Next: Code walkthrough, Previous: Math Worksheet Generator, Up: Math Worksheet Generator [Contents]
This is a math worksheet generator. The worksheets are randomly generated based on templates that define what kinds of problems to include along with the order and relative frequency that each type of problem should appear on the worksheet.
Next: Examples, Previous: Description, Up: Overview [Contents]
This could be useful for anyone that wants to provide math practice to someone else. It could be useful for a teacher, tutor, homeschooling parent, or any parent.
Next: Requirements, Previous: Audience, Up: Overview [Contents]
Here are some example worksheets generated by this tool, along with the templates from which they were built. Template syntax is described in greater in the "Problem Templates" section below.
w | o | template --+---+------------------------------------ 3 | 2 | [1..10] + [8..15] 2 | 2 | [a=3..10] - [0..$a] 1 | 3 | [1..10] + [1..7] + [1..5] 1 | 4 | [a=1..10] + [0..10] - [0..$a] 1 | 5 | [a=1..10] + [b=0..10] - [0..($a+$b)]
w | o | template --+---+------------------------------------ 3 | 1 | x / ([2..4] + [a=0..5]) = [$a..10] 2 | 2 | [$a*[2..10]] / x = [a=1,2,4] 2 | 3 | x/[-5..-1,1..5] + [1..10] = [-10..10] 1 | 3 | x = x/[a=2..6] + [round([1..20]/$a)] 1 | 3 | x^2 = sqrt([16 - $a] + [a=1..5])
Groff is required to generate mathsheets. If groff is not installed on
the system PDF generation will fail and there will be a command not
found message in the mini-buffer.
Previous: Requirements, Up: Overview [Contents]
Next: Defining a Worksheet, Up: Usage [Contents]
Open mathsheet using M-x mathsheet-open
Next: Customization, Previous: Starting Mathsheet, Up: Usage [Contents]
Worksheets are defined using a form. Forms-mode provides a way to add, save, load records based on a form. See forms-mode doc for details. The mathsheet form specifies the following fields:
nameThe base name of the file to write. Spaces will be converted
to dashes and a pdf extension will be added.
countthe total number of problems to put on the worksheet
columnsthe number of columns the worksheet should have.
instructiona brief, one sentence instruction that will be included at the top of the sheet to guide the student.
problemsA multi-line, pipe (|) delimited string describing the
problems to include on the worksheet.
Consider this example value for problems:
3 | 1 | [1..10] + [1..20] 1 | 2 | [a=1..10] - [0..$a]
Each problems line contains the following fields:
weight (w)The relative number of this type of problem to include on the worksheet. A weight of zero means the template will not be used. In the example above, three fourths of the worksheet problems will be addition.
order (o)Problems are ordered on the sheet in ascending order. Two problems with the same order will be intermingled. In the example above, all of the addition problems will come before the subtraction problems.
templatethis is the template used to generate problems of this type.
Generate a worksheet by running C-c C-r from the mathsheet form.
Next: Problem Templates, Previous: Defining a Worksheet, Up: Usage [Contents]
Mathsheet allows for the following customizations:
mathsheet-data-fileThis is where mathsheet data is stored. It defaults to a file in your emacs user directory. You can probably leave it there.
mathsheet-output-directoryThis is where worksheets should be written. It defaults to your home directory. You’ll probably want to move it somewhere else.
Previous: Customization, Up: Usage [Contents]
The worksheet is made of a set of math problems. Each problem is defined by a template that lays out an equation or expression and shows where variables or numbers should be.
