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1: \hrule
2: \vskip 0.2in
3: \section{\capa{} Functions}
4:
5: \vskip 0.2in
6: \hrule
7: \vskip 0.2in
8: %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
9: All of the examples and descriptions used below are for
10: student submissions of answers through a Web or telnet session.
11: There are some changes and additions to the {\sl set$x$.qz} code when using
12: \capa\ for machine scored exams. Please see the next section for those
13: examples.
14:
15: \subsection{\bf Question source text}
16: \capa\ assumes that any characters in the
17: {\sl set$x$.qz} without a special command at the beginning of a line will be
18: displayed as text for the student. The following are those special commands: \\
19: {\tt /LET, \ /BEG, \ /DIS, \ /IMP, \ //, \ /HIN, \ /EXP, \ /MAP, \ /RMAP, \
20: /IF, \ /ELSE, \ /ENDIF, \ /WHILE, \ /ENDWHILE, \ /ANS, \ /AND, \ /OR, \ /SUBJECTIVE, \ /VERB, \ /ENDVERB, \ /START,} and \ {\tt /END}.\\
21: Text (excluding white space) preceding the forward slash will disable the all
22: of the commands except {\tt //} and {\tt /DIS}. Variables must be defined
23: before use.
24:
25: \subsection{\bf Variable Definitions and Expressions ({\tt /LET}\index{/LET} and
26: {\tt /BEG}\index{/BEG} )}
27:
28: \begin{itemize}
29: \item Definitions are specified in the form: \\
30: \fbox{\tt /LET VariableName=expression}
31: \item Variable definitions and expressions begin on a single line with a {\tt /LET} command that is terminated by a carriage return.
32: Long entries will be line-wrapped by the editor and may appear to extend past one
33: line on the display. The line continuation symbol (\verb"\" followed by a carriage return)
34: can be used to break a long line into several lines and still be considered as
35: a single long line.
36: \item {\tt /BEG} is simply an alias for {\tt /LET}, and is used to indicate the beginning of each problem in the
37: following manner: \\
38: \fbox{{\tt /BEG prob\_val=3}}. \\
39: This sets the variable prob\_val which can
40: then be used to define the weight of the problem in the {\tt /ANS} specification the signals the end of the
41: problem.
42:
43: \item The \capa\ system does reserve variable names for certain
44: functions used in the system. They are listed in the {\bf Intrinsic Functions
45: Table}, and must not be used as variable names.
46: \normalsize
47:
48: \item {\bf List of Available Expressions}:
49: \begin{tabbing}
50: 1234567890123456789012345\= 12345678901234567890 \= \kill
51: {\it Integer} \> $\diamond $ An integer. \\
52: {\it Real number} \> $\diamond $ A real number. It could be of the form
53: \\{\it $$ } \> $$
54: 123.4, 1.234E+2, 1.234E+2, 1.234E+02, 1.234e+02. \\
55: {\it ``string''} \> $\diamond $ A string. It is specified in the
56: form \verb+"A block of text"+. \\
57: % \> Quotes may be imbedded in string by prefixing them
58: % with a `\verb"\\"'. \\
59: {\it Variable Name} \> $\diamond $ A variable previously defined. \\
60: {\it ( expression )} \> $\diamond $ Precedence, evaluate {\it expression}
61: first. \\
62: {\it - expression } \> $\diamond $ Negative of {\it expression}. \\
63: {\it function([expression, $\cdots$]) } \> $\diamond $ Call a function with
64: arguments. (see below) \\
65:
66: {\it expression $*$ expression } \> $\diamond $ Multiply expressions. \\
67: {\it expression $/$ expression } \> $\diamond $ Divide expresssions. \\
68: {\it expression $+$ expression } \> $\diamond $ Add expressions, concatenate
69: strings \\
70: {\it expression $-$ expression } \> $\diamond $ Subtract expressions. \\
71: {\it expression $==$ expression } \> $\diamond $ Logical; expressions equal?
72: Returns 0 {\small if false}, 1
73: {\small if true}\\
74: {\it expression $!=$ expression } \> $\diamond $ Logical; expressions
75: different? Returns 0 or 1\\
76: {\it expression $>=$ expression } \> $\diamond $ Logical; greater than or
77: equal? Returns 0 or 1\\
78: {\it expression $<=$ expression } \> $\diamond $ Logical; less than or equal?
79: Returns 0 or 1\\
80: {\it expression $>$ expression } \> $\diamond $ Logical; greater than? Returns
81: 0 or 1\\
82: {\it expression $<$ expression } \> $\diamond $ Logical; smaller than? Returns
83: 0 or 1\\
84: \end{tabbing}
85:
86: \item There are three types of variables: integer, real and string. The type
87: is not explicitly specified but rather is assigned by context at the time the
88: variable is defined.
89:
90: \item {\bf Note:} If you define a variable with an equation consisting
91: of only integer numbers, then the resulting answer will be an integer.
92: For example, we have the following code: \\
93: \fbox{\tt /LET variable1=1/2} \\
94: \fbox{\tt /LET variable2=35/12} \\
95: Then {\em variable1} will be assigned the value of ``0'' and {\em variable2} will be assigned the value of ``2''.
96: On the other hand, \\
97: \fbox{\tt /LET variable1=1.0/2.0} \\
98: will now be assigned the value of 0.5 because at least one real number was used
99: in the equation.
100:
101: \item The variable names must begin with a letter but may contain letters,
102: numbers, and underline characters.
103:
104: \item Variable names (and function names) {\bf are case sensitive}, and
105: there is no limit on the length of a variable name.
106:
107: \item Variables must be defined before they are used in any other expression.
108: \normalsize
109: \item {\bf Note:} Quotation marks indicate the beginning and end of strings. You must use a
110: backslash to display the quotation marks within a string. For example: \\
111: \fbox{\tt /LET string= ``I'll be back.'' } \\
112: will produce
113: the ouput ``I'll be back.''
114:
115: \item An expression may be be broken down into
116: several lines using the line continuation character \verb"\" followed
117: \underline{immediately} by a carriage return. This can help improve the legibility
118: of the code. Do not use the line continuation character \verb"\"
119: within a command, variable, or function name.
120: \begin{capacode}
121: /LET a_long_line = "This is a very, very, very long statement. It is convenient to \
122: divide it into two lines."
123: \end{capacode}
124:
125: \item Once defined, the same variable can be used at any subsequent point in
126: the entire problem set or alternatively it could be be redefined.
127: \end{itemize}
128:
129:
130:
131: \subsection{\bf Display of Variables \index{/DIS}( {\tt /DIS} )}
132: \begin{itemize}
133:
134: \item The {\em value} of a previously defined variable can be displayed in the displayed text
135: by placing the variable name in the {\tt /DIS()} command,
136: e.g. {\tt/DIS(}{\em variable}{\tt )}.
137: \item The format of the display of a numerical value can be controlled
138: using a colon and a format specification. For example, {\tt /DIS(LENGTH:3f)} means
139: display the variable {\em LENGTH} as a floating point number with three places
140: \underline{after} the decimal ({\em x}.{\em xxx}). {\tt /DIS(LENGTH:2E)} will
141: display the variable in scientific notation with two decimal places
142: ({\em x}.{\em xx}{\tt E}{\em x}). The colon is a delimiter indicating that
143: a format specification follows.
144:
145: \item {\sf Quizzer} shows a default line length of 80 characters. In the x-windows version, a greater line length can be obtained by resizing the window,
146: accomplished by dragging the lower right corner.
147:
148: \item {\tt /DIS(\index{stdline}stdline)} will display a short line that is used to
149: seperate problems. When you build sets
150: with {\sf Quizzer} using import, you have the option of displaying a ``standard line'' or a
151: {\tt webonlyline} (a line that appears on the web only) after the problem. When printing two sided,
152: you have the option of diplaying a {\tt stdlineOvr} which displays the word "Over" so students realize
153: that the set is two sided. All of these variables are defined in the {\sl /demolibrary/Tools/StdMacros} file.
154:
155: \item {\bf Note:} A total of 37 lines are available for telnet display for each question on the VT100 terminal.
156: These lines are separated onto two pages
157: with 20 lines available on the first page and 17 available on the second. Three lines are repeated for reading
158: consistency. Hints and explanations are displayed on separate screens, each of which can have up to 20 lines. There are no line limitations on the printed
159: or Web versions of the text.
160:
161: \end{itemize}
162:
163: %\item
164: \subsection{\bf The Import Function ( \index{/IMP}{\tt /IMP} )}
165:
166: \begin{itemize}
167: \item The {\tt /IMP} function calls and uses the contents of the
168: specified file, however the file's content is not displayed in the {\sl set$x$.qz}
169: file.
170: \item The /IMP command requires a string input, either the string
171: filename or a variable which provides the string filename.
