branch: externals/org-mathsheet
commit d7db7a61d13ee660bc342ce7be694dc9722497fd
Author: Ian Martins <ia...@jhu.edu>
Commit: Ian Martins <ia...@jhu.edu>
Can produce algebra worksheets
---
example.org | 54 ++++++++------------
mathsheet.org | 157 ++++++++++++++++++++++++++++++++++++----------------------
2 files changed, 119 insertions(+), 92 deletions(-)
diff --git a/example.org b/example.org
index 3abcae6d71..aec3af0dbb 100644
--- a/example.org
+++ b/example.org
@@ -1,12 +1,12 @@
* add and subtract
#+name: add-sub-1
-| weight | order | template | descr
|
-|--------+-------+---------------------+-------------------------------------------|
-| 3 | 1 | [1..10] + [0..10] | simple
|
-| 2 | 2 | [1..10] + [8..12] | second number bigger
|
-| 2 | 2 | [1..12] + [0..10] | first number bigger
|
-| 1 | 3 | [a=2..10] - [1..$a] | small number subtraction, positive
result |
+| weight | order | template | descr
|
+|--------+-------+-----------------------+-------------------------------------------|
+| 3 | 1 | [1..10] + [0..10] | simple
|
+| 2 | 2 | [1..10] + [8..12] | second number bigger
|
+| 2 | 2 | [1..12] + [0..10] | first number bigger
|
+| 1 | 3 | [a=2..10] - [1..$a] | small number subtraction, positive
result |
#+name: add-sub-2
| weight | order | template | descr
|
@@ -19,34 +19,22 @@
| 0 | 0 | [$a*[1..5]] / [a=1..10] | division
|
#+name: algebra-1
-| weight | order | template | descr |
-|--------+-------+----------------------------+--------|
-| 3 | 1 | x/2 + [a=0..20] = [$a..21] | simple |
+| weight | order | template | descr |
+|--------+-------+------------------------------------+--------|
+| 3 | 1 | x / ([2..4] + [a=0..5]) = [$a..10] | simple |
+| 3 | 2 | [$a*[2..10]] / x = [a=1,2,4] | simple |
-#+BEGIN: problem-set :templates "algebra-1" :count 21
-| problem | answer |
-|---------------+-----------------------|
-| x/2 + 12 = 13 | x / 2. = 1 |
-| x/2 + 11 = 18 | x / 14. = 1 |
-| x/2 + 11 = 16 | x / 10. = 1 |
-| x/2 + 6 = 19 | x / 26. = 1 |
-| x/2 + 3 = 5 | x / 4. = 1 |
-| x/2 + 19 = 19 | x / 2 = 0 |
-| x/2 + 19 = 20 | x / 2. = 1 |
-| x/2 + 2 = 9 | x / 14. = 1 |
-| x/2 + 12 = 20 | x / 16. = 1 |
-| x/2 + 0 = 11 | x / 22. = 1 |
-| x/2 + 2 = 18 | x / 32. = 1 |
-| x/2 + 7 = 15 | x / 16. = 1 |
-| x/2 + 0 = 9 | x / 18. = 1 |
-| x/2 + 17 = 17 | x / 2 = 0 |
-| x/2 + 13 = 17 | x / 8. = 1 |
-| x/2 + 0 = 6 | x / 12. = 1 |
-| x/2 + 3 = 4 | x / 2. = 1 |
-| x/2 + 8 = 12 | x / 8. = 1 |
-| x/2 + 16 = 19 | x / 5.99999999999 = 1 |
-| x/2 + 7 = 13 | x / 12. = 1 |
-| x/2 + 9 = 20 | x / 22. = 1 |
+#+BEGIN: problem-set :templates "algebra-1" :count 8
+| problem | answer |
+|-----------------+--------|
+| x / (2 + 2) = 2 | x = 8 |
+| x / (2 + 0) = 8 | x = 16 |
+| x / (3 + 1) = 1 | x = 4 |
+| x / (3 + 4) = 7 | x = 49 |
+| 2 / x = 1 | x = 2 |
+| 7 / x = 1 | x = 7 |
+| 10 / x = 2 | x = 5 |
+| 28 / x = 4 | x = 7 |
#+END:
* bigger addition and multiplications
diff --git a/mathsheet.org b/mathsheet.org
index 17b962d067..386147c5b2 100644
--- a/mathsheet.org
+++ b/mathsheet.org
@@ -44,12 +44,6 @@ that generates the worksheet. Only the first three columns
are used.
| 1 | 4 | [a=1..10] + [0..10] - [0..$a] | three terms with
subtraction |
| 0 | 0 | [$a*[1..5]] / [a=1..10] | division
|
-*** TODO handle templates with variables
-can be done like this
-#+begin_export
-(calc-eval "solve(2x = 1 + 2, [x])")
-#+end_export
-
* Code walkthrough
** Problem generation
*** Dependencies
@@ -81,13 +75,22 @@ end of the problem. returns a list of fields, formatted as:
'(var (deps) start-marker end-marker nil)
#+end_example
-~var~ is a variable name if there is an assignment, otherwise it is a
-placeholder like ~_0~, ~_1~, etc.