Expression templates define an expression which must be evaluated. For example, consider this template:
[0..15] + [1..10]
The parts within the brackets are fields. When a template is made into
a problem and added to a worksheet, each field is replaced by a number
based on a set of rules. The supported rules are described in more
detail below, but [0..15] means pick a random number between 0 and 15,
inclusive, so the above template could result in problems like these:
1 + 2 15 + 10 5 + 1
In addition to expressions where the answer is a number, templates can be equations where the solution is found by solving for the variable. For example, consider this template:
[1..5] x + 3 = [-10..10]
This can produce the following problems:
3 x + 6 = -1 4 x + 2 = 2 1 x + 8 = -3
These are the different ways fields can be defined:
[-2..8]choose a random number from -2 to 8, inclusive
[1,3,5]choose randomly from 1, 3 or 5
[-3..-1,1..3]choose a random number from -3 to -1 or 1 to 3
[10/(2-1)]evaluate the expression
[round(sin(0.3))]expressions can use math functions
[a=...]assign the variable a to the number chosen for this field
[-2..$a]any number from -2 to the value another field assigned
to a
[0..[$a/2]]any number from 0 to half the value assigned to a.
The ability to keep track of the random number chosen in one field and use it to influence another allows the template to be written to avoid answers that are negative or don’t divide evenly.
These math functions are allowed: sqrt, sin, cos, tan, asin, acos,
atan, floor, ceil, round. Find more details about each of these
functions in the Emacs Calc manual.
Here are a few more examples:
Division problem that divides evenly
[$a*[1..5]] / [a=1..10]
Addition and subtraction, but ensure a positive result
[a=1..10] + [b=0..10] - [0..($a+$b)]
Division but ensure we don’t divide by zero
[-10..10] / [-5..-1,1..5]
Next: Literate Programming, Previous: Overview, Up: Math Worksheet Generator [Contents]
Next: UI Form, Up: Code walkthrough [Contents]
Next: Full header, Up: Front matter [Contents]
This lays out some standard header content that is repeated for each file.
Next: Dependencies, Previous: GNU header components, Up: Front matter [Contents]
This is the standard Emacs package header.
peg is used to parse the problem templates. calc is used to solve the
problems as well as converting them to mathematical notation in EQN
format.
;;; mathsheet.el --- Generate dynamic math worksheets -*- lexical-binding:t -*- ;; Copyright (C) 2025 Free Software Foundation, Inc. ;; Author: Ian Martins <ianxm@jhu.edu> ;; Keywords: tools, education, math ;; Homepage: https://gitlab.com/ianxm/mathsheet ;; Version: 1.1 ;; Package-Requires: ((peg "1.0") ;; (emacs "28.1")) ;; This file is not part of GNU Emacs. ;; GNU Emacs is free software: you can redistribute it and/or modify ;; it under the terms of the GNU General Public License as published by ;; the Free Software Foundation, either version 3 of the License, or ;; (at your option) any later version. ;; GNU Emacs is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY; without even the implied warranty of ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ;; GNU General Public License for more details. ;; You should have received a copy of the GNU General Public License ;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>. ;;; Commentary: ;; This package generates dynamic math worksheets. The types and ;; distribution of problems is highly customizable. Problem sets are ;; defined using templates and exported to PDF for printing. ;;; Code:
Next: Variables, Previous: Full header, Up: Front matter [Contents]
This package needs forms-mode, peg, calc. Forms mode and Calc are included in Emacs but we need to make sure they have been loaded.
(require 'forms) (require 'peg) (require 'calc) (declare-function math-read-expr "calc-ext") (declare-function calc-set-language "calc-lang")
Previous: Dependencies, Up: Front matter [Contents]
Here we define a customize group, some customize variables that provide for configuring where form records are stored and where output is written, and some non-customize variables used internally.
(defgroup mathsheet nil "Options for customizing Mathsheet." :prefix "mathsheet-" :group 'applications :tag "mathsheet") (defcustom mathsheet-data-file (expand-file-name "mathsheet.dat" user-emacs-directory) "Where to store saved mathsheet configurations. The default is to save them to a file in the private emacs configuration directory." :type 'file :group 'mathsheet) (defcustom mathsheet-output-directory (expand-file-name "~") "Where to write generated worksheets. The default is to write the to the home directory." :type 'directory :group 'mathsheet)
We need mathsheet--var-list to keep track of the variables between
fields since we need to access the list from multiple top level
functions.
mathsheet--worksheet-template is the Groff template for the
worksheet, which is defined in an example block below. This
assigns the constant directly to that named block.
mathsheet--num-pat is defined here since it is referenced in a macro
that is used in multiple places. If it was in the macro it would be
redefined by expansion, and since the macro is called from different
scopes we’d have to define it in multiple places to define it in the
scope where the macro is called.