172: \begin{enumerate}
173: \item For example:
174: \\ \fbox{\tt /IMP "HWTop"} \\
175: will import the {\sl HWTop} file from the local directory.
176: \item For files in other
177: directories, use either relative or absolute paths as part of the filename,
178: such as: \\
179: \fbox{\tt /IMP "/demolibrary/Tools/StdMacros"} \\
180: or: \\
181: \fbox{\tt /IMP "../mystuff"}. \\
182: {\bf Note} that if relative paths are used, the {\tt /IMP} command will not work unless it
183: is the appropriate directory and can cause errors if the file is moved.
184: \item The file may be selected
185: dynamically
186: from a set, for example,
187: \begin{capacode}
188: /LET integer=random(1,10,1)
189: /LET filename="File"+integer
190: /IMP filename
191: \end{capacode}
192: which will import a randomly selected {\sl File$x$} from {\sl File1, File2, ...File10}.
193: \end{enumerate}
194: {\bf Note:} Adding an integer to a string results in a concatenated
195: newstring. This can be used to provide even greater variety among
196: sets for students, since different problems or graphics on a given topic can be selected.
197: This feature may be especially useful for producing standardized tests.
198: With a large
199: enough problem base, students can be given a randomly selected set to prepare
200: for the test.
201: \end{itemize}
202:
203:
204: \subsection{\bf Comment Lines (\index{//} {\tt //} )}
205:
206: \begin{itemize}
207: \item Comments are any character strings after a double forward
208: slash, ({\tt //}).
209: For example:
210: \begin{capacode}
211: //A line of comments
212: //You can also put comments after code.
213: /LET number=random(1,4,1) // chooses a random number
214: \end{capacode}
215: \item The comments are only displayed by the {\sf Quizzer} module and are for
216: the benefit of the persons writing and reviewing the actual problem code.
217: \item Instructors are strongly encouraged to include comment lines in order to
218: indicate authorship and to describe the structure of the problems for future use.
219: \end{itemize}
220:
221:
222: \subsection{\bf Hints (\index{/HIN} {\tt /HIN} )}
223: \begin{itemize}
224: \item Hints are optional. There can only be one hint per problem.
225: The hint becomes available after a wrong answer is entered by the student.
226: The answer function has reserved syntax for changing the number of entries before displaying the hint. The notation {\tt /ANS(variable:2f, hint=6)}
227: would require that a student enter 6 incorrect answers hefore being presented with the hint.
228:
229: \item The text for hints contain character strings (no expressions) and can
230: display string variables defined before the hint to match a problems content,
231: and is specified as:
232:
233:
234: \begin{capacode}
235: /LET index=random(1,4)
236: /LET pronoun=choose(index,"he","she","she","he")
237: /LET ppronoun=choose(index,"his","her","her","his")
238: /LET person=choose(index,"son","daughter","niece","nephew")
239: /HIN While her /DIS(person) was being picked up, /DIS(pronoun)
240: /HIN accidently let /DIS(ppronoun) balloon escape.
241: \end{capacode}
242:
243: \normalsize
244: \item This hint has two lines and two carriage returns. The contents of both
245: lines are displayed simultaneously; it is not two separate hints.
246:
247: \item Content of all lines typed with a {\tt /HIN} at the
248: beginning are displayed as the hint. The relative ordering of the hint lines is
249: preserved, and the hint is displayed as a separate page on the
250: VT100 screen and below the answer box on the web version.
251:
252: \item Only one {\tt /HIN} is needed if the text is very long and uses the continuation character.
253: \begin{capacode}
254: /HIN A hint is often welcomed by students. It sometimes requires \
255: a large amount of text and might require several lines.
256: \end{capacode}
257: Or (no carriage return at all, line wraps automatically):
258: \begin{capacode}
259: /HIN A hint is often welcomed by students. It sometimes requires a large amount of text and
260: might require several lines.
261: \end{capacode}
262: \item Hints can also be viewed after a problem set's due date.
263: \end{itemize}
264: \subsection{\bf Explanations (\index{/EXP} {\tt /EXP} )}
265: \begin{itemize}
266: \item Lines of explanations begin with the {\tt /EXP} characters and are
267: displayed on the login-terminal only when requested after a problem set is
268: closed. The VT100 display offers the option to view a separate page containing
269: the explanation. The web version automatically displays the coded explanation
270: when the student views a closed problem set.
271: \item The syntax for coding explanations is very similar to hints. It is
272: useful to include a detailed explanation for some problems.
273: Students often review old problem sets at exam time and may not exactly
274: remember how to solve a specific problem.
275: \item The following are explanation examples:
276: \begin{capacode}
277: /EXP An explanation is often welcomed by students.
278: /EXP It sometimes requires a large amount of text
279: /EXP and might require several lines.
280: \end{capacode}
281: Or:
282: \begin{capacode}
283: /EXP An explanation is often welcomed by students. It sometimes requires \
284: a large amount of text and might require several lines.
285: \end{capacode}
286: Or (no carriage return at all, line wrap automatic):
287: \begin{capacode}
288: /EXP An explanation is often welcomed by students. It sometimes requires a large amount of
289: text and might require several lines.
290: \end{capacode}
291:
292: \end{itemize}
293:
294: %\item
295: \subsection{\bf The Mapping Function ( \index{/MAP}{\tt /MAP} and \index{/RMAP}
296: {\tt /RMAP} )}
297: \begin{itemize}
298: \item The {\tt /MAP} function is used to map and permute the assigned values
299: from a set of variables onto another set of variables according to a given
300: seed value.
301: \item For example:
302:
303: \begin{capacode}
304: /LET seed=random(1,3000,1)
305: /MAP(seed;M1,M2,M3;m,n,o)
306: \end{capacode}
307:
308: Assigns to the variables $M1$, $M2$, and $M3$ the values of the variables $m$, $n$, and $o$.
309: The correspondence (i.e. which of $m$, $n$, or $o$ is assigned to $M1$, etc....) is
310: determined by the value of the variable `seed', which in this example is
311: selected from 1 to 300.
312:
313: \item The arguments of the {\tt /MAP} function are divided into three portions
314: by a semicolon symbol (the seed, the variable set, and the defined variable
315: set). The value of the seed is used to setup a random number generator
316: which is needed to
317: select one value from the {\bf second} set of variables and assign it to one of the
318: variables in the {\tt first} set. In the above example, two random numbers will
319: be generated.
320: The first random number is then divided by three and the remainder is used to
321: determine the first value to be selected from the set of three values and
322: gets assigned to the first variable in the list. The second random number
323: is then divided by two and the remainder is used to determine the second
324: value from the remaining two values and
325: is mapped to the second variable. The very last value left is then
326: assigned to the last variable. Therefore, the number of variables in both sets
327: must be equal. If any of the variables that appear in the second variable set
328: were not previously assigned a value, a warning will be issued. Variables used in the
329: first variable set may contain no data at first, but all variables in the first
330: variable set will
331: receive some value after the {\tt /MAP} function is called.
332:
333:
334: \item The {\tt /MAP} function is used in all the auxiliary files of the multiple
335: choice templates prepared to facilitate coding of qualitative or conceptual
336: questions.
337:
338: \item The {\tt /RMAP} function does the reverse action of the {\tt /MAP} function.
339: The value of the seed is used to setup a random number generator
340: which is needed to
341: select one variable from the {\bf first} set of variables and map it with one of the
342: values from the {\tt first} set.
343: For example, we have the following code:
344: \begin{capacode}
345: /LET seed=random(1,300,1)
346: /LET w=1
347: /LET x=2
348: /LET y=3
349: /LET z=4
350: /MAP(seed;a,b,c,d;w,x,y,z)
351: /DIS(a), /DIS(b), /DIS(c), /DIS(d)
352:
353: output: 3, 1, 2, 4
354: \end{capacode}
355: The values of the the second set of variables were randomly assigned (dependent
356: on the seed value) to the first set variables.
357: See how the {\bf value} of {\em w} (the first of the four values in its value set) is
358: mapped to the {\bf variable} {\em b} (the second of the variables in its set).
359: If we used {\tt /RMAP} instead with
360: the same seed value used above in the code below, the resulting mapping is reversed.
361: Notice how the {\bf variable} {\em a} (the first of the four variables in its set) has the
362: {\bf value} of {\em x} (the second of the four values) mapped to it.
