EquationImplicitFunction1: Difference between revisions

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{{historical}}
<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/EquationImplicitFunction.html a newer version of this problem]</p>
<h2>Answer is an Equation that Implicitly Defines a Function</h2>
<h2>Answer is an Equation that Implicitly Defines a Function</h2>


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This PG code shows how to have an answer that is an equation that implicitly defines a function.
This PG code shows how to have an answer that is an equation that implicitly defines a function.
</p>
</p>
* Download file: [[File:EquationImplicitFunction1.txt]] (change the file extension from txt to pg when you save it)
<!-- * File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1.pg FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1.pg] -->
* File location in NPL: <code>FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1.pg</code>
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1_PGML.pg FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1_PGML.pg]


<br clear="all" />
<br clear="all" />
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<tr valign="top">
<tr valign="top">
<th> PG problem file </th>
<th style="width: 50%"> PG problem file </th>
<th> Explanation </th>
<th> Explanation </th>
</tr>
</tr>
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DOCUMENT();   
DOCUMENT();   


loadMacros(
loadMacros('PGstandard.pl','MathObjects.pl',
"PGstandard.pl",
  'parserImplicitEquation.pl','PGML.pl','PGcourse.pl');
"MathObjects.pl",
"parserImplicitEquation.pl",
"AnswerFormatHelp.pl",
);    
 
TEXT(beginproblem());
TEXT(beginproblem());
</pre>
</pre>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
<td style="background-color:#ffffdd;border:black 1px dashed;">
<pre>
<pre>
Context("ImplicitEquation");
Context('ImplicitEquation');
Context()->{error}{msg}{
Context()->{error}{msg}{
"Can't find any solutions to your equation"} = " ";
"Can't find any solutions to your equation"} = ' ';
Context()->{error}{msg}{
Context()->{error}{msg}{
"Can't generate enough valid points for comparison"} = " ";
"Can't generate enough valid points for comparison"} = ' ';


Context()->variables->set(
Context()->variables->set(
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$b = random(1,5,1);
$b = random(1,5,1);
$r = random(2,5,1);
$r = random(2,5,1);
$p = Compute("($a,$b)");


$answer = ImplicitEquation(
$answer = ImplicitEquation(
   "(x-$a)^2 + (y-$b)^2 = $r^2",
   "(x-$a)^2 + (y-$b)^2 = $r^2",
   solutions=>[  
   solutions=>[
     [$a,$b+$r],
     [$a,$b+$r],
     [$a,$b-$r],
     [$a,$b-$r],
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<p>
<p>
<b>Setup:</b>  
<b>Setup:</b>  
We quash some error messages by redefining them to be a blank string <code>" "</code> (notice the space).  Since the circle will always be contained in a rectangle with two opposite corners at <code>(-4,-4)<code> and <code>(10,10)</code>, we set the limits for the variables x and y to be outside of this rectangle.  The <code>ImplicitEquation</code> object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator.
We quash some error messages by redefining them to be a blank string <code>" "</code> (notice the space).  Since the circle will always be contained in a rectangle with two opposite corners at <code>(-4,-4)</code> and <code>(10,10)</code>, we set the limits for the variables x and y to be outside of this rectangle.  The <code>ImplicitEquation</code> object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator.
</p>
</p>
<p>
<p>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
<td style="background-color:#ffdddd;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML
BEGIN_TEXT
Enter an equation for a circle in the [`xy`]-plane
Enter an equation for a circle in the xy-plane  
of radius [` [$r] `] centered at [` [$p] `].
of radius \( $r \) centered at \( ($a,$b) \).
 
$BR
[________________________]{$answer}
$BR
 
\{ ans_rule(40) \}
[@ helpLink('equation') @]*
\{ AnswerFormatHelp("equation") \}
END_PGML
END_TEXT
Context()->normalStrings;
</pre>
</pre>
<td style="background-color:#ffcccc;padding:7px;">
<td style="background-color:#ffcccc;padding:7px;">
<p>
<p>
<b>Main Text:</b>
<b>Main Text:</b>
</p>
</td>
</tr>
<!-- Answer evaluation section -->
<tr valign="top">
<td style="background-color:#eeddff;border:black 1px dashed;">
<pre>
$showPartialCorrectAnswers = 1;
ANS( $answer->cmp() );
</pre>
<td style="background-color:#eeccff;padding:7px;">
<p>
<b>Answer Evaluation:</b>
The answer evaluator used is very sensitive and finicky.  We strongly recommended that you read about it at [http://webwork.maa.org/pod/pg_TRUNK/macros/parserImplicitEquation.pl.html parserImplicitEquation.pl.html]
</p>
</p>
</td>
</td>
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<td style="background-color:#ddddff;border:black 1px dashed;">
<td style="background-color:#ddddff;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML_SOLUTION
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
Solution explanation goes here.
END_SOLUTION
END_PGML_SOLUTION
Context()->normalStrings;
 
COMMENT("MathObject version.");


ENDDOCUMENT();
ENDDOCUMENT();
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[[Category:Top]]
[[Category:Top]]
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[[Category:Sample Problems]]
[[Category:Sample Problems]]
[[Category:Subject Area Templates]]
[[Category:Subject Area Templates]]

Latest revision as of 09:43, 18 July 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem


Answer is an Equation that Implicitly Defines a Function

Click to enlarge

This PG code shows how to have an answer that is an equation that implicitly defines a function.


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();   

loadMacros('PGstandard.pl','MathObjects.pl',
  'parserImplicitEquation.pl','PGML.pl','PGcourse.pl');
TEXT(beginproblem());

Initialization: 

Context('ImplicitEquation');
Context()->{error}{msg}{
"Can't find any solutions to your equation"} = ' ';
Context()->{error}{msg}{
"Can't generate enough valid points for comparison"} = ' ';

Context()->variables->set(
  x=>{limits=>[-6,11]},
  y=>{limits=>[-6,11]},
);

$a = random(1,5,1);
$b = random(1,5,1);
$r = random(2,5,1);
$p = Compute("($a,$b)");

$answer = ImplicitEquation(
  "(x-$a)^2 + (y-$b)^2 = $r^2",
  solutions=>[
     [$a,$b+$r],
     [$a,$b-$r],
     [$a+$r,$b],
     [$a-$r,$b],
     [$a+$r*sqrt(2)/2,$b+$r*sqrt(2)/2],
  ]
);

Setup: We quash some error messages by redefining them to be a blank string " " (notice the space). Since the circle will always be contained in a rectangle with two opposite corners at (-4,-4) and (10,10), we set the limits for the variables x and y to be outside of this rectangle. The ImplicitEquation object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator.

If your equation is linear of the form x=3, 4x+3y=12, or 4x+3y+5z=21, or..., you should probably use the [ImplicitPlane1 implicit plane] context and answer evaluator. 

BEGIN_PGML
Enter an equation for a circle in the [`xy`]-plane
of radius [` [$r] `] centered at [` [$p] `].

[________________________]{$answer}

[@ helpLink('equation') @]*
END_PGML

Main Text: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution:

Templates by Subject Area

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