(defvar mathsheet--var-list '() "List of variables used within a problem.") (defconst mathsheet--worksheet-template page "Groff template for the worksheet.") (defconst mathsheet--num-pat (rx string-start (+ num) string-end) "Pattern for integers.") (defvar mathsheet--field-sheet-name nil "The form record name field.") (defvar mathsheet--field-count nil "The form record count field.") (defvar mathsheet--field-cols nil "The form record cols field.") (defvar mathsheet--field-instruction nil "The form record instruction field.") (defvar mathsheet--field-problems nil "The form record problems field.")
Next: Extract configuration from form, Previous: Front matter, Up: Code walkthrough [Contents]
Next: New record defaults, Up: UI Form [Contents]
See details here.
(setq forms-file mathsheet-data-file)
(setq forms-number-of-fields
(forms-enumerate
'(mathsheet--field-sheet-name
mathsheet--field-count
mathsheet--field-cols
mathsheet--field-instruction
mathsheet--field-problems)))
(setq forms-field-sep "||")
Next: Clean up template rows, Previous: Form configuration, Up: UI Form [Contents]
When new records are created using the form, initialize them with default values.
(defun mathsheet--new-record-filter (record) "Set defaults in new RECORD." (aset record 2 "20") ; default (aset record 3 "2") ; default (aset record 4 "Find the answer.") ; default (aset record 5 "1 | 1 | ") ; lay out structure record) (setq forms-new-record-filter 'mathsheet--new-record-filter)
Next: Layout the actual form, Previous: New record defaults, Up: UI Form [Contents]
When the form is saved, clean up the template field by lining up the columns.
(defun mathsheet--format-templates (record)
"Format the template rows in RECORD to line up with the header."
(let ((rows (string-split (aref record 5) "\n"))
(pat (rx (* space) (group (+ alnum)) (* space) "|"
(* space) (group (+ alnum)) (* space) "|"
(* space) (group (+ nonl)))))
(setq rows (mapconcat
(lambda (row)
(string-match pat row)
(format "%s | %s | %s"
(match-string 1 row)
(match-string 2 row)
(match-string 3 row)))
rows
"\n"))
(aset record 5 rows))
record)
(setq forms-modified-record-filter 'mathsheet--format-templates)
Previous: Clean up template rows, Up: UI Form [Contents]
This defines the form itself and the locations of the fields.
(setq forms-format-list
(list
"====== Math Sheet Generator ======"
"\nSee https://gitlab.com/ianxm/mathsheet for details."
"\n\nThe base-name of the mathsheet file to write, not including extension."
"\nName: " mathsheet--field-sheet-name
"\n\nThe total number of problems to put on the sheet."
"\nCount: " mathsheet--field-count
"\n\nThe number of columns the sheet should have."
"\nColumns: " mathsheet--field-cols
"\n\nThe instruction to give at the top of the sheet."
"\nInstruction: " mathsheet--field-instruction
"\n\nThe problem templates from which to generate problems for the sheet."
"\nOne per line, formatted as \"(w)eight | (o)rder | template\".\n\n"
"w | o | template\n"
"--+---+------------------------------------\n"
mathsheet--field-problems
"\n"))
Next: Problem generation, Previous: UI Form, Up: Code walkthrough [Contents]
Next: Extract and parse, Up: Extract configuration from form [Contents]
This adds validation checks as needed for each field.
(defmacro mathsheet--validate (field-name field-str checks)
"Add specified checks to validate field input.
FIELD-NAME is the name of the field. FIELD-STR is the string
value in the record. CHECKS is a list of symbols specifying
which validation checks to perform."