363: \begin{capacode}
364: /LET w=1
365: /LET x=2
366: /LET y=3
367: /LET z=4
368: /RMAP(seed;a,b,c,d;w,x,y,z)
369: /DIS(a), /DIS(b), /DIS(c), /DIS(d)
370:
371: output: 2, 3, 1, 4
372: \end{capacode}
373:
374: Therefore, {\tt /RMAP} can also be used to unscramble {\tt /MAP}:
375: \begin{capacode}
376: /LET seed=random(1,300,1)
377: /LET w=1
378: /LET x=2
379: /LET y=3
380: /LET z=4
381: /MAP(seed;a,b,c,d;w,x,y,z) //same seed as above - not redefined
382: /RMAP(seed;p,q,r,s;a,b,c,d)
383: /DIS(p), /DIS(q), /DIS(r), /DIS(s)
384:
385: output: 1, 2, 3, 4
386: \end{capacode}
387:
388: \item To view an example of both the {\tt /MAP} and {\tt /RMAP} see the second
389: problem in {\sl set19.qz} from the {\sl nsc121s9} class directory({\sl /demolibrary/type-other/OR-MAP-RMAP}).
390:
391: \end{itemize}
392:
393:
394: \subsection{\bf Conditional Statements ( \index{/IF}{\tt /IF}, \index{/ELSE}{\tt /ELSE},
395: and \index{/ENDIF}{\tt /ENDIF} )}
396: \begin{itemize}
397: \item {\tt /IF}, {\tt /ELSE}, and {\tt /ENDIF} are used to add conditions within the \capa\
398: coding.
399:
400: \item For example:
401: \begin{capacode}
402: //NOTE: Each /IF needs an /ENDIF
403: /LET choice=random(1,4,1)
404: /IF (choice==1)
405: If the statement within the parentheses is true, this text
406: will be printed for the student to read.
407: /ELSE
408: /IF (choice==2)
409: This line will be printed instead.
410: /ELSE
411: /IF (choice==3)
412: This line will be printed.
413: /ELSE
414: If all the conditions above are false, then this text
415: will be printed.
416: /ENDIF //ends the last /IF condition
417: /ENDIF //ends the second /IF condition
418: /ENDIF //ends the first /IF condition
419: \end{capacode}
420:
421: \item Other commands can be entered in the {\tt /IF} statement. For example,
422: you may have the following:
423: \begin{capacode}
424: /IF (choice!=1)
425: /ANS(5)
426: /ELSE
427: /ANS(0)
428: /ENDIF
429: \end{capacode}
430: Therefore, if the variable choice happens to {\bf not} equal the interger 1 then the
431: the answer is 5, otherwise the answer is 0. \\
432: \end{itemize}
433:
434: \subsection{\bf Loops ( \index{/WHILE}{\tt /WHILE} and \index{/ENDWHILE}{\tt /ENDWHILE} )}
435: \begin{itemize}
436:
437: \item Below is an example of the {\tt /WHILE} and {\tt /ENDWHILE} commands:
438: \begin{capacode}
439: Written below are the multiples of 5 up to 12:
440: /LET integer=0
441: /WHILE (integer <= 12)
442: /LET answer = 5*integer
443: /DIS(integer) * 5 = /DIS(answer) /DIS(web("","//",""))
444: //see the functions table to see how web() works
445: /LET integer=integer+1
446: /ENDWHILE
447:
448: The output will display:
449:
450: Written below are the multiples of 5 up to 12:
451: 0 * 5 = 0
452: 1 * 5 = 5
453: 2 * 5 = 10
454: 3 * 5 = 15
455: 4 * 5 = 20
456: 5 * 5 = 25
457: 6 * 5 = 30
458: 7 * 5 = 35
459: 8 * 5 = 40
460: 9 * 5 = 45
461: 10 * 5 = 50
462: 11 * 5 = 55
463: 12 * 5 = 60
464: \end{capacode}
465:
466: As long as the condition in the parentheses is true, the code between
467: the {\tt /WHILE} and {\tt /ENDWHILE} will be processed. When the condition
468: (in this case, the value of the variable {\em integer} is less than or equal
469: to 12) is false, control passes to the next line below the {\tt /ENDWHILE}.
470:
471: \item Every {\tt /WHILE} was must have a {\tt /ENDWHILE} to mark the end of the {\tt /WHILE} loop. \\
472: \end{itemize}
473:
474:
475: \subsection{\bf Answers (\index{/ANS()} {\tt /ANS} )}
476: \begin{itemize}
477: \item Each individual problem must be ended by an expression specifying the
478: answer. This answer expression consists of the keyword {\tt /ANS()}
479: starting on a new line.
480: \item The
481: answers are indicated specifically by the {\tt /ANS()} command, with the
482: parentheses containing the answer and the attributes of the answer.
483: The answers to problems can be previously defined variables.
484: There must be at least a variable, integer, real number, of string defining the answer within
485: the parentheses, ({\tt /ANS(variable), /ANS(5)}, etc.).
486: \item Several options are available to format the answer.
487: The attributes of the {\tt /ANS()} function are {\bf case insensitive}.
488: The available options for defining {\tt /ANS()} attributes are:
489:
490:
491:
492: %**********************************************
493: \item {\bf List of Available Expressions:}
494: \begin{tabbing}
495: 12345678901234567890123456789\= 12345678901234567890 \= \kill
496: {\tt wgt=} \> $\diamond $ problem weight \\
497: {\tt tries=} {\em or} {\tt try=} \> $\diamond $ number of allowed tries to input the answer\\
498: {\tt tol=} \> $\diamond $ answer tolerance \\
499: {\tt calc=fmt/unfmt} \> $\diamond $ sets tolerance to be calculated
500: from the \\
501: $$ \> $ $ \ formatted or unformatted answer. \\
502: {\tt sig=} \> $\diamond $ fixed number of significant digits. \\
503: {\tt sig=}{\em x} {\tt minus} {\em y} {\tt plus} {\em z}
504: \> $\diamond $ a range of significant digits from \\
505: $$ \> $ $ \ {\em x} minus {\em y} to {\em x} plus {\em z} \\
506: {\tt unit=} {\em or} {\tt units=} \> $\diamond $ units of answer (dimensions)\\
507: {\tt hint=} \> $\diamond $ number of wrong student entered
508: answers \\
509: $$ \> $ $ \ before the hint appears. \\
510: {\tt str=mc/cs/ci/fml} \> $\diamond $ different ways of accepting
511: a string answer \\
512: $$ \> $ $ \ with fml for math formula as answer. \\
513: {\tt hgr=on} \> $\diamond $ hand graded answer \\
514: {\tt pc=on} \> $\diamond $ partial credit \\
515: {\tt ansbox=on/off} \> $\diamond $ Web generated answer box \\
516: {\tt br=on/off} \> $\diamond $ Web line break \\
517: \end{tabbing}
518: \item {\bf More detailed explanations are found below:}
519: %**********************************************
520: \begin{enumerate}
521: %BEGIN DISCRIPTION OF ANSWER OPTIONS
522: %***********************************************PROBLEM WEIGHT
523: \item {\bf Problem Weight:\index{WGT=}} The problem point value (or weight)
524: is set by: \\
525: \fbox{\tt /ANS(variable, wgt=2)}\\
526: The problem value can
527: be an integer value between 0 and 9. A variable can be can be
528: defined at
529: the beginning of a problem by either of the following commands:
530: \\ \fbox{\tt /BEG prob\_val=3} \\
531: or \\
532: \fbox{\tt /LET prob\_val=3} \\
533: Then, this
534: value can be used in the {\tt /ANS()} function:\\
535: \fbox{\tt /ANS(variable, wgt=prob\_val, tries=20)}. \\
536: If the problem weight is not defined, the default value
537: of 1 point is used.
538: %******************************************TRIES
539: \item {\bf Tries:\index{TRY=}\index{TRIES=}} The number of attempts to enter an incorrect
540: answer can be limited to an integer value less than
541: or equal to 99.
542: \begin{itemize}
543: \item The format for setting the number of tries is: \\
544: \fbox{\tt /ANS(variable, tries=35)} \\
545: or \\
546: \fbox{\tt /ANS(variable, tries=try\_val)}
547: \item In the second example shown above, {\em try\_val} is assumed to be a previously defined
548: variable.
549: The student
550: receives a message near the answer field stating the number of
551: attempts and the total number of tries available for each
552: problem in which the {\tt tries=$x$} has been specified.
553: A warning message is displayed when only one try
554: remains.
555: Errors in either
556: significant figures or units will {\bf not} decrease the
557: number of remaining tries for the student. Both the
558: significant figure
559: and unit must be correct before
560: a ``Correct'' or ``Incorrect''
561: response to the numerical portion of the answer is given to
562: the student.
563: \item {\bf Note:} {\tt try=} is equivalent to {\tt tries=} \end{itemize}
564: %*********************************************TOLERANCE
565: \item {\bf Tolerance: \index{TOL=}}
566: The tolerance can be specified as (1) a numerical value, (2) as a percentage of the correct answer or as (3) a pre-defined variable.
567: \begin{enumerate}
568: \item The format for a set numerical value would be given by:\\
569: \fbox{\tt /ANS(variable:3f,tol=0.5)}
570: \item The format of a \% tolerance would be given by: \\
571: \fbox{\tt /ANS(variable:3f, tol=1.1\%)}. \\
572: This is specified if there is a possibility that the
573: answer will be calculated as equal to zero. The tolerance
574: is thus given a value rather than a percentage.
