stylewarning / Formulador

                          FORMULADOR
                          ==========

                       By Robert Smith

Formulador is intended to be a text-based formula renderer, and maybe editor one day.

It is still a work-in-progress; we can't reinvent an ad hoc, informally-specified, bug-ridden, slow implementation of half of TeX overnight.

The way it works right now is simple: build your typesetting object, and draw it out to a canvas. Formulador will take the liberty of making the canvas for you.

Fundamentally, as it stands, input is composed of boxes. Each box contains an element you'd like to typeset. Right now we have the following boxes

* empty-box (a sort of no-op; typesets as nothing)
* strings (typeset as themselves)
* characters (typeset as themselves)
* string-box (a wrapper for a string)
* frac-box (fractions)
* row-box (a horizontal concatenation of boxes)
* frame-box (a box with decorative appeal)
* script-box (superscripts and subscripts)
* limits-box (limits for operators)
* sqrt-box (Nth roots)

These will be extended and given more options over time.

Here is a simple example:

FORMULADOR> (draw (frac-box (box "x") (box "y"))) #<CANVAS +---+ | x | |---| | y | +---+ with 3 defined regions>

And a more complex example:

FORMULADOR> (draw (frac-box (row-box (list (frac-box (box "x") (box "y")) (box "+") (frac-box (box "w") (row-box (list (box "u") (box "+") (box "v")) :padding 1))) :padding 1) (frac-box (row-box (list (box "p") (box "+") (box "q")) :padding 1) (row-box (list (box "r") (box "+") (frac-box (box "1") (box "s"))) :padding 1)))) #<CANVAS +---------------+ | x w | | --- + ------- | | y u + v | |---------------| | p + q | | --------- | | 1 | | r + --- | | s | +---------------+ with 23 defined regions>

Demonstration of the use of combinators:

FORMULADOR> (defun interleave (x list) (rest (mapcan (lambda (y) (list x y)) list))) INTERLEAVE FORMULADOR> (interleave '* '(x y z)) (X * Y * Z) FORMULADOR> (draw (frac-box (box "1") (row-box (interleave (box "+") (map 'list (lambda (c) (frac-box (box "1") (box c))) "harmonic")) :padding 1))) #<CANVAS +-----------------------------------------------+ | 1 | |-----------------------------------------------| | 1 1 1 1 1 1 1 1 | | --- + --- + --- + --- + --- + --- + --- + --- | | h a r m o n i c | +-----------------------------------------------+ with 34 defined regions>

Formulador is aware of baselines. Note the correct baselines in the following example.

FORMULADOR> (draw (glue +sigma+ (row-box (list (frac-box (frac-box (box "x + y") (box "z")) (box "b")) (box "+") (parens-box (row-box (list (frame-box (frac-box (box "c") (row-box (list (frac-box (box "p") (box "q")) (box "+") (box "r")) :padding 1))) (box "*") (box "r")) :padding 1))) :padding 1))) #<CANVAS +----------------------------------+ | x + y | |=== ------- / +---------+ | |\ z | | c | || | > --------- + | |---------| * r || |/ b | | p | || |=== | | --- + r | || | | | q | || | \ +---------+ /| +----------------------------------+ with 22 defined regions>

If your terminal supports unicode, it can print using unicode by setting the appropriate so-called "charmaps". Charmaps are alternative character sets for different decorations or constructions.

FORMULADOR> (let ((frame-charmap unicode-plain-frame-charmap) (vinculum-charmap unicode-vinculum-charmap) (paren-charmap unicode-paren-charmap)) (draw (glue +sigma+ (row-box (list (frac-box (frac-box (box "x + y") (box "z")) (box "b")) (box "+") (parens-box (row-box (list (frame-box (frac-box (box "c") (row-box (list (frame-box (frac-box (box "p") (box "q"))) (box "+") (box "r")) :padding 1))) (box "*") (box "r")) :padding 1))) :padding 1)))) #<CANVAS +------------------------------------+ | x + y | |=== ─────── ⎛ ┌───────────┐ ⎞| |\ z ⎜ │ c │ ⎟| | > ───────── + ⎜ │───────────│ * r ⎟| |/ b ⎜ │ ┌───┐ │ ⎟| |=== ⎜ │ │ p │ │ ⎟| | ⎜ │ │───│ + r │ ⎟| | ⎜ │ │ q │ │ ⎟| | ⎜ │ └───┘ │ ⎟| | ⎝ └───────────┘ ⎠| +------------------------------------+ with 23 defined regions>

Superscripts and subscripts are supported. Here's the standard Euclidean metric in 3-space:

FORMULADOR> (flet ((x_ (n) (script-box (box "x") :superscript (box "2") :subscript (box (prin1-to-string n))))) (draw (glue (box "r") (box " = ") (script-box (parens-box (glue (x_ 1) (box " + ") (x_ 2) (box " + ") (x_ 3))) :superscript (box "1/2"))))) #<CANVAS +-----------------------+ | 1/2| | / 2 2 2 \ | |r = | x + x + x | | | \ 1 2 3 / | +-----------------------+ with 22 defined regions>

There are more examples in examples.lisp. One such is Chudnovsky's formula.

FORMULADOR> (draw chudnovsky) #<CANVAS +------------------------------------------------------------------------+ | _______ ∞ | | | 3 === k| | 1 |640320 \ (6k)! (545140134k + 13591409) / 1 \ | |--- = ----------- > ------------------------------- | - --------- | | | π 12 / 3 | 3 | | | === (3k)! (k!) \ 640320 / | | k = 0 | +------------------------------------------------------------------------+ with 39 defined regions>

We can extract parts of a drawn expression and see the associated tree. This is useful for editing tasks.

FORMULADOR> (mapcar #'draw (objects-at-point (draw chudnovsky) 67 4)) (#<CANVAS +-+ |3| +-+ with 1 defined region> #<CANVAS +-------+ | 3| |640320 | +-------+ with 4 defined regions> #<CANVAS +---------+ | 1 | |---------| | 3 | | 640320 | +---------+ with 6 defined regions> #<CANVAS +-----------+ | 1 | |- ---------| | 3 | | 640320 | +-----------+ with 8 defined regions> #<CANVAS +---------------+ |/ 1 | || - --------- || || 3 || |\ 640320 /| +---------------+ with 9 defined regions> #<CANVAS +----------------+ | k| |/ 1 \ | || - --------- | | || 3 | | |\ 640320 / | +----------------+ with 12 defined regions> #<CANVAS +------------------------------------------------------------------------+ | _______ ∞ | | | 3 === k| | 1 |640320 \ (6k)! (545140134k + 13591409) / 1 \ | |--- = ----------- > ------------------------------- | - --------- | | | π 12 / 3 | 3 | | | === (3k)! (k!) \ 640320 / | | k = 0 | +------------------------------------------------------------------------+ with 39 defined regions>)