(let (ret)
(dolist (check checks)
(pcase check
('not-null-p
(push
`(when (null ,field-str)
(error (format "`%s' cannot be empty" ,field-name)))
ret))
('is-num-p
(when (not (null field-str))
(push
`(when (not (string-match-p mathsheet--num-pat ,field-str))
(error (format "`%s' must be a number" ,field-name)))
ret)))
(`(in-range-p ,min ,max)
(push
`(when
(or
(< (string-to-number ,field-str) ,min)
(> (string-to-number ,field-str) ,max))
(error (format "`%s' must be between %s and %s, inclusive"
,field-name ,min ,max)))
ret))
(_
(push
`(error (format "Unknown check: %s" ,check))
ret))
))
(append '(progn) ret)))
Next: Initiate sheet generation, Previous: Validate form fields, Up: Extract configuration from form [Contents]
emacs-forms treats everything like strings so we have to validate and
convert the numbers. Also the problem field contains multi-line delimited
data so we have to parse it.
This is also where limits are set. The max problems on a sheet
is 50. The max columns allowed is 4.
(defun mathsheet--parse (record)
"Parse all of the fields of the current RECORD into an alist."
(let (count cols problems)
(pcase record
(`(,name ,count-str ,cols-str ,instruction ,problems-str)
;; validate the form fields
(mathsheet--validate "name" name (not-null-p))
(mathsheet--validate "count" count-str (not-null-p is-num-p (in-range-p 1 50)))
(mathsheet--validate "cols" cols-str (not-null-p is-num-p (in-range-p 1 4)))
(mathsheet--validate "problems" problems-str (not-null-p))
;; convert the numbers and parse the problems field
(setq count (string-to-number count-str)
cols (string-to-number cols-str)
problems (mapcar ; parse rows
#'mathsheet--parse-problem-row
(seq-filter ; remove possible trailing empty line
(lambda (x) (not (string-empty-p x)))
(string-split ; split lines
problems-str
"\n"))))
`((:name . ,name)
(:count . ,count)
(:cols . ,cols)
(:instr . ,instruction)
(:probs . ,problems)))
(_ (error "Invalid form data")))))
This function is used to parse each problem row.
(defun mathsheet--parse-problem-row (row)
"Parse one ROW of the problem field into a list."
(let* ((fields (mapcar ; trim whitespace
#'string-trim
(split-string ; split fields
row
"|")))
(weight-str (nth 0 fields))
(order-str (nth 1 fields))
(template (nth 2 fields))
weight order)
(mathsheet--validate "weight" weight-str (not-null-p is-num-p))
(mathsheet--validate "order" order-str (not-null-p is-num-p))
(mathsheet--validate "template" template (not-null-p))
(setq weight (string-to-number weight-str)
order (string-to-number order-str))
(list weight order template)))
Previous: Extract and parse, Up: Extract configuration from form [Contents]
(defun mathsheet-generate-sheet ()
"Generate sheet for current form data."
(interactive)
(when (not (string= major-mode "forms-mode"))
(error "Mathsheet must be open to generate a sheet"))
(let ((config (mathsheet--parse forms--the-record-list)))
(let ((problems (mathsheet--generate-problems
(alist-get :probs config)
(alist-get :count config)))
;; absolute path without extension
(fname (concat
(file-name-as-directory mathsheet-output-directory)
(string-replace " " "-" (alist-get :name config)))))
(mathsheet--write-worksheet
fname
(alist-get :instr config)
problems
(alist-get :cols config))
(message "Wrote %s problems to %s.pdf"
(alist-get :count config)
fname))))
Next: Generate PDF, Previous: Extract configuration from form, Up: Code walkthrough [Contents]
Next: Reduce field, Up: Problem generation [Contents]
This scans a problem to find the locations of fields and dependencies between them. It must be called with point at the start of the problem. It moves the point to the end of the problem unless there’s an error, in which case it stops at the place where the error occurred. This returns a list of fields, with each field formatted as:
'(asn-var (deps) (start-marker . end-marker) nil)
asn-var is a variable name if this field is being assigned to a
variable, 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.
deps is a list of are dependencies if this field has any, otherwise
nil. Dependencies could be variables or placeholders.
start-marker and end-marker are markers in the (temp) buffer. The
end-marker is configured to insert text before the marker.