575: \item The format for a defined tolerance variable would be: \\
576: \fbox{\tt /ANS(variable:3f, tol=TolVar)}. \\
577: \item The format for a \% tolerance with a defined variable would be: \\
578: \fbox{\tt /ANS(variable:3f, tol=TolVar\%}
579: \end{enumerate}
580: {\em Note that the display of the answer can be formatted according to the same commands used
581: in /DIS.}
582: \begin{itemize}
583: \item {\bf Real answers:} A tolerance should be specified
584: for `real' answers. It can be
585: absolute or relative. An absolute tolerance can be a variable.
586: Answers with real values can be {\bf formatted} with
587: specifications {\tt :1E, :3E,
588: :2f,}
589: etc., where {\tt 1E} means exponential notation with one decimal place,
590: {\tt :3E} means exponential notation with three
591: decimal places, and {\tt :2f} means two floating decimals.
592: \begin{enumerate}
593: \item \fbox{\tt /ANS(variable:2E,tol=1.2\%,wgt=prob\_val,tries=try\_val)}
594: \\ When
595: an answer submitted by a student is within the relative
596: tolerance (1.2\% ) of the correct answer, the student receives
597: `correct'. {\bf Note:} The relative tolerances are based
598: on the {\bf unformatted} answer.
599: \item \fbox{\tt /ANS(variable:2E,tol=5.0,wgt=prob\_val,tries=try\_val)}
600: \\ An answer
601: submitted by a student within the absolute tolerance of 5.0,
602: would be graded `correct'. That is the answer must lie within the range {\em variable}-5
603: to {\em variable}+5.
604:
605: \item \fbox{\tt /ANS(variable:3E,tol=tol\_val,wgt=prob\_val, tries=try\_val)} \\
606: Here the tolerance is a previously defined quantity,
607: {\tt tol\_val}.
608: \item {\tt calc=fmt/unfmt}: Selects the application of the
609: tolerance range for the formatted or unformatted numerical
610: answer value. For example, say we have {\tt variable=2/3} for the following answer line: \\
611: \fbox{\tt /ANS(variable:3f,tol=.01,wgt=prob\_val, tries=try\_val)} \\
612: the error would be between two-thirds plus or minus .01. If we used this instead though: \\
613: \fbox{\tt /ANS(variable:3f,tol=.01,calc=fmt,wgt=prob\_val,tries=try\_val)} \\
614: the error would be between 0.667 plus or minus 0.01. The default value is unformatted.
615: \end{enumerate}
616: \item {\bf Integer answers:} You may not want a tolerance for an
617: integer answer. \\
618: \fbox{\tt /LET variable=34}
619: \begin{enumerate}
620: \item \fbox{\tt /ANS(variable, tol=0, wgt=prob\_val,tries=try\_val, hint=hint\_val)}\\
621: Only the number ``34'' will be
622: accepted as correct.
623: \item \fbox{\tt /ANS(variable, wgt=prob\_val, tries=try\_val, hint=hint\_val)}\\
624: Same as above. Only the number ``34'' will be accepted as
625: correct.
626: \item You can also use a percentage tolerance or a non-integer real
627: number as a tolerance, but then students can get a ``correct'' answer
628: by entering in an appropriate non-integer number. For example: \\ \fbox{\tt /ANS(variable, tol=4, wgt=prob\_val, tries=try\_val, hint=hint\_val)}
629: \\ Any answer within plus or
630: minus 4 units is accepted as correct. For example, the
631: real number, 36.5 will be accepted as ``correct''.
632: \end{enumerate}
633:
634: \item {\bf Note:} If you define your answer variable with an equation consisting
635: of only integer numbers, then the resulting answer will be an integer.
636: For example, we have the following code: \\
637: \fbox{\tt /LET variable1=1/2} \\
638: \fbox{\tt /LET variable2=35/12} \\
639: Then {\em variable1} will be assigned the value of ``0'' and {\em variable2} will be assigned the value of ``2''. On the other hand, \\
640: \fbox{\tt /LET variable1=1.0/2.0} \\
641: will now be assigned the value of 0.5 because at least one real number was used
642: in the equation.
643: \footnote{You may have noticed this text from the /LET section, but it is worth repeating because it can be
644: a major source of frustration to the instructor and students if real numbers and integer numbers are not
645: dealt with correctly.}
646: \end{itemize}
647: %************************************************SIGNIFICANT FIGURES
648: \item {\bf Significant Figures:\index{SIG=}}
649: If unspecified, significant figures are not checked and
650: any number of significant figures between 1 and 15 are
651: accepted provided the answer entered falls within the
652: specified numerical tolerance range. The number of acceptable
653: significant figures can be specified by the following format:
654: \begin{enumerate}
655: \item \fbox{\tt /ANS(variable, sig=4 plus 1 minus 1, tries=try\_val, wgt=prob\_val, hint=hint\_val)} \\
656: This will accept 3, 4, or 5 significant figures in the answer.
657: \item \fbox{\tt /ANS(variable, sig=3 plus 2, tries=try\_val, wgt=prob\_val, hint=hint\_val)} \\
658: This will accept 3, 4, or 5 significant figures in the answer.
659: \item \fbox{\tt /ANS(variable, sig=4 , tries=try\_val, wgt=prob\_val, hint=hint\_val)} \\
660: This will only accept 4 significant figures in the answer.
661: \end{enumerate}
662: Care must be exercised when limiting the significant figures
663: when a percentage tolerance is used. It is possible to create a situation where the student cannot enter a correct answer for a problem. For example, the server might calculate the unformatted {\em variable} to be equal to 0.409. The following answer format will create such a situation: \\
664: \fbox{\tt /ANS(variable:0f, sig=1, tol=1\%, wgt=prob\_val)} \\
665: The student will calculate this answer to be 4E-1 which is not within 1\% of the
666: answer.
667:
668: %********************************************UNITS
669: \item {\bf Units:\index{unit=}} A file in the class
670: directory named {\sl capa.config} lists all SI units and other
671: user defined acceptable units with
672: their relationships.
673: That file can be edited by the instructor.
674: Units are entered as strings.
675: \begin{itemize}
676: \item A typical format for
677: answers requiring a unit is: \\
678: \fbox{\tt /ANS(perimeter:3f,unit="cm",sig=4)}\\
679: or\\
680: \fbox{\tt /ANS(area:2f,unit="cm\^{}2")}
681: \item For a specially defined unit, one can use a variable, e.g.
682: \begin{capacode} /LET StringVar="dollar"
683: /ANS(cost:2f,unit=StringVar,tol=.005,wgt=2,tries=6,sig=4 plus 3)
684: \end{capacode}
685: \item {\sl /demolibrary/type03/msu-prob22.txt} and
686: {\sl /demolibrary/type03/msu-prob23.txt} \\ are two problems
687: included in the distribution
688: package which aid in teaching students the rules for entering
689: answers with units in a \capa\ session. These are useful for students in an initial \capa\ set.
690: \item {\bf Note:} {\tt units=} is equivalent to {\tt unit=}
691: \end{itemize}
692: %************************************************SHOW HINTS
693: \item {\bf Show Hints:\index{hint=}} The hint can be configured so that it
694: is available or displayed only after a certain number of tries.
695: This is achieved by setting {\tt hint=AnInteger} (e.g. {\tt hint=3})
696: in the answer format.
697: For example: \\
698: \fbox{\tt /ANS(variable, hint=3, tries=10, wgt=1)} \\
699: or \\
700: \fbox{\tt /ANS(variable, hint=hint\_val, tries=10, wgt=1)}\\
701: will both
702: (1) show the hint on a Web browser after 3 tries
703: and (2) allow it to be viewed on telnet after 3 or more tries
704: by entering :H which shows up on the menu lines.
705: %***********************************************STRING ANSWERS
706:
707:
708: \item {\bf String answers} can be exact comparisons, or have the order
709: and/or case disregarded.
710: \begin{enumerate}
711: \item \fbox{\tt /ANS(letters,str=ci,wgt=prob\_val,tries=20)} \\
712: {The command {\tt str=ci} is the default value, the order is checked but case insensitive.}
713: \item \fbox{\tt /ANS("KCl",wgt=prob\_val,tries=20)}\\
714: { The default is case insensitive. Therefore, answers such as ``kcl'' and
715: ``KcL'' are accepted as correct.}
716: \item \fbox{\tt /ANS(letters,wgt=prob\_val,tries=20)}\\
717: { {\em letters} is a string variable previously defined. This works
718: like the example above. (The order is essential, but
719: not case sensitive.)}
720: \item \fbox{\tt /ANS(letters,str=mc,wgt=prob\_val,tries=20)}\\
721: {The command
722: {\tt str=mc} accepts any order of the correct responses.
