LaTeX Printing Proposals
Freddie Witherden
I have been toying around with a couple of ideas which might be worth
investigating for the LaTeX printer. First off, different bracket
styles depending on the nesting level. So it might go:
{ [ ( ( ) ) ] }; exactly how to do this I am unsure. It depends on how
easy it is to maintain the nesting level. Ideally {} and [] should
only be used for adjacent brackets, for example:
(x*(y+3)+4)^3 doesn't really require nested brackets, but:
[a*exp(z*I)] does.
This is the kind of thing that I might be tempted towards the evils of
regular expressions to achieve. Hopefully, however there is a much
more elegant solution.
Secondly, constant expanding. If one has a fraction <x>/k where k is a
constant it is often nice to pull the constant out front when
printing, giving 1/k * <x> where <x> is an arbitrary expression. This,
again sacrifices horizontal space for better readability (a larger
font size can be used for <x>). I am yet to look into how hard this
would be to achieve, however.
Finally, an option to use exp() as opposed to {e}^{<x>}. This is most
useful when outputting the solutions to differential equations, which
often raise e to quite a large fraction/expression. Using exp() leads
to better readability (due to the larger font size and greater
spacing). I propose the following: we have a configuration option to
choose between {e}^{x}, exp(x) and auto, where auto uses heuristics to
decide (as soon as you get to needing brackets or fractions exp() is
often nicer).
Be interested to know what you all think -- and if you have any
implementation hints.
Regards, Freddie.
Alan Bromborsky
you can turn the option off and on for different parts of the program.
Freddie Witherden
On 24 Dec 2008, at 23:36, Alan Bromborsky wrote:
> When you say configuration option I assume you mean a global switch so
> you can turn the option off and on for different parts of the program.
I was thinking more along the lines as an optional parameter passed to
latex(expr, expFormat='auto') or something along those lines. That way
there is no need for any kind of global state variable and so no need
to set/restore it.
Although having to pass multiple configuration options each time is
not the nicest thing in the world, in 99% of cases the defaults will
probably be what most people want.
Regards, Freddie.
Ondrej Certik
On Thu, Dec 25, 2008 at 12:30 AM, Freddie Witherden
<fre...@witherden.org> wrote:
> Hi all,
>
> I have been toying around with a couple of ideas which might be worth
> investigating for the LaTeX printer. First off, different bracket
> styles depending on the nesting level. So it might go:
> { [ ( ( ) ) ] }; exactly how to do this I am unsure. It depends on how
> easy it is to maintain the nesting level. Ideally {} and [] should
> only be used for adjacent brackets, for example:
>
> (x*(y+3)+4)^3 doesn't really require nested brackets, but:
>
> [a*exp(z*I)] does.
Yes, I like what you propose.
>
> This is the kind of thing that I might be tempted towards the evils of
> regular expressions to achieve. Hopefully, however there is a much
> more elegant solution.
If the regular expression is maintainable, why not.
>
> Secondly, constant expanding. If one has a fraction <x>/k where k is a
> constant it is often nice to pull the constant out front when
> printing, giving 1/k * <x> where <x> is an arbitrary expression. This,
> again sacrifices horizontal space for better readability (a larger
> font size can be used for <x>). I am yet to look into how hard this
> would be to achieve, however.
Yes, I also agree with you.
>
> Finally, an option to use exp() as opposed to {e}^{<x>}. This is most
> useful when outputting the solutions to differential equations, which
> often raise e to quite a large fraction/expression. Using exp() leads
> to better readability (due to the larger font size and greater
> spacing). I propose the following: we have a configuration option to
> choose between {e}^{x}, exp(x) and auto, where auto uses heuristics to
> decide (as soon as you get to needing brackets or fractions exp() is
> often nicer).
Again +1.
>
> Be interested to know what you all think -- and if you have any
> implementation hints.
I am all for it, thanks for thinking about it. Thanks also for your
other patch in #1248.
Yes, I am also for latex(expr, exp_format='auto') or something, rather
than a global option.
Ondrej
Freddie Witherden
> I have been toying around with a couple of ideas which might be worth
> investigating for the LaTeX printer. First off, different bracket
> styles depending on the nesting level. So it might go:
> { [ ( ( ) ) ] }; exactly how to do this I am unsure. It depends on how
> easy it is to maintain the nesting level. Ideally {} and [] should
> only be used for adjacent brackets, for example:
>
> (x*(y+3)+4)^3 doesn't really require nested brackets, but:
>
> [a*exp(z*I)] does.
>
> This is the kind of thing that I might be tempted towards the evils of
> regular expressions to achieve. Hopefully, however there is a much
> more elegant solution.
Currently the best idea on the table, so far as I can discern, is the
following:
- Use a regular expression to find pairs and triplets of brackets
adjacent to each other, so (( and (((;
- for the outermost bracket(s) find the complementary bracket (so
its opposite) -- this is easy to do using a stack;
- replace it and its complement with the appropriate substitution,
'[' or '{'.
It is not possible to use closing brackets and work backwards as
function calls should *always* use ( ), e.g., in (x + ln(x*(x+1)))^n
working backwards would give us {x + ln[x*(x+1)]} -- not what we want.
> Secondly, constant expanding. If one has a fraction <x>/k where k is a
> constant it is often nice to pull the constant out front when
> printing, giving 1/k * <x> where <x> is an arbitrary expression. This,
> again sacrifices horizontal space for better readability (a larger
> font size can be used for <x>). I am yet to look into how hard this
> would be to achieve, however.
I am currently putting together some examples where I feel this has a
positive impact on readability. A good example is sin(1/2 * x), on in
LaTeX \operatorname{sin}\frac{1}{2} x as opposed to \operatorname{sin}
\frac{x}{2}. The output of Wolfram's Interator, http://integrals.wolfram.com/index.jsp
is usually quite good at deciding whether to pull the constant out
or not. (Although do not believe the claim about it being the "world's
only full-power integration solve", Axiom eats it for breakfast :)
> Finally, an option to use exp() as opposed to {e}^{<x>}. This is most
> useful when outputting the solutions to differential equations, which
> often raise e to quite a large fraction/expression. Using exp() leads
> to better readability (due to the larger font size and greater
> spacing). I propose the following: we have a configuration option to
> choose between {e}^{x}, exp(x) and auto, where auto uses heuristics to
> decide (as soon as you get to needing brackets or fractions exp() is
> often nicer).
Again, some examples are needed. e^{\operatorname{tan}x} looks okay,
as does e^{ax+b} but two fractions (so a/b + p/q) usually don't. A way
to see if a mul will end up as a fraction would be nice.
Finally, while playing around some more with the LaTeX output (and
showing it to whoever was willing to listen) I found that some have an
affinity for tan-1 (\operatorname{tan}^{-1}x as opposed to atan or
arctan. G&R use arc<x> where <x> is an trigonometric function.
My proposal here is to support all three inverse trigonometric forms,
arc<x> being the default (it is what LaTeX defines, \arctan{x}) but
also supporting the other two forms by way of an optional parameter to
latex(expr,...).
The simplest way of implementing this is probably to use a look-up
table to identify a function as an inverse trigonometric function.
Then it is a simple case of stripping the first character and
appending either 'arc', 'a' or suffixing '^{-1}'.
In the case of atan(x)**2 being output in the form of tan-1 the output
would be: \operatorname{tan}^{-1}\left(x\right)^{2}. (Even if bracket
folding is enabled and applicable, when outputting as tan-1 where tan
is raised to a power brackets would be mandatory.)
Regards, Freddie.