MediaWiki API result

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        "gapcontinue": "RecursivelyDefinedFunctions",
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        "main": {
            "*": "Subscribe to the mediawiki-api-announce mailing list at <https://lists.wikimedia.org/mailman/listinfo/mediawiki-api-announce> for notice of API deprecations and breaking changes."
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            "*": "Because \"rvslots\" was not specified, a legacy format has been used for the output. This format is deprecated, and in the future the new format will always be used."
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        "pages": {
            "2565": {
                "pageid": 2565,
                "ns": 0,
                "title": "Real (MathObject Class)",
                "revisions": [
                    {
                        "contentformat": "text/x-wiki",
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                        "*": "=== Real class ===\n\nThe Real class implements real numbers with \"fuzzy\" comparison (governed by the same tolerances and settings that control student answer checking).  For example, <code>Real(1.0) == Real(1.0000001)</code> will be true, while <code>Real(1.0) &lt; Real(1.0000001)</code> will be false.  Reals can be created in any Context, but the <code>Numeric</code> Context is the most frequently used for Reals.\n\n\n=== Creation ===\n\nReals are created via the <code>Real()</code> function, or by <code>Compute()</code>.  Reals can be added, subtracted, and so on, and the results will still be MathObject Reals.  Similarly, <code>sin()</code>, <code>sqrt()</code>, <code>ln()</code>, and the other functions return Real objects if their arguments are Reals.  For example:\n\n    Context(\"Numeric\");\n    \n    $a = Real(2);\n    $b = $a + 5;     # same as Real(7);\n    $c = sqrt($a);   # same as Real(sqrt(2));\n\nThis allows you to compute with Reals just as you would with native Perl real numbers.\n\n\n=== Pre-defined Reals ===\n\nThe value <code>pi</code> can be used in your Perl code to represent the value of <math>\\pi</math>.  Note that you must use <code>-(pi)</code> for <math>-\\pi</math> in Perl expressions (but not in strings that will be parsed by MathObjects, such as student answers or arguments to <code>Compute()</code>). For instance:\n\n    $a = pi + 2;              # same as Real(\"pi + 2\");\n    $b = 2 - (pi);            # same as Real(\"2 - pi\");\n    $c = sin(pi/2);           # same as Real(1);\n    $d = Compute(\"2 - pi\");   # parens only needed in Perl expressions\n\nThe value <code>e</code>, for the base of the natural log, <math>e</math>, can be used in student answers and parsed strings.\n\n    $e = Compute(\"e\");\n    $p = Compute(\"e^2\");\n\n\n=== Answer Checker ===\n\nAs with all MathObjects, you obtain an answer checker for a Real object via the <code>cmp()</code> method:\n\n    ANS(Real(2)->cmp);\n\nThe Real class supports the [[Answer_Checker_Options_(MathObjects)| common answer-checker options]], and the following additional options:\n\n{| class=\"wikitable\"\n! Option !! Description !! style=\"padding:5px\" | Default\n|- style=\"vertical-align: top\"\n| style=\"padding: 5px; white-space: nowrap\" | <code>ignoreInfinity => 1</code> or <code>0</code>\n| style=\"padding: 5px\" | Do/don't report type mismatches if the student enters an infinity.\n| style=\"text-align:center\" | <code>1</code>\n|}\n\n\n=== Methods ===\n\nThe Real class supports the [[Common MathObject Methods]].  There are no additional methods for this class.\n\nThe command\n\n    Parser::Number::NoDecimals();\n\nwill add a check so that a number with decimal places is not allowed.  This can be used to require students to enter values in terms of `pi` or `sqrt(2)` for example.  You can also supply a Context as an argument to disallow decimals in that context:\n\n    Parser::Number::NoDecimals($context);\n\nWithout a parameter, the current context is assumed.\n\n\n=== Properties ===\n\nThe Real class supports the [[Common MathObject Properties]], and the following additional ones:\n\n{| class=\"wikitable\"\n! Property !! Description !! style=\"padding:5px\" | Default\n\n|- style=\"vertical-align: baseline\"\n| style=\"padding: 5px; white-space: nowrap\" | <code>$r->{period}</code>\n| style=\"padding: 5px\" | When set, this value indicates that the real is periodic, with period given by this value.  So angles might use <code>period</code> set to <code>2*pi</code>.\n\n'''Example:'''\n: <code>$r = Real(pi/3)->with(period => 2*pi);</code>\n: <code>$r == 7*pi/3;  # will be true</code>\n| style=\"text-align:center\" | <code>undef</code>\n\n|- style=\"vertical-align: baseline\"\n| style=\"padding: 5px; white-space: nowrap\" | <code>$r->{logPeriodic}</code>\n| style=\"padding: 5px\" | When <code>period</code> is defined, and <code>logPeriodic</code> is set to <code>1</code> this indicates that the periodicity is logarithmic (i.e., the period refers to the log of the value, not the value itself).\n\n'''Example:'''\n: <code>$r = Real(4)->with(period => 10, logPeriodic => 1);</code>\n: <code>$r == 88105;  # true since 88105 is nearly exp(10+log(4))</code>\n| style=\"text-align:center\" | <code>0</code>\n|}\n\n\n<br>\n\n[[Category:MathObject_Classes]]\n[[Category:MathObjects]]"
