Unnecessary parentheses in LaTEX output

[cshaa]

There are many functions in mathjs that, when rendered with toTex(), put too many parens around the arguments. For example a simple cross(c, d) will produce: \left( c\right)\times\left( d\right) instead of c \times d. This was already mentioned in #307 where @FSMaxB said he isn't going to have time for that, so it was closed. However some two years later, things could be different. And if not, I could look into the code myself and see what I can do…

Steps needed:

• remove parens that enclose a single identifier
  • eg. not(a) ⇒ \neg\left( a\right) × \neg a
• remove parens that enclose the whole expression
  • eg. expm1(x) ⇒ \left(e^{ x}-1\right)) × e^{ x}-1
  • the whole output doesn't need to be wrapped in parentheses
• remove parens that enclose a fraction
  • eg. -(1/2) ⇒ -\left(\frac{1}{2}\right) × -\frac{1}{2}
  • this feature probably shouldn't be recursive, so that users can force parens around a fraction by writing this: -((a/b))
• investigate the possibility to detect precedence based on semantics of the expression
  • eg. add(x, add(y, z)) ⇒ \left( x+\left( y+ z\right)\right) × x+y+z
  • probably quite hard to implement – I'm not sure whether it's worth the time…

@josdejong What do you think about this?

[FSMaxB]

It is still true that I have no time to do this myself but feel free to ask questions anytime!

[FSMaxB]

The underlying problem if I remember correctly is that functions don't have a notion of precedence, other than operators, and the function cross isn't parsed as an OperatorNode so the code that takes care of the necessary parentheses doesn't apply. The parentheses are actually part of the LaTeX-Template in src/function/matrix/cross.js and are there just to be safe because the actual precedence isn't known.

In order for this to be fixed I guess that the precedence logic from OperatorNode needs to be added to FunctionNode as well and certain functions added to the list of properties in src/expression/operators.js after deciding on their precedence, but that is kind of a hard question in and by itself.

Or maybe there is a better solution than everything I've done previously.

[FSMaxB]

Another approach would be to replace some of the LaTeX templates with actual functions that have their own logic in them. But that probably won't scale because it would be a case by case solution.

[cshaa]

I think that implementing precedence logic for FunctionNode is what I meant by “detect precedence based on semantics of the expression” in the last point. This sounds quite hard and I don't think I'll have time for that either.

On the other hand, putting logic to the toTex methods of individual functions would be much easier and could easily solve the first three points. You're right that scalability is worse with this approach, but if we defined some kind of helper function to create templates that take care of that, it could be fine…

[FSMaxB]

You don't need to define a helper function to create templates. If I remember correctly you can put a function in there directly instead of the template string (similar or equal to the custom LaTeX handler described in the documentation).

[FSMaxB]

This is the relevant code:

mathjs/src/expression/node/FunctionNode.js

Lines 385 to 415 in 47a291a

	let latexConverter
	if (math[this.name] && ((typeof math[this.name].toTex === 'function') || (typeof math[this.name].toTex === 'object') || (typeof math[this.name].toTex === 'string'))) {
	// .toTex is a callback function
	latexConverter = math[this.name].toTex
	}
	let customToTex
	switch (typeof latexConverter) {
	case 'function': // a callback function
	customToTex = latexConverter(this, options)
	break
	case 'string': // a template string
	customToTex = expandTemplate(latexConverter, this, options)
	break
	case 'object': // an object with different "converters" for different numbers of arguments
	switch (typeof latexConverter[args.length]) {
	case 'function':
	customToTex = latexConverter[args.length](this, options)
	break
	case 'string':
	customToTex = expandTemplate(latexConverter[args.length], this, options)
	break
	}
	}
	if (typeof customToTex !== 'undefined') {
	return customToTex
	}
	return expandTemplate(latex.defaultTemplate, this, options)

If the .toTex property of a function is of type function, it get's called with the FunctionNode and options as parameters instead of expanding a template string.

[josdejong]

Thanks for your inputs @m93a . Would be nice to improve the LaTeX output for the cases you reported. We should indeed pay close attention to correctly handling precedence like Max points out.

[thunderkid]

Another case that I noticed is where parentheses surround the numerator and denominator of a fraction. So
math2.parse('(1 - y)/(1+ 2*x)').toTex()
yields
\frac{\left(1- y\right)}{\left(1+2\cdot x\right)}
So you get ugly surrounding brackets on both the numerator and denominator.
It seems that whenever \left and \right occur as the outermost parts of a \frac numerator or denominator, they could be killed off. Unless I'm missing some latex special cases?

[cshaa]

For anyone interested in working on this, here's how Sympy does it: sympy/printing/precedence.py

[josdejong]

@thunderkid you're right, in that case the parentheses can be removed from LaTeX output.