The last entry is nil for "not visited." It is used by dfs-visit.
for example:
[$a + 2 + [a=1..5]] => '((nil (a) m1 m19 nil) (a nil m11 m18 nil))
'((:fields (_0 (a a) (marker . marker) nil) (a nil (marker . marker) nil)) (:alg-vars))
This uses peg to parse the problem. Instead of using the peg return value we build the list of fields outside of the peg stack.
open-fields is a stack of fields with the current field on top. We
push a new field to the stack when we start a new field.
closed-fields is a list of fields that have been completed. We push a
new field to the list when we close the current field, taking it off
of open-fields.
(defun mathsheet--scan-problem ()
"Scan a problem.
This parses the problem and produces a list containing info about
its fields. For each field it returns a list containing:
1. a symbol for the assigned variable or a unique placeholder
2. a list of variables this field depends on
3. a cons containing start and end markers for the field in the current buffer
4. nil which is used by `dfs-visit' later"
(let ((field-index 0)
open-fields ; stack
closed-fields ; list
alg-vars)
(with-peg-rules
((stuff (* (or asn-var math-func alg-var digit symbol field space)))
(field open (opt assignment) stuff close)
(space (* [space]))
(open (region "[")
`(l _ -- (progn
(push (list
(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))
".")))
(assignment (substring letter) "="
`(v -- (progn
(setcar
(car open-fields)
(intern v))
".")))
(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 _ -- (progn
(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)
".")))
(math-func (or "sqrt" "sin" "cos" "tan" "asin" "acos" "atan" "floor" "ceil" "round"))
(letter [a-z])
(digit [0-9])
(symbol (or "." "," "+" "-" "*" "/" "^" "(" ")" "=")))
(peg-run (peg stuff)
(lambda (x) (message "Failed %s" x))
(lambda (x)
(funcall x)
`((:fields . ,closed-fields)
(:alg-vars . ,alg-vars)))))))
Next: Replace field, Previous: Scan problem, Up: Problem generation [Contents]
This must be called with point at the start of a field. This moves the
point to the end of the field. This returns the value to which the
field reduces. peg-run returns its stack and the value is the last
thing remaining on the stack when peg completes so peg returns a list
with one value. We take the value out of the list and return it.
This uses the peg package to parse the field. This time there shouldn’t be any fields embedded within the field. We should have already evaluated and replaced them.
We use .. instead of - for range because if we used - then this would
be ambiguous:
[1-5]
The list of supported operators and math functions are listed both
here and in mathsheet--scan-problem, so changes must be made in
both places to keep them synced.
(defun mathsheet--reduce-field ()
"Reduce the field to a number.
Parse the field again, replacing spans with random numbers and
evaluating arithmetic operations. The field shouldn't have any
internal fields so this should result in a single number. Return
that number."
(with-peg-rules
((field "[" space (or math-func expression sequence assignment value) space "]")
(expression (list value space operation space value (* space operation space value))
`(vals -- (string-to-number
(calc-eval
(list
(mapconcat
(lambda (x) (if (numberp x) (number-to-string x) x))
vals
" "))
calc-prefer-frac nil))))
(operation (substring (or "+" "-" "*" "/")))
(assignment var-lhs space "=" space (or range sequence)
`(v r -- (progn
(push (cons (intern v) r) mathsheet--var-list)
r)))
(sequence (list (or range value) (* "," space (or range value)))
`(vals -- (seq-random-elt vals)))
(range value ".." value
`(min max -- (if (>= min max)
(error "Range bounds must be increasing")
(+ (random (- max min)) min))))
(value (or (substring (opt "-") (+ digit)) var-rhs parenthetical)
`(v -- (if (stringp v) (string-to-number v) v)))
(parenthetical "(" (or expression value) ")")
(var-lhs (substring letter)) ; var for assignment
(var-rhs "$" (substring letter) ; var for use
`(v -- (let ((val (alist-get (intern v) mathsheet--var-list)))
(or val (error "Var %s not set" v)))))
(math-func (substring (or "sqrt" "sin" "cos" "tan" "asin" "acos" "atan" "floor" "ceil" "round"))
parenthetical
`(f v -- (string-to-number (calc-eval (format "%s(%s)" f v)))))
(space (* [space]))
(letter [a-z])
(digit [0-9]))
(peg-run (peg field)
(lambda (x) (message "Failed %s" x))
(lambda (x) (car (funcall x))))))
Next: DFS visit, Previous: Reduce field, Up: Problem generation [Contents]
Replace a field with the value returned from reducing it. This uses
mathsheet--reduce-field to determine the value to use in place of
the field.