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            "1339": {
                "pageid": 1339,
                "ns": 0,
                "title": "RecursiveSequence1",
                "revisions": [
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                        "contentformat": "text/x-wiki",
                        "contentmodel": "wikitext",
                        "*": "{{historical}}\n\n<p style=\"font-size: 120%;font-weight:bold\">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Sequences/RecursiveSequence.html a newer version of this problem]</p>\n\n<h2>Sequences and Recursively Defined Functions</h2>\n\n[[File:RecursiveSequence1.png|300px|thumb|right|Click to enlarge]]\n<p style=\"background-color:#f9f9f9;border:black solid 1px;padding:3px;\">\nThis PG code shows how to add a named function to the context and use it to ask students to come up with a recursive formula.\n</p>\n* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/RecursiveSequence1.pg FortLewis/Authoring/Templates/Sequences/RecursiveSequence1.pg]\n* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/RecursiveSequence1_PGML.pg FortLewis/Authoring/Templates/Sequences/RecursiveSequence1_PGML.pg]\n\n<br clear=\"all\" />\n<p style=\"text-align:center;\">\n[[SubjectAreaTemplates|Templates by Subject Area]]\n</p>\n\n<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\">\n\n<tr valign=\"top\">\n<th> PG problem file </th>\n<th> Explanation </th>\n</tr>\n\n\n<!-- Problem tagging section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#eeeeee;border:black 1px dashed;\">\n[http://webwork.maa.org/wiki/Tagging_Problems Problem tagging data]\n</td>\n<td style=\"background-color:#eeeeee;padding:7px;\">\n<p>\n<b>Problem tagging:</b>\n</p>\n</td>\n</tr>\n\n\n<!-- Initialization section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#ddffdd;border:black 1px dashed;\">\n<pre>\nDOCUMENT();\n\nloadMacros(\n\"PGstandard.pl\",\n\"MathObjects.pl\",\n\"parserFunction.pl\",\n);\n\nTEXT(beginproblem());\n</pre>\n</td>\n<td style=\"background-color:#ddffdd;padding:7px;\">\n<p>\n<b>Initialization:</b>\nWe will be defining a new named function and adding it to the context, and the easiest way to do this is using <code>parserFunction.pl</code>.  There is a more basic way to add functions to the context, which is explained in example 2 at\n[http://webwork.maa.org/wiki/AddingFunctions AddingFunctions]\n</p>\n</td>\n</tr>\n\n\n<!-- Setup section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#ffffdd;border:black 1px dashed;\">\n<pre>\nContext(\"Numeric\")->variables->are(n=>\"Real\");\nparserFunction(f => \"sin(pi^n)+e\");\n\n$fn = Formula(\"3 f(n-1) + 2\");\n</pre>\n</td>\n<td style=\"background-color:#ffffcc;padding:7px;\">\n<p>\n<b>Setup:</b> \nWe define a new named function <code>f</code> as something the student is unlikely to guess.  The named function <code>f</code> is, in some sense, just a placeholder since the student will enter expressions involving <code>f(n-1)</code>, WeBWorK will interpret it internally as <code>sin(pi^(n-1))+e</code>, and the only thing the student sees is <code>f(n-1)</code>.   If the \nrecursion has an closed-form solution (e.g., the Fibonacci numbers are given by f(n) = (a^n - (1-a)^n)/sqrt(5) where a = (1+sqrt(5))/2) and you want to allows students to enter the closed-form solution, it would be good to define f using that explicit solution in case the student tries to answer the question by writing out the explicit solution (a^n - (1-a)^n)/sqrt(5) instead of using the shorthand f(n).\n</p>\n</td>\n</tr>\n\n<!-- Main text section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#ffdddd;border:black 1px dashed;\">\n<pre>\nContext()->texStrings;\nBEGIN_TEXT\nThe current value \\( f(n) \\) is three \ntimes the previous value, plus two.  Find\na recursive definition for \\( f(n) \\).  \nEnter \\( f_{n-1} \\) as \\( f(n-1) \\).\n$BR\n\\( f(n) \\) = \\{ ans_rule(20) \\} \nEND_TEXT\nContext()->normalStrings;\n</pre>\n<td style=\"background-color:#ffcccc;padding:7px;\">\n<p>\n<b>Main Text:</b>\nWe should tell students to use function notation rather than subscript notation so that they aren't confused about syntax.\n</p>\n</td>\n</tr>\n\n<!-- Answer evaluation section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#eeddff;border:black 1px dashed;\">\n<pre>\n$showPartialCorrectAnswers=1;\n\nANS( $fn->cmp() );\n</pre>\n<td style=\"background-color:#eeccff;padding:7px;\">\n<p>\n<b>Answer Evaluation:</b>\n</p>\n</td>\n</tr>\n\n<!-- Solution section -->\n\n<tr valign=\"top\">\n<td style=\"background-color:#ddddff;border:black 1px dashed;\">\n<pre>\n\nContext()->texStrings;\nBEGIN_SOLUTION\nSolution explanation goes here.\nEND_SOLUTION\nContext()->normalStrings;\n\nCOMMENT('MathObject version.');\n\nENDDOCUMENT();\n</pre>\n<td style=\"background-color:#ddddff;padding:7px;\">\n<p>\n<b>Solution:</b>\n</p>\n</td>\n</tr>\n</table>\n\n<p style=\"text-align:center;\">\n[[SubjectAreaTemplates|Templates by Subject Area]]\n</p>\n\n[[Category:Top]]\n[[Category:Sample Problems]]\n[[Category:Subject Area Templates]]"
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