723: Hence, ``abc'' and ``acb'' are equivalent.}
724: \item \fbox{\tt /ANS(letters,str=cs,wgt=prob\_val,tries=20)} \\
725: {This is an exact string comparison. Both the order and
726: the case are required.}
727: \item {\bf Formula as string answer:}
728: \begin{capacode}
729: /ANS(fm1,str=fml,eval=<"x" @ pt1:pt2#20>,TOL=1E-3, tries=try_val,
730: wgt=prob_val,hint=hint_val) \end{capacode}
731: In this one-variable case, \capa\ will sample the student's input formula and the formula fm1, the string formula representing the correct answer. Comparison will be at 20 values of x between x = pt1 and x = pt2). All comparisons must fall with the tolerance, here 1E-3, for a correct answer.\\
732: {\em For examples, see the templates: \\{\tt /demolibrary/MCTools/equationA} and {\tt /demolibrary/MCTools/equationXY} }
733: \end{enumerate}
734: %********************************************HAND GRADING
735: \item {\bf Hand Grading:\index{hgr=}} A problem can be designated to be hand
736: graded. For this case students are not allowed to answer
737: via telnet or web sessions and the question is graded by the instructor using the {\sf Grader} application.
738: The format for this is: \\
739: {\tt /ANS(variable,hgr=on, tries=1, wgt=1)} \\
740: {\em (See /SUBJECTIVE for telnet or
741: Web submitted essay questions for hand grading.)}
742: %*******************************************PARTIAL CREDIT
743: \item {\bf Partial Credit:\index{pcr=}} A multiple point problem can be
744: specified to have partial credit. This attribute works like
745: {\tt hgr=on} in that students cannot login to
746: answer the question. The format for this is: \\
747: \fbox{\tt /ANS(variable, wgt=9, pcr=on, tries=1)}\\
748: This allows an instructor to
749: manually enter an integer point value from 0 to 9 through the
750: {\sf Grader} application.
751:
752:
753: %**********************************************MISCELLANEOUS ANSWER ATTRIBUTES
754:
755: \item {\bf Miscellaneous Answer Attributes}
756: \begin{enumerate}
757: \item {\tt br=on/off}: This starts/stops the generation of
758: $<$br$>$ (a line break) on the Web display. The default value is on.
759: \item {\tt ansbox=on/off}: Controls the generation and display
760: of the answer box for the Web. The default value is on.
761: \item {\tt Yes/no} is equivalent to {\tt on/off}.
762: \end{enumerate}
763: %*******************************************END OF ANSWER ATTRIBUTES
764: \end{enumerate}
765: \end{itemize}
766:
767: \subsection{\bf Multiple Answers ( \index{/AND}\index{/OR}{\tt /AND} and {\tt /OR} )}
768: \begin{itemize}
769: \item {\tt /AND} or {\tt /OR} after an answer specification requires another {\tt /ANS} statement be present.
770: In the case of {\tt /AND}, two successive answers will be required from the student. In the case of {\tt /OR},
771: the student will receive credit if either answer is supplied.
772: \item Below is an example for {\tt /AND}:
773: \begin{capacode}
774: /ANS(variable_1, wgt=prob_val, tries=try_value)
775: /AND
776: /ANS(variable_2, wgt=prob_val, tries=try_value)
777: \end{capacode}
778:
779: The above example requires two answers from the student.
780: During a telnet session the student will be prompted to enter the first
781: answer and then the second {\bf in the order that they are coded}.
782: During a web session, there will be multiple answer boxes labeled ``Answer 1''
783: and so on. Again, they must be entered in order by the student. It is
784: recommended that the problem text give instructions to the student to answer the questions in order.
785: Note that the problem is worth the number of points of the last defined {\tt wgt} specification, i.e. if in the
786: first answer {\tt wgt=3} and in the second answer {\tt wgt=1}, the student will only receive one point for
787: the total question.
788: \item Below is an example for {\tt /OR}:
789: \begin{capacode}
790: /ANS(variable_1, wgt=prob_val, tries=try_value)
791: /OR
792: /ANS(variable_2, wgt=prob_val, tries=try_value)
793: \end{capacode}
794:
795: The {\tt /OR} is suitable for questions such as asking the student to choose one
796: of the correct answers from a list.
797: \item Note that the variable {\em try\_val} was used in the examples above
798: to simplify the script. If the number of tries is different within the answer
799: specifications, the last defined
800: number of tries is given to the student for their amount of tries in that
801: problem.
802: \end{itemize}
803:
804:
805: \subsection{\bf Essay Questions (\index{/SUBJECTIVE} {\tt /SUBJECTIVE} )}
806: {\tt /SUBJECTIVE} is used instead of {\tt /ANS} when the instructor wants to allow students
807: to submit a short essay.
808: The student can type their essay in either
809: the telnet or web session. The instructor grades this essay with the
810: {\sf Grader} application and the score is recorded in the database.
811: {\tt hgr=on} must be specified when using {\tt /SUBJECTIVE}.
812: \begin{capacode} /SUBJECTIVE(wgt=prob_val, hgr=on, tries=try_val)
813: \end{capacode}
814: You may choose to set a number of tries also. The student will be allowed to rewrite their essay according
815: to the number of tries that the instructor allows.
816:
817: \subsection{\bf Displaying text verbatim (\index{/VERB} \index{/ENDVERB} {\tt /VERB} and {\tt /ENDVERB} )}
818: Used to display text verbatim:
819: \begin{capacode}
820: Enter the answer as in a calculator:
821: /VERB
822: Example: 4.567 + 2.431 * x^4 - 0.310 * x^2
823: /ENDVERB
824: \end{capacode}
825:
826:
827:
828: \subsection{\bf Displaying Information Before the Problem Set (\index{/START} {\tt /START} )}
829: All the material coded before {\tt /START} in a {\sl set$x$.qz} file is both printed
830: out and displayed on the Web for students to see. See {\sl set19.qz} in the
831: {\sl nsc121s9} class directory for an example (note the placement of the imported {\sl HWTop} file).
832:
833: \subsection{\bf Ending the Problem Set ( \index{/END}{\tt /END} )}
834: \begin{itemize}
835: \item {\tt /END()} or {\tt /END(\index{stdendline}stdendline)} causes the parser to stop and ignore all input
836: characters beyond that command. String variables can be defined and constructed and additional text
837: (such as instructions for students) may be displayed between the last {\tt /ANS()} and
838: {\tt /END}.
839:
840: \item All sets should include {\tt /END(stdendline)}, so that both on
841: paper and on the Web, the department is identified and the
842: copyright nature of the \capa\ software is indicated. The string for
843: {\tt stdendline} is created in the {\sl HWTop} file in the class directory and can be
844: edited by users, such as changing the Dept. ID for your particular class.
845:
846: \item The \capa\ system counts the number of problems in a problem set by
847: counting the number of {\bf proper} answer lines (lines containing {\tt /ANS} or {\tt /SUBJECTIVE}). If there is
848: an error in coding and the answer cannot be evaluated, that problem is not
849: counted by {\sf Quizzer}.
850: \end{itemize}
851: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
852: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
853: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
854: {\small
855: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
856: \multicolumn{2}{|c|}{\bf Table of Intrinsic Functions: Names Are Case
857: Sensitive.}\\ \hline
858: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
859: { Functions}& Description, Sample quizzer input and output for printing \\ \hline
860: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
861: \index{sin()}\index{cos()}\index{tan()}{\tt sin(x), cos(x), tan(x)}& Trigonometric functions. x is in radians.
862: \begin{verbatim}/LET angle=60.0
863: /LET var1=sin(angle*3.141592654/180)
864: Sine of /DIS(angle:1f) degrees is /DIS(var1:3f).
865: \end{verbatim}
866: Output: {\tt Sine of 60.0 degrees is 0.866. }\\ \hline
867: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
868: \index{asin()}\index{acos()}\index{atan()}\index{atan2()}{\tt asin(x), acos(x), atan(x), atan2(y,x)}& Inverse trigonometric functions. Returns
869: radians. asin() computes the principal value of the arc sine of x, in the
870: interval [-pi/2,pi/2] radians. The value of x must be in the domain [-1,1].
871: acos() computes the principal value of the arc cosine of x, in
872: the interval [0,pi] radians. The value of x must be in the domain [-1,1].
873: atan2() computes the principal value of the arc tangent of y/x,
874: in the interval [-pi,pi] radians. The sign of atan2() is
875: determined by the sign of y.
876: \begin{verbatim}/IMP "demolibrary/Tools/StdConst"
877: //pi_c is a variable set to equal pi and is found in the imported file above.