(defun mathsheet--replace-field (node)
"Replace a field in NODE with the number to which it reduces.
Update the current buffer by replacing the field at point in the
current buffer with the number it reduces to. NODE contains the
info for the current field."
(let ((start (caaddr node))
(end (1+ (cdaddr node)))
val)
(goto-char start)
(when (looking-at "\\[")
(setq val (mathsheet--reduce-field))
(goto-char start)
(delete-char (- end start) t)
(insert (number-to-string val)))))
Next: Fill fields in problem, Previous: Replace field, Up: Problem generation [Contents]
This uses a depth first search to ensure that we visit (reduce and replace) the fields in dependency order. We check dependencies then visit the node. We use the last field in the field structure to keep track of which fields have been visited.
(defun mathsheet--dfs-visit (node fields)
"Visit NODE as part of a DFS of the problem.
Traverse the fields of a problem using depth first search to
ensure that field replacement happens in dependency order.
FIELDS is a list of all fields in the problem."
(pcase (cadddr node)
(1 (error "Cycle detected")) ; cycle
(2) ; skip
(_ ; process
(setcar (cdddr node) 1) ; started
(dolist (dep (cadr node))
(mathsheet--dfs-visit
(assq dep fields)
fields))
(mathsheet--replace-field node) ; visit
(setcar (cdddr node) 2)))) ; mark done
Next: Generate problem set from templates, Previous: DFS visit, Up: Problem generation [Contents]
processes all fields in a problem.
(full-problem (buffer-substring (point-at-bol) (point-at-eol)))
(defun mathsheet--fill-problem (full-problem)
"Replace all fields in FULL-PROBLEM.
Goes through all fields in the given problem in dependency order
and replaces fields with numbers. When this completes the problem
will be ready to solve."
(with-temp-buffer
;; stage problem in temp buffer
(insert full-problem)
(goto-char (point-min))
;; find fields, assignment variables, algebraic variables, dependencies
(let* ((scan-ret (mathsheet--scan-problem))
(fields (alist-get :fields scan-ret))
(alg-vars (alist-get :alg-vars scan-ret)))
;; visit fields ordered according to dependencies
(dolist (node fields)
(mathsheet--dfs-visit node fields))
(setq mathsheet--var-list '())
;; return filled problem
`((:problem . ,(buffer-string))
(:alg-vars . ,alg-vars)))))
Previous: Fill fields in problem, Up: Problem generation [Contents]
This reads in the templates, figures out how many of each based on weights and the number of problems needed, generates the problem set, figures out the answers, then reorders.
The reordering is done because if multiple templates are assigned the
same order, they should be intermingled, but we add all problems for
each template sequentially. In order to mix them up we shuffle the
whole set and then reorder by order.
(defun mathsheet--generate-problems (templates count)
"Use TEMPLATES to generate COUNT problems.
Generate problems and answers based on what is defined in the
given template table. The template table defines problem
templates as well as relative weights and how they should be
ordered."
