length(C)
	for i = 1:n
		if C[i] == ' '		# \thinspace for geometric product
			C[i] = '*'
		elseif C[i] == '∧'	# \wedge for outer product
			C[i] = '^'
		elseif C[i] == '∨'	# \vee for regressive product
			C[i] = '&'
		elseif C[i] == '·'	# \cdotp for inner product
			C[i] = '|'
		elseif C[i] == '\u20f0'	# \asteraccent for dual
			j = i-1
			while j > 0 # shift operator from postfix to prefix
				if isletter(C[j]) || isnumeric(C[j])
					C[j+1] = C[j]
					j -= 1
				else
					break
				end
			end
			C[j+1] = '!' # prefix '!'
		end
	end
	return esc(Meta.parse(String(C)))
end

The macro’s translation from math syntax to programming syntax slowed my unit test down by just 2.5% (4.69 us versus 4.58 us, according to @btime utest(false)).

I’m not yet sure if I will implement the translation for the sandwich operator because I am content with the look and speed of the geometric product operator and the tilde (i.e., reverse) operator implementing the sandwich operation.

Next week’s task: integrating the Julia reference implementation of projective geometric algebra with the interactive graphics of Makie.

Thanks for the help and the feedback.