878: /LET var1=-1.65
879: /LET var2r=atan(var1)
880: /LET var3d=atan(var1)*180.0/PI
881: The angle whose tangent is /DIS(var1:3f) can be expressed
882: as /DIS(var2r:3E) radians or as /DIS(var3d:3E) degrees.
883: \end{verbatim}
884: Output for telnet session:
885: {\tt The angle whose tangent is -1.650 can be expressed
886: as -1.026E+00 radians or as -5.878E+01 degrees.}
887: \\ \hline
888: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
889: \index{log()}\index{log10()}{\tt log(x), log10(x)}& Natural logarithm and base-10 logarithm. Note that the
890: the variables {\tt natlog} and {\tt tenlog} were defined to simplify the coding
891: of this problem by allowing complicated text (with subscripts and superscripts)
892: to be printed by displaying a variable.
893: \begin{verbatim}
894: /LET natlog=tex("$log_e$","log_e")
895: /LET tenlog=tex("$log_{10}$","log_10")
896: /LET x=2546.7
897: /LET var1=log(x)
898: /LET var2=log10(x)
899: /LET ratio=var1/var2
900: /LET var3=log(10.0)
901: The /DIS(natlog) of /DIS(x:1f) is /DIS(var1:3E) while its /DIS(tenlog)
902: is /DIS(var2:3E). Note that the ratio /DIS(natlog)//DIS(tenlog)
903: = /DIS(ratio:3f), which is just /DIS(natlog)(10), i.e. /DIS(var3:3E).
904: \end{verbatim}
905: Output for print out or Web:
906: The $log_e$ of 2546.7 is $7.843$ while its
907: $log_{10}$
908: is $3.406$. Note that the ratio $log_e$/$log_{10}$
909: = 2.303, which is just $log_e$(10), i.e. $2.303$.
910: \\ \hline
911: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
912: \index{exp()}\index{pow()}\index{sqrt()}{\tt exp(x), pow(x,y), sqrt(x)}& Exponential, power, and square root.
913: Compute $e^x$, $x^y$, and $\sqrt{x}$ respectively.
914: \begin{verbatim}/LET varx=1.526
915: /LET vary=0.5
916: /LET var1=exp(varx)
917: /LET var2=pow(varx,0.5)
918: /LET var3=pow(varx,vary)
919: /LET var4=sqrt(varx)
920: var1=/DIS(var1:2f); var2=/DIS(var2:2f); var3=/DIS(var3:2f);
921: var4=/DIS(var4:2f).
922:
923: \end{verbatim}
924: Output: {\tt var1 = 4.60; var2 = 1.24; var3 = 1.24; var4 =
925: 1.24.}
926: \\ \hline
927: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
928: \end{tabular}\end{center}}
929: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
930: {\small
931: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
932: { Functions}& Description, sample quizzer code and output \\ \hline
933: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
934: \index{abs()}\index{sgn()}{\tt abs(x), sgn(x)}& {\tt abs(x)} returns the absolute value of $x$.
935: {\tt sgn(x)} returns $1$, $0$ or $-1$ depending on value
936: of $x$
937: \begin{verbatim}/LET xx=-2.5
938: /LET var1=abs(-4.5)
939: /LET var2=sgn(xx)
940: /LET var3=sgn(-4.5*xx)
941: var1=/DIS(var1:2f) var2=/DIS(var2) var2=/DIS(var2:2f) var3=/DIS(var3)
942: \end{verbatim}
943: Output: {\tt var1=4.50 var2=-1 var2=-1.00 var3=1
944: }\\ \hline
945: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
946: \index{erf()}\index{erfc()}{\tt erf(x), erfc(x)}& Error functions. ${erf}(x) = \frac{2}{\sqrt{\pi}}
947: \int_0^{x} e^{-t^2} dt$ and
948: ${erfc}(x) = 1.0 - {erf}(x)$.
949: \begin{verbatim}/LET varx=0.51
950: Evaluate the Normal Probability Integral from -/DIS(varx)
951: to /DIS(varx). /DIS(newline)
952: /LET prob = erf(varx/sqrt(2.0))
953: Probability = /DIS(prob:4f)
954: \end{verbatim}
955: Output: {\tt Evaluate the Normal Probability Integral from -0.51
956: to 0.51. }
957: \newline {\tt Probability = 0.3899}
958: \\ \hline
959: %$\mathrm{erfc}(x) = 1.0 - \mathrm{erf}(x)$.}\\ \hline
960: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
961: \index{ceil()}\index{floor()}{\tt ceil(x), floor(x)}& Ceiling and floor functions.
962: ${ceil}(x) = \lceil x \rceil$ and ${floor}(x) = \lfloor
963: %$\mathrm{ceil}(x) = \lceil x \rceil$ and $\mathrm{floor}(x) = \lfloor
964: x \rfloor$. The ceiling function returns an integer rounding x toward positive
965: infinity. The floor function rounds toward negative infinity.
966: \begin{verbatim}/LET varx=ceil(3.65)
967: /LET vary=floor(3.65)
968: /LET varz=ceil(-5.73)
969: /LET varw=floor(-5.73)
970: varx=/DIS(varx) vary=/DIS(vary) varz=/DIS(varz) varw=/DIS(varw)
971: \end{verbatim}
972: Output: {\tt varx=4 vary=3 varz=-5 varw=-6
973: }\\ \hline
974: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
975: \index{min()}\index{max()}{\tt min(...), max(...)}& Minimum and maximum functions, with indefinite number
976: of arguments.
977: Arguments must be of either all integer or real type. String comparison are
978: such that $A < a$. In other words,
979: lower case letters have a higher value than upper case letters.
980: \begin{verbatim}/LET a=min(23,45,12,7,9)
981: /LET b=max(23.1,45.3,12.6,7.1,9.0)
982: /LET c=min("a","ae","aeg","Aeg")
983: /LET d=max("a","ae","aeg","Aeg")
984: a=/DIS(a:2f) b=/DIS(b:2f) c=/DIS(c) d=/DIS(d)
985: \end{verbatim}
986: Output: {\tt a=7 b=45.30 c=Aeg d=aeg
987: }\\ \hline
988: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
989: \end{tabular}\end{center}}
990: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
991: {\small
992: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
993: { Functions}& Description, sample quizzer code and output \\ \hline
994: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
995: \index{factorial()}{\tt factorial(n)}& Arguments must be an integer. Returns an integer if n is or
996: smaller, else or real value.
997: \begin{verbatim}/LET number=factorial(6)
998: /DIS("6!=")/DIS(number)/DIS(newline)
999: /DIS("0!=")/DIS(factorial(0))/DIS(newline)
1000: /LET number2=factorial(21)
1001: /DIS("21!=")/DIS(number2:3E)/DIS(newline) \end{verbatim}
1002: Output: {\tt
1003: 6!=720\newline
1004: 0!=1\newline
1005: 21!=$5.109 \times 10^{19}$
1006: }\\ \hline
1007: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1008: \index{modulus operator, \%}
1009: {\tt N\% M}& N and M are integers, and the remainder of the integer ratio is
1010: returned.
1011: \begin{verbatim}
1012: /LET ratio = 98/5
1013: /DIS("ratio=")/DIS(ratio)/DIS(newline)
1014: /LET leftover=98%5
1015: /DIS("remainder=")/DIS(leftover) \end{verbatim}
1016:
1017: Output: {\tt
1018: ratio=19\newline
1019: remainder=3 }\\ \hline
1020: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1021: \index{hyperbolic functions}
1022: {\tt sinh(x), cosh(x), tanh(x)} & Hyperbolic functions.\\ \hline
1023: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1024: \index{hyperbolic functions, inverse}
1025: {\tt asinh(x), acosh(x), atanh(x)}& Inverse hyperbolic functions.\\ \hline
1026: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1027: \index{roundto()}
1028: {\tt roundto(var1,n)} & Rounds the value of real variable `var1' to n places (fixed point notation).
1029: \begin{verbatim}
1030: /LET value=100.0/3.0
1031: Initial value = /DIS(value:5f)/DIS(newline)
1032: /LET value=roundto(value,2)
1033: The new value is now /DIS(value:5f) and can be used as
1034: /DIS(value:2f) with no rounding error. \end{verbatim}
1035:
1036: Output: {\tt Initial value =
1037: 33.33333
1038: The new value is now 33.33000 and can be used as 33.33 with no rounding
1039: error.}\\ \hline
1040: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1041: \index{web()}{\tt web("a","b","c") or web(a,b,c) }& ASCII (a), tex(b) and html(c) strings or
1042: variables displayed respectively.
1043: \begin{verbatim}
1044: Example: \verb+{/DIS(web("M2","M$_2$","M<sub>2</sub>")) }+
1045:
1046: Output for telnet session: M2
1047: Output for printout or Web: M$_2$
1048: \end{verbatim}
1049: \\ \hline
1050: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1051: \index{html()}{\tt html(a) or html("a")} & variable or string `a' parsed for Web browser only.