(let (total-weight problems)
;; sort by weight (low to high)
(setq templates (sort templates #'car-less-than-car)
;; calc total weight
total-weight (seq-reduce (lambda (total item) (+ total (car item)))
templates
0.0))
;; calculate number for each row
(dotimes (ii (length templates))
(let* ((item (nth ii templates))
(weight (car item))
(needed (cond ; number of problems to add for this template
((= weight 0)
0)
((= ii (1- (length templates)))
(- count (length problems)))
(t
(max (round (* (/ weight total-weight) count) ) 1))))
(added 0)
(dup-count 0)
problem-set)
(while (< added needed) ; add until "needed" are kept
(let* ((fill-ret (mathsheet--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 (seq-uniq alg-vars) ","))))
(solution
(replace-regexp-in-string (rx (or "[" ".]" "]"))
""
(calc-eval `(,calc-string
calc-prefer-frac t
calc-frac-format ("/" nil))))))
(cond
((member problem problem-set) ; dedup problems
(setq dup-count (1+ dup-count))
(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))
(let ((jj (+ (random (- (length problems) ii)) ii)))
(cl-psetf (elt problems ii) (elt problems jj)
(elt problems jj) (elt problems ii))))
;; sort by order
(setq problems (sort problems (lambda (a b) (< (caddr a) (caddr b)))))
;; return problems and answers, drop header
problems))
Next: Convenience functions, Previous: Problem generation, Up: Code walkthrough [Contents]
Next: Convert calc to EQN, Up: Generate PDF [Contents]
This lays out the page in Groff, with placeholders for where details must be filled in.
This template doesn’t use noweb but it uses noweb syntax (<<label>>)
to mark where mathsheet will insert content. It’s not possible
actually use noweb here since the problems and answers are coming from
elisp and generated at runtime. Instead this template must be tangled
to mathsheet.el as a template so the elisp functions can use it.
.VM 0 -0.5i \" reduce bottom margin .PH "'Name: \l'20\_'''Date:\l'10\_''" \" header <<instruction>> .SP 1 .fam C \" set font <<layout>> .MC \n[clen]p 10p \" start columns mode <<problems>> .1C 1 \" end of columns mode .BS \" floating bottom box \l'\n(.lu' \" horizontal rule .S 8 10 \" reduce font and vertical space .ss 6 \" reduce horizontal space .gcolor grey \" answers color <<answers>> .BE
Next: Write PDF, Previous: Lay out page, Up: Generate PDF [Contents]
This converts a calc expression to EQN format for use with Groff. The problems and answers are generated in Emacs Calc normal format. Emacs Calc already knows how to convert between formats, so we let it do it.
(defun mathsheet--convert-to-eqn (expr)
"Format the given calc expression EXPR for groff.
EXPR should be in normal calc format. The result is the same
expression (not simplified) but in eqn format for groff."
(let ((current-language calc-language))
(calc-set-language 'eqn)
(let* ((calc-expr (math-read-expr expr))
(eqn-expr (math-format-stack-value (list calc-expr 1 nil)))
(eqn-expr-cleaned (replace-regexp-in-string (rx "1:" (* space)) "" eqn-expr)))
(calc-set-language current-language)
eqn-expr-cleaned)))
(defun mathsheet--convert-to-eqn (expr)
"Format the given calc expression EXPR for groff.
EXPR should be in normal calc format. The result is the same
expression (not simplified) but in eqn format for groff."
(let ((current-language calc-language))
(calc-set-language 'eqn)
(let* ((calc-expr (math-read-expr expr))
(eqn-expr (math-format-stack-value (list calc-expr 1 nil)))
(eqn-expr-cleaned (replace-regexp-in-string (rx "1:" (* space)) "" eqn-expr)))
(calc-set-language current-language)
eqn-expr-cleaned)))
(mathsheet--convert-to-eqn "x/(1+2)=3")
Previous: Convert calc to EQN, Up: Generate PDF [Contents]
This inserts instruction line and generated problems into the page
template, writes it to a local file, then runs groff to build a PDF
named [template-name].pdf. Each execution with the same template name
will overwrite that file.
Sub-sections are identified by noweb syntax (<<section>>). The details
of how each section is filled in is described below.
(defun mathsheet--write-worksheet (fname instruction problems prob-cols)
"Write a worksheet to FNAME with INSTRUCTION and PROBLEMS.
Write a file named FNAME. Include the INSTRUCTION line at the
top. The problems will be arranged in PROB-COLS columns. The
answers will be in 5 columns."