+change to
+
+#+begin_example
+'(asn-var (deps) (start-marker . end-marker) nil)
+#+end_example
+
+~asn-var~ is a variable name if there is an assignment, otherwise it is a
+placeholder like ~_0~, ~_1~, etc. ~asn-var~ must be interned and must
+be the first index since we use this list as an alist later.
+
+~alg-vars~ are algebraic variables if there are any in this problem,
+otherwise ~nil~.
~start-marker~ and ~end-marker~ are markers in the (temp) buffer.
-The last entry is ~nil~ for "not visited." ~var~ must be interned and
-must be the first index since we use this as an alist later.
+The last entry is ~nil~ for "not visited." It is used by ~dfs-visit~.
for example:
#+begin_example
@@ -107,18 +110,21 @@ new field to the list when we close the current field.
(defun ianxm/scan-problem ()
"Scan problem"
(let ((field-index 0)
- open-fields ; stack (open close (vars) deps)
- closed-fields) ; list (open close (vars) deps)
+ open-fields ; stack
+ closed-fields ; list
+ alg-vars)
(with-peg-rules
- ((stuff (* (or var letter digit symbol field space)))
+ ((stuff (* (or asn-var alg-var digit symbol field space)))
(field open (opt assignment) stuff close)
(space (* [space]))
(open (region "[")
`(l r -- (progn
(push (list
- (intern (concat "_" (number-to-string
field-index)))
- nil (copy-marker l) nil nil)
+ (intern (concat "_" (number-to-string
field-index))) ; asn-var
+ nil ; deps
+ (cons (copy-marker l) nil) ; start and end
markers
+ nil) ; not visited
open-fields)
(setq field-index (1+ field-index))
".")))
@@ -128,41 +134,46 @@ new field to the list when we close the current field.
(car open-fields)
(intern v))
".")))
- (var "$" (substring letter)
+ (asn-var "$" (substring letter)
`(v -- (progn
(push (intern v) (cadar open-fields))
".")))
+ (alg-var (substring letter)
+ `(v -- (progn
+ (push v alg-vars)
+ ".")))
(close (region "]")
`(l r -- (progn
- (setcar (cdddar open-fields) (copy-marker l t))
- (when (> (length open-fields) 1)
+ (setcdr (caddar open-fields) (copy-marker l t))
+ (when (> (length open-fields) 1) ; add parent to
child dependency
(push (caar open-fields) (cadadr open-fields)))
(push (pop open-fields) closed-fields)
".")))
(letter [a-z])
(digit [0-9])
- (symbol (or "." "+" "-" "*" "/" "(" ")" "=")))
+ (symbol (or "." "," "+" "-" "*" "/" "(" ")" "=")))
(peg-run (peg stuff)
(lambda (x) (message "failed %s" x))
(lambda (x)
(funcall x)
- closed-fields)))))
+ `((:fields . ,closed-fields)
+ (:alg-vars . ,alg-vars)))))))
#+end_src
test scan
-#+begin_src elisp :noweb yes
+
+#+begin_src elisp :results verbatim :noweb yes
<<scan-problem>>
(with-temp-buffer
- (insert "y = [1..4] + [5..9]")
+ (insert "y = [1..4] + [5,7,9]")
(goto-char (point-min))
(ianxm/scan-problem))
#+end_src
#+RESULTS:
-| _1 | nil | #<marker in no buffer> | #<marker (moves after insertion) in no
buffer> | nil |
-| _0 | nil | #<marker in no buffer> | #<marker (moves after insertion) in no
buffer> | nil |
+: ((:fields (_1 nil (#<marker in no buffer> . #<marker (moves after insertion)
in no buffer>) nil) (_0 nil (#<marker in no buffer> . #<marker (moves after
insertion) in no buffer>) nil)) (:alg-vars "y"))
*** Reduce field
@@ -214,7 +225,8 @@ already evaluated and replaced them.
#+end_src
test with
-#+begin_src elisp :noweb yes :var page=page
+
+#+begin_src elisp :results verbatim :noweb yes :var page=page
<<variables>>
<<reduce-field>>
@@ -225,16 +237,17 @@ test with
#+end_src
#+RESULTS:
-| 3 |
+: (1)
*** Replace field
Replace a field with the value returned from reducing it.
+#+name: replace-field
#+begin_src elisp :tangle mathsheet.el
(defun ianxm/replace-field (node)
- (let ((start (caddr node))
- (end (1+ (cadddr node)))
+ (let ((start (caaddr node))
+ (end (1+ (cdaddr node)))
val)
(goto-char start)
(when (looking-at "\\[")
@@ -250,21 +263,23 @@ This uses a depth first search to ensure that we visit
(reduce and
replace) the fields in dependency order. Check dependencies then visit
the node.