1052: \begin{verbatim}
1053: Example:
1054: /DIS(html("<br><a href=/nsc121s9/Links/webPulley.html> Motion of Masses \
1055: on a Pulley</a><p>"))
1056: \end {verbatim}
1057: Displays link "Motion of Masses on a Pulley"
1058: \\ \hline
1059: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1060: \end{tabular}\end{center} }
1061: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1062: {\small
1063: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
1064: { Functions}& Description, sample quizzer code and output \\ \hline
1065: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1066: {\tt \index{Bessel functions, jn() and yn()}jn(0,x), jn(1,x), jn(n,x)}& Bessel functions of the first kind, with orders
1067: $0$, $1$ and $n$ respectively. Note that the first argument is integer, the
1068: second real.
1069: \begin{verbatim}/LET aa=jn(0,3.0)
1070: /LET bb=jn(1,3.0)
1071: /LET cc=jn(2,3.0)
1072: aa=/DIS(aa:4f) bb=/DIS(bb:4f) cc=/DIS(cc:4f)
1073: \end{verbatim}
1074: Output: {\tt aa=-0.2601 bb=0.3391 cc=0.4861
1075: }\\ \hline
1076: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1077: {\tt \index{yn()}yn(0,x), yn(1,x), yn(n,x)}& Bessel functions of the second kind, with
1078: orders $0$, $1$ and $n$ respectively. Note that the first argument is integer,
1079: the second real.
1080: \begin{verbatim}/LET dd=yn(1,3.0)
1081: dd=/DIS (dd:4f)
1082: \end{verbatim}
1083: Output: {\tt dd=0.3247
1084: }\\ \hline
1085: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1086: {\tt \index{random()}random(l,u,d)}& Returns a uniformly distributed random number
1087: between $l$ and $u$ with steps of $d$. Note that all
1088: arguments must be the same type, integer or real. {\footnotesize [When real number are used, avoid having
1089: the step size such that the highest value lands on "u" as different machines may have different representations and accuracy.]}
1090: \begin{verbatim}/LET index=random(2,5,2) //returns integers 2 or 4
1091: /LET value=random(2.3,5.15 ,0.2 ) //returns 2.3, 2.5, 2.7,...., 5.1
1092: index=/DIS(index) value=/DIS(value:2f)
1093: \end{verbatim}
1094: Output: {\tt index=4 value=3.70
1095: }\\ \hline
1096: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1097: \index{choose()}
1098: {\tt choose(i,...)}& Choose the $i$th item in the argument list. Integer $i$
1099: must be greater than zero and
1100: it's maximum possible value must not exceed the number of arguments following
1101: it.
1102: \begin{verbatim}/LET indx=3
1103: /LET realvar=choose(indx, 23.0,45.4,67.3) // will select 67.3
1104: /LET intvar=choose(indx, 23,45,67) // will select 67
1105: /LET stringvar=choose(indx,"No","Yes","Maybe") // will select "Maybe"
1106: realvar=/DIS(realvar:2f) intvar=/DIS(intvar) stringvar=/DIS(stringvar)
1107: \end{verbatim}
1108: Output: {\tt realvar=67.30 intvar=67 stringvar=Maybe
1109: }\\ \hline
1110: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1111: \index{tex()}
1112: {\tt tex(a,b)}, {\tt tex("a","b")}& When in TeX mode, return the first argument
1113: $a$, and return the second argument $b$ in enscript mode (ASCII).
1114: \begin{verbatim}/DIS(tex("This, in the .tex file.","This, in the ASCII version."))
1115: /LET A=33
1116: /LET B=66
1117: /DIS(tex(A,B))
1118: \end{verbatim}
1119: Tex Output: This, in the .tex file. 33
1120: \\ \hline
1121: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1122: {\tt var\_in\_tex(a)}& Equivalent to {\tt tex("a","")}
1123: \\ \hline
1124: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1125: \end{tabular}\end{center}}
1126: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1127: {\small
1128: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
1129: { Functions}& Description, sample quizzer code and output \\ \hline
1130: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1131: \index{to\_string()}{\tt to\_string(x)}, {\tt to\_string(x,y)}& If variable x is an integer,
1132: to\_string(x) returns a string. If x
1133: is real the format is given by y as follows:
1134: \begin{verbatim}
1135: /LET name1=to_string(34.56789)
1136: /LET name2=to_string(34.56789, ".3E")
1137: /LET name3=to_string(34.56789, ".3f")
1138:
1139: No format is /DIS(name1), with ".3E" format is /DIS(name2),
1140: and with ".3f" format is /DIS(name3)
1141: \end{verbatim}
1142: Output:
1143: No format is 34.56789, with ".3E" format is 3.457E+01,
1144: and with ".3f" format is 34.568
1145: \\ \hline
1146: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1147: \index{capa\_id()}\index{class()}\index{section()}\index{set()}\index{problem()}
1148: {\tt capa\_id(), class(), section(), set(), problem()}& The \capa\ ID number,
1149: class name, section number, set number
1150: and problem number respectively. Variables can be assigned to their current values
1151: or they can be displayed directly as shown below.
1152: \begin{verbatim}/LET capaIDval=capa_id()
1153: Your CAPA ID is /DIS(capaIDval). /DIS(newline)
1154: The class name entered at login is /DIS(class()). /DIS(newline)
1155: Your section number is /DIS(section()). /DIS(newline)
1156: This is part of problem set /DIS(set()). /DIS(newline)
1157: The current problem number is /DIS(problem()). /DIS(newline)
1158:
1159: Output:
1160: Your CAPA ID is 8659.
1161: The class name entered at login is nsc121s9.
1162: Your section number is 1.
1163: This is part of problem set 2.
1164: The current problem number is 2.
1165: \end{verbatim}
1166: \\ \hline
1167: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1168: \index{name()}\index{student\_number()}{\tt name(), {\tt student\_number()}}& student name and student number. The
1169: latter can be printed on quizzes when the student\_number is used for identification to
1170: resolve ambiguities.\begin{verbatim}
1171: /DIS(name()) /DIS(student_number())
1172: \end{verbatim}
1173: Output: Student, Jamie . A12345678
1174: \\ \hline
1175: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1176: \index{open\_date()}\index{due\_date()}\index{answer\_date()}\index{due_day()}
1177: {\tt open\_date(), due\_date(), answer\_date()}& Problem set open date, due
1178: date, and answer date. \begin{verbatim}
1179: /DIS(open_date()) /DIS(newline)
1180: /DIS(due_date()) /DIS(newline)
1181: /DIS(answer_date()) /DIS(newline)
1182: /DIS(due_day()) /DIS(newline)
1183:
1184: Output:
1185: Mon, May 3, 1999 at 08:00. \newline
1186: Thr, May 6, 1999 at 08:00. \newline
1187: Fri, May 7, 1999 at 08:00. \newline
1188: Thr, May 6, 1999.
1189: \end{verbatim}
1190: \\ \hline
1191: %************************************
1192: \end{tabular}\end{center}}
1193: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1194: {\small
1195: \begin{center}\begin{tabular}{|p{2.9cm}|p{14.2cm}|} \hline
1196: { Functions}& Description, sample quizzer code and output \\ \hline
1197: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1198: \index{get\_seed()}\index{set\_seed()}{\tt get\_seed(), set\_seed()}
1199: & get\_seed() returns the value of the seed for the random number generator.
1200: set\_seed() allows resetting the value of the random number generated seed to
1201: an earlier value of the seed.
1202: \begin{verbatim}
1203: /LET seed1=get_seed()
1204: /LET number=random(1,1000,1)
1205: The current seed is: /DIS(seed1)
1206: The random number was: /DIS(number)
1207:
1208: /LET seed2=get_seed()
1209: /LET number=random(1,1000,1)
1210: The current seed is: /DIS(seed2)
1211: The random number was: /DIS(number)
1212:
1213: /LET any_variable=set_seed(seed1)
1214: /LET seed3=get_seed()
1215: /LET number=random(1,1000,1)
1216: The current seed is: /DIS(seed3)
1217: The random number was: /DIS(number)
1218:
1219: Output:
1220: The current seed is: 1516840802 1582785437
1221: The random number was: 727
1222: The current seed is: 539910159 1530382995
1223: The random number was: 671
1224: The current seed is: 1516840802 1582785437
1225: The random number was: 727
1226: \end{verbatim}
1227: Note: get\_seed() works like name(), i.e. /DIS(get\_seed()) displays the current seed. On the other hand, set\_seed() behaves like most other functions, i.e. seed=set\_seed(previous\_seed\_variable) which is similar to y=sin(x).
1228: \\ \hline
1229: %*************************************
1230: \index{sub\_string(a,b,c)}{\tt sub\_string(a,b,c)}
1231: & Allows instructor to retrieve part of a previously defined string (a=initial
1232: string, b=place of starting character, c=length of substring).
