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From: Chris S. <san...@us...> - 2005-11-09 13:00:47
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Update of /cvsroot/stack/stack-1-0/lang/en/doc In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv4922/lang/en/doc Modified Files: author_gettingstarted.php Log Message: Index: author_gettingstarted.php =================================================================== RCS file: /cvsroot/stack/stack-1-0/lang/en/doc/author_gettingstarted.php,v retrieving revision 1.8 retrieving revision 1.9 diff -C2 -d -r1.8 -r1.9 *** author_gettingstarted.php 8 Nov 2005 19:39:42 -0000 1.8 --- author_gettingstarted.php 9 Nov 2005 13:00:35 -0000 1.9 *************** *** 393,396 **** --- 393,510 ---- item as being entirely self contained. </p> + <h2>Expressions, Equations, Inequalities, Sets, Lists, and Matrices</h2> + + There are six kinds of mathematical objects in STACK. + + <ol> + <li><b>Expressions</b><br /> + Expressions are the basic mathematical objects, such as polynomials. Anything not + considered to be one of the "types" below is an "expression". + </li> + + <li><b>Equations</b><br /> + It is possible for the student to enter an equation, such as + <pre> y=x^2-1</pre> + You might like to consider + looking at the <?php stack_doc_dispstackqfield('SyntaxHint','stackOptions'); ?> option, + to help the student know the form/type that their answer should take. + </li> + + <li><b>Inequalities</b><br /> + Maxima only allows single inequalities, such as + <pre>x-1>y</pre> + Chained inequalities, eg <tt>1<x<3</tt> or inequalities joined by + logical connectives, eg <tt>1<x and x<3</tt> are not currently supported. + </li> + + <li><b>Sets</b><br /> + In Maxima sets are not native and so STACK uses + <a href="maximadocs/maxdoc/nset.html"><tt>nset</tt></a> which is automatically loaded. + Note that, in addition to Maxima's use of <tt>set(a1,a2,...,an)</tt> + to construct a set with members <em>a1,a2,...,an</em>, STACK allows the use of + curly braces: <tt>{a1,a2,...,an}.</tt> + </li> + + <li><b>Lists</b><br /> + In Maxima ordered lists are entered using square brackets, for example as + <pre>p:[1,1,2,x^2]</pre> + An element is accessed using the syntax <tt>p[1]</tt> + </li> + + <li><b>Matrices</b><br /> + The basic syntax for a matric is + <pre> + p:matrix([1,2],[3,4]) + </pre> + Each row is a <em>list</em>. Elements are accessed as <tt>p[1,2]</tt> etc. + </li> + </ol> + + <p>Please read Section 6 of <a href="maximadocs/minimal-maxima.pdf">Minimal-Maxima</a> for more examples.</p> + + <h2>The AlgEquiv Answer test.</h2> + + The AlgEquiv Answer Test does its best to cope with each of the "types" of objects. Let us assume + we are comparing two inputs, called <tt>SAns</tt> and <tt>TAns</tt> with this test, where the first + is the student's answer and the second the teacher's. + + <p><b>Validity</b><br /> + The "types" of the teacher's and student's answer should match. If + not, then the attempt is <em>invalid</em>, rather than <em>incorrect</em>, and + feedback is give. Eg, if the teacher types in an equation, but + the student an expression the test will say so.</p> + + <p><b>Correctness</b><br /> + + Once we have two objects, <tt>SAns</tt> and <tt>TAns</tt>, of the same type we + proceed as follows. + + <ol> + <li><b>Expressions</b><br /> + We simplify <tt>(SAns-TAns)</tt> in as many ways as + possible, and compare the result to algebraic 0. + </li> + + <li><b>Equations</b><br />The canonical form for equations, such as <tt>SAns</tt>, is + the fully simplification of <tt>RHS(SAns)-LHS(SAns))</tt>. We compare this + with <tt>+-</tt> the corresponding expression for <tt>TAns</tt>. + </li> + + <li><b>Inequalities</b><br />The canonical form for inequalities in the form + <tt>? > 0</tt> or <tt>? >= 0</tt> where we fully simplify the ?'s. Comparisons are + then made on these forms of the inequalities. + </li> + + <li><b>Sets</b><br /> + Elements of sets are simplified as fully as possible, and + equations and inequalities put in canonical forms. Set comparison + is then made on the expressions. This is subtly different from + the comparison performed in (1), since we are comparing + expressions, not simplifying the differences of expressions and + comparing with zero. + + If incorrect, feedback is given in the form of the set difference + between the simplified <tt>SAns</tt> and <tt>TAns</tt>. + </li> + + <li><b>Lists</b><br /> + If lists are of unequal length, then the attempt is + valid but incorrect. For lists of the same length, the above + procedure is applied recursively to corresponding elements of + lists. + + If any of the elements is incorrect or invalid, feedback is + provided. + </li> + + <li><b>Matrices</b><br />Currently matrices mimic the procedure in (1). They + should probably be more like (5), since it is perfectly possible + to have a matrix with entries which are lists, sets, etc etc. eg + <pre> + matrix([matrix([1,2],[3,4]),2],[x>3,set(4,x^2)]); + </pre> + </li> + </ol> + </p> <?php *************** *** 470,506 **** ?> - - <h2>Lists, sets, equations, inequalities and matrices</h2> - - It is possible for the student to enter expressions which are - lists, sets, equations, inequalities and matrices. - - The <?php stack_doc_dispstackqfield('AnsTest','stackOptions'); ?> <tt>AlgEquiv</tt> can - be applied to all of these kinds of objects. - - <h3>Lists</h3> - In Maxima ordered lists are entered using square brackets, for example as - <pre>p:[1,1,2,x^2]</pre> - An element is accessed using the syntax <tt>p[1]</tt> - - <h3>Sets</h3> - In Maxima sets are not native and so STACK uses - <a href="maximadocs/maxdoc/nset.html"><tt>nset</tt></a> which is automatically loaded. - Note that, in addition to Maxima's use of <tt>set(a1,a2,...,an)</tt> - to construct a set with members <em>a1,a2,...,an</em>, STACK allows the use of - curly braces: <tt>{a1,a2,...,an}.</tt> - - <h3>Equations and Inequalities</h3> - It is possible for the student to enter an equation, such as - <pre> y=x^2-1</pre> - The <tt>AlgEquiv</tt> answer test is useful here. You might like to consider - looking at the <?php stack_doc_dispstackqfield('SyntaxHint','stackOptions'); ?> option. - - <h3>Matrices</h3> - The basic syntax for a matric is - <pre> - p:matrix([1,2],[3,4]) - </pre> - Each row is a <em>list</em>. Elements are accessed as <tt>p[1,2]</tt> etc. - - <p>Please read Section 6 of <a href="maximadocs/minimal-maxima.pdf">Minimal-Maxima</a> for more examples.</p> --- 584,585 