(with-temp-buffer
(insert mathsheet--worksheet-template)
(let ((probs-per-col (ceiling (/ (float (length problems)) prob-cols))))
<<fill-instruction>>
<<fill-layout>>
<<fill-problems>>
<<fill-answers>>)
;; write the groff file for debugging
;; (write-region (point-min) (point-max) (concat fname ".mm"))
;; run groff to generate the pdf
(let* ((default-directory mathsheet-output-directory)
(ret (shell-command-on-region
(point-min) (point-max)
(format "groff -mm -e -Tpdf - > %s" (concat fname ".pdf")))))
(unless (eq ret 0)
(error "PDF generation failed")))))
This fills in the instruction line. It’s just a single string taken from the config and added to the top of the sheet.
fill-instruction:
(goto-char (point-min))
(search-forward "<<instruction>>")
(replace-match
(if (null instruction)
""
(concat ".B \"" instruction "\"")))
This figures out the column with and spacing between rows and sets them in registers.
Column width is computed based on line length. Line length (\n[.l]) is
reported in basic units, which are 1/72000 of an inch. Line length is
6.5 inches for letter paper.
To find the space between rows we take page height, subtract header and footer, a little more for the instruction, some more for each of the problems, then divide the remainder by the number of problems per column plus one.
Groff has no rules for order of operations but calculates left to right and numbers are integers, so we need to include parenthesis to ensure order of operations and use large units (like points) to reduce loss of precision due to integer division.
fill-layout:
(goto-char (point-min)) (search-forward "<<layout>>") (replace-match "") (insert (format ".nr ncols %d\n" prob-cols)) (insert ".nr clen ((\\n[.l]/1000)-((\\n[ncols]-1)*10)/\\n[ncols])\n") (insert (format ".nr cl %d\n" probs-per-col)) (insert ".nr vs (\\n[.p]/1000-(2*72)-20-(12*\\n[cl]))/(\\n[cl]+1)")
Here we fill the problems into the sheet. First we group them into columns.
fill-problems:
(goto-char (point-min))
(search-forward "<<problems>>")
(replace-match "")
(insert ".AL\n")
(let ((colsize probs-per-col))
(seq-do-indexed
(lambda (group index)
(unless (= index 0)
(insert ".NCOL\n"))
(dolist (row group)
(message "convert to eqn %s -> %s" (car row) (mathsheet--convert-to-eqn (car row)))
(insert (format (if (nth 3 row)
".LI\n.EQ\n%s\n.EN\n.SP \\n[vs]p\n"
".LI\n.EQ\n%s =\n.EN\n\\l'5\\_'\n.SP \\n[vs]p\n")
(mathsheet--convert-to-eqn (car row))))))
(seq-partition problems colsize)))
(insert ".LE")
Here we fill in the answers. They are written as a comma delimited list at the bottom of the sheet.
fill-answers:
(goto-char (point-min))
(search-forward "<<answers>>")
(replace-match "")
(let ((index 0))
(dolist (row problems)
(setq index (1+ index))
(insert
(format ".EQ\n%d. %s%s\n.EN%s"
index
(mathsheet--convert-to-eqn (cadr row))
(if (< index (length problems)) "\",\"~" "")
(if (< index (length problems)) "\n" "")))))
Next: Footer, Previous: Generate PDF, Up: Code walkthrough [Contents]
Next: Open mathsheet, Up: Convenience functions [Contents]
This adds the keybinding to run the mathsheet generator from the mathsheet form.
(when (null forms-mode-map)
(add-to-list
'forms-mode-hook
(lambda ()
(when (string= "mathsheet.el" (buffer-name))
(define-key forms-mode-map "\C-r" #'mathsheet-generate-sheet)))))
Previous: Add key binding to form, Up: Convenience functions [Contents]
This is a helper to open mathsheet with the configured data file.
;;;###autoload (defun mathsheet-open () "Open mathsheet." (interactive) (forms-find-file (locate-file "mathsheet.el" load-path)))
Previous: Code walkthrough, Up: Math Worksheet Generator [Contents]
This is written as a literate program using Emacs org-mode. The org file contains the code and documentation for the math worksheet generation script. When this file is saved, the source code is generated using ‘org-babel-tangle’ and the readme is generated using ‘org-md-export-to-file’.
The first line of the org file configures emacs to run those commands whenever this file is saved, which generates the scripts and readme.