1233: \begin{verbatim}
1234: /LET string1="Have a nice day."
1235: /LET string2=sub_string(string1,8,4)
1236: /DIS(string2)
1237:
1238: Output: nice \end{verbatim}
1239: \\ \hline
1240: \end{tabular}\end{center}}
1241: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1242: {\small
1243: \begin{center}\begin{tabular}{|p{3.1cm}|p{14.0cm}|} \hline
1244: { Functions}& Description, sample quizzer code and output \\ \hline
1245: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1246: %*************************************
1247: \index{array[xx]}{\tt array[xx]}
1248: & "xx" can be a variable or a calculation. For example, for the array with name "NaMe":
1249: \begin{verbatim}
1250: /LET index=1
1251: /WHILE ( index<10 )
1252: /LET NaMe[index]=index*10.5
1253: /LET index=index+1
1254: /ENDWHILE
1255: The value of NaMe[7] is /DIS(NaMe[7]:1f)
1256:
1257: Output: The value of NaMe[7] is 73.5 \end{verbatim}
1258: \\ \hline
1259: %**************************************
1260: %*************************************
1261: \index{array\_max(Name)}{\tt array\_max(Name)},
1262: \index{array\_min(Name)}{\tt array\_min(Name)}
1263: & For example, for the array NaMe[xx] defined above:
1264: \begin{verbatim}
1265: maximum value of array element = /DIS(array_max(NaMe))
1266: minimum value of array element = /DIS(array_min(NaMe))
1267:
1268: Output: maximum value of array element = 94.5
1269: minimum value of array element = 10.5 \end{verbatim}
1270: \\ \hline
1271: %*************************************
1272: \index{array\_moments(B,A)}{\tt array\_moments(B,A)}
1273: & The moments of array A[] are put into array B[i] with i=0 to 4.
1274: B[0]=number of elements, B[1]=mean, B[2]=variance, B[3]= skewness, and B[4]=kurtosis. Note (standard deviation =square root of variance. Example (using NaMe[] array above]
1275: \begin{verbatim}
1276: /LET elements=array_moments(MMT,NaMe)
1277: Displaying the moments:
1278: number of elements=/DIS(MMT[0]:2f)
1279: mean=/DIS(MMT[1]:2f)
1280: variance=/DIS(MMT[2]:2f)
1281: skewness=/DIS(MMT[3]:2f)
1282: kurtosis=/DIS(MMT[4]:2f)
1283:
1284: Output: Displaying the moments:
1285: number of elements=9
1286: mean=52.50
1287: variance=826.87
1288: skewness=0.00
1289: kurtosis=-1.60 \end{verbatim}
1290: \\ \hline
1291: %*************************************
1292: \index{init\_array(Name)}{\tt init\_array(Name)}
1293: & Important to initialize when the same array name is used in more than 1 problem in a set. For example, for the array NaMe[xx] above:
1294: \begin{verbatim}
1295: Current value of NaMe[5] = /DIS(NaMe[5]:1f)
1296: /LET deletd=init_array(NaMe)
1297: New value of NaMe[5] = /DIS(NaMe[5]:1f)
1298: Number of array elements deleted = /DIS(deletd)
1299:
1300: Output: Current value of NaMe[5] = 52.5
1301: New value of NaMe[5] = VAR "NaMe[5]" NOT DEFINED!
1302: Number of array elements deleted = 9 \end{verbatim}
1303: \\ \hline
1304: %*************************************
1305: \end{tabular}\end{center}}
1306: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1307: {\small
1308: \begin{center}\begin{tabular}{|p{4.9cm}|p{12.2cm}|} \hline
1309: { Functions}& Description, sample quizzer code and output \\ \hline
1310: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1311: \index{random\_normal()}
1312: \index{random\_beta()}
1313: \index{random\_gamma()}
1314: \index{random\_exponential()}
1315: \index{random\_poisson()}
1316: \index{random\_chi()}
1317: \index{random\_noncentral\_chi()}
1318: \tt{random\_normal(,,,,)}
1319: \tt{random\_beta(,,,,)}
1320: \tt{random\_gamma(,,,,)}
1321: \tt{random\_exponential(,,,)}
1322: \tt{random\_poisson(,,,)}
1323: \tt{random\_chi(,,,)}
1324: \tt{random\_noncentral\_chi(,,,,)}
1325: &
1326: \tt{random\_normal(return\_array,item\_cnt,seed,av,std\_dev)} \newline
1327: \tt{random\_beta(return\_array,item\_cnt,seed,aa,bb)} \newline
1328: \tt{random\_gamma(return\_array,item\_cnt,seed,a,r)} \newline
1329: \tt{random\_exponential(return\_array,item\_cnt,seed,av)} \newline
1330: \tt{random\_poisson(return\_array,item\_cnt,seed,mu)} \newline
1331: \tt{random\_chi(return\_array,item\_cnt,seed,df)} \newline
1332: \tt{random\_noncentral\_chi(return\_array,item\_cnt,seed,df,xnonc)} \newline
1333:
1334: Generate item\_cnt of random numbers according to the particular distribution
1335: with the specified parameters and seed and store them in the array named return\_array.
1336: \\ \hline
1337: Sample Code&Sample Code for \tt{random\_poisson(,,,)} and \tt{random\_normal(,,,,)} is shown on the next page.
1338: \\ \hline
1339: %*************************************
1340: \end{tabular}\end{center}}
1341: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1342: {\small
1343: \begin{center}\begin{tabular}{|p{3.3cm}|p{13.8cm}|} \hline
1344: %{ Functions}& Description, sample quizzer code and output \\ \hline
1345: %*************************************
1346: \index{random\_poisson(,,,)}{\tt random\_poisson(,,,)}
1347: & FORM: random\_poisson(return\_array,item\_cnt,seed,av) \\
1348: & Array name and 3 parameters needed. Below, the return\_array is called ``RET":
1349: \begin{verbatim}/LET dleted=init_array(RET) // initialize array "RET"
1350: /LET myseed=777 // could be = random(1,10000)
1351: /LET count=10
1352: /LET average=2.2
1353: /LET samples=random_poisson(RET,count,myseed,average)
1354: samples=/DIS(samples); Note `samples' it is the same as `count'
1355: /LET j=0
1356: /WHILE (j <10)
1357: RET[/DIS(j)] = /DIS(RET[j])
1358: /LET j=j+1
1359: /ENDWHILE
1360: OUTPUT: samples=15; Note `samples' it is the same as `count'
1361: RET[0] = 3 RET[1] = 0
1362: RET[2] = 3 RET[3] = 1
1363: RET[4] = 2 RET[5] = 4
1364: RET[6] = 2 RET[7] = 2
1365: RET[8] = 1 RET[9] = 2
1366: \end{verbatim}
1367: \\ \hline
1368: %**************************************
1369: %*************************************
1370: \index{random\_normal(,,,,)}{\tt random\_normal(,,,,)}
1371: & FORM: random\_normal(return\_array,item\_cnt,seed,av,std\_dev) \\
1372: & Array name and 4 parameters needed. (return\_array called ``RET")
1373: \begin{verbatim}/LET dleted=init_array(RET) // initialize array "RET"
1374: /LET myseed=555 // could be = random(1,10000)
1375: /LET count=10
1376: /LET average=6.2
1377: /LET stddev=2
1378: /LET samples=random_normal(RET,count,myseed,average,stddev)
1379: samples=/DIS(samples); Note `samples' it is the same as `count'
1380: /LET j=0
1381: /WHILE (j <10)
1382: /LET RETB[j] = roundto(RET[j],2) // This array is rounded to 2 places
1383: RET[/DIS(j)] = /DIS(RET[j]:4f) and RETB[/DIS(j)] = /DIS(RETB[j]:2f)
1384: /LET j=j+1
1385: /ENDWHILE
1386: OUTPUT: samples=15; Note `samples' it is the same as `count'
1387: RET[0] = 2.9195 and RETB[0] = 2.92
1388: RET[1] = 6.4934 and RETB[1] = 6.49
1389: RET[2] = 7.2427 and RETB[2] = 7.24
1390: RET[3] = 7.0054 and RETB[3] = 7.01
1391: RET[4] = 7.1111 and RETB[4] = 7.11
1392: RET[5] = 8.8491 and RETB[5] = 8.85
1393: RET[6] = 6.9555 and RETB[6] = 6.96
1394: RET[7] = 9.7349 and RETB[7] = 9.73
1395: RET[8] = 8.1034 and RETB[8] = 8.10
1396: RET[9] = 6.8346 and RETB[9] = 6.83 \end{verbatim}
1397: \\ \hline
1398: %**************************************
1399: %*************************************
1400: \end{tabular}\end{center}}
1401: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1402: \clearpage
1403:
1404:
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