+#+name: dfs-visit
#+begin_src elisp :tangle mathsheet.el
(defun ianxm/dfs-visit (node fields)
- (pcase (nth 4 node)
+ (pcase (cadddr node)
(1 (error "cycle detected")) ; cycle
(2) ; skip
(_ ; process
- (setcar (cddddr node) 1) ; started
+ (setcar (cdddr node) 1) ; started
(let ((deps (cadr node)))
(dolist (dep deps)
(ianxm/dfs-visit
(assq dep fields)
fields)))
(ianxm/replace-field node) ; visit
- (setcar (cddddr node) 2)))) ; mark done
+ (setcar (cdddr node) 2)))) ; mark done
#+end_src
+
*** Fill fields in problem
processes all fields in a problem.
@@ -275,37 +290,44 @@ processes all fields in a problem.
#+begin_src elisp :tangle mathsheet.el
(defun ianxm/fill-problem (full-problem)
- (interactive)
- (let (fields)
- (with-temp-buffer
- ;; stage problem in temp buffer
- (insert full-problem)
- (beginning-of-buffer)
+ (with-temp-buffer
+ ;; stage problem in temp buffer
+ (insert full-problem)
+ (beginning-of-buffer)
- ;; find fields, assignments, dependencies
- (setq fields (ianxm/scan-problem))
+ ;; find fields, assignment variables, algebraic variables, dependencies
+ (let* ((scan-ret (ianxm/scan-problem))
+ (fields (alist-get :fields scan-ret))
+ (alg-vars (alist-get :alg-vars scan-ret)))
- ;; order fields according to dependencies
+ ;; visit fields ordered according to dependencies
(dolist (node fields)
(ianxm/dfs-visit node fields))
(setq ianxm/var-list '())
- (buffer-string))))
+
+ ;; return filled problem
+ `((:problem . ,(buffer-string))
+ (:alg-vars . ,alg-vars)))))
#+end_src
test with this
-#+begin_src elisp :noweb yes
- <<full>>
+#+begin_src elisp :results verbatim :noweb yes :var page=page
+ <<variables>>
+ <<scan-problem>>
+ <<reduce-field>>
+ <<replace-field>>
+ <<dfs-visit>>
- ;;(ianxm/fill-problem "[1..12] + [1..10]")
+ (ianxm/fill-problem "[1..12] + [1,4,6,10]")
;;(ianxm/fill-problem "[1..[2..[10..100]]]")
;;(ianxm/fill-problem "[$a*[1..10]] / [a=1..10]")
;;(ianxm/fill-problem "[$a]/(3+[a=1..5])")
- (ianxm/fill-problem "[-10..[10..20]]")
+ ;; (ianxm/fill-problem "1/x + 2 = [-10..[10..20]]")
#+end_src
#+RESULTS:
-: -7
+: ((:problem . "6 + [1,4,6,10]") (:alg-vars))
other examples
#+begin_example
@@ -374,16 +396,32 @@ other examples
(let ((added 0)
(dup-count 0)
problem-set
- problem)
+ fill-ret problem solution)
(while (< added needed) ; add until "needed" are kept
- (setq problem (ianxm/fill-problem (caddr item)))
- (if (member problem problem-set) ; dedup problems
+ (let* ((fill-ret (ianxm/fill-problem (caddr item)))
+ (problem (alist-get :problem fill-ret))
+ (alg-vars (alist-get :alg-vars fill-ret))
+ (calc-string (if (not alg-vars)
+ problem
+ (format "solve(%s,[%s])" problem
(string-join alg-vars ","))))
+ (solution
+ (replace-regexp-in-string (rx (or "[" ".]" "]"))
+ ""
+ (calc-eval calc-string))))
+ (cond
+ ((member problem problem-set) ; dedup problems
(setq dup-count (1+ dup-count))
- (push problem problem-set)
- (push (list problem (calc-eval problem) (cadr item)) problems)
- (setq added (1+ added)))
- (when (> dup-count 100)
- (error "Giving up, too many dups"))))))
+ (when (> dup-count 100)
+ ;; high number of dups indicates a narrow problem space
relative to problem count
+ (error "Giving up, too many dups")))
+ (t
+ (push problem problem-set)
+ (push (list problem ; problem
+ solution ; solution
+ (cadr item) ; order
+ (not (null alg-vars))) ; true if algebraic
variables exist
+ problems)
+ (setq added (1+ added)))))))))
;; shuffle
(dotimes (ii (- (length problems) 1))
@@ -395,9 +433,7 @@ other examples
(sort problems (lambda (a b) (< (caddr a) (caddr b))))
;; return problems and answers, drop header
- (mapcar
- (lambda (x) (seq-take x 2))
- problems)))
+ problems))
#+end_src
** Update problem-set block
@@ -517,8 +553,11 @@ same file.
(search-forward "<<problems>>")
(replace-match "")
(dolist (row problems)
- (insert (format"\\CircledItem %s =
\\rule[-.2\\baselineskip]{2cm}{0.4pt}\n\n"
- (car row))))
+ (if (cadddr row)
+ (insert (format"\\CircledItem %s\\vspace{4cm}\n"
+ (car row)))
+ (insert (format"\\CircledItem %s =
\\rule[-.2\\baselineskip]{2cm}{0.4pt}\n"
+ (car row)))))
(goto-char (point-min))
(search-forward "<<answers>>")
(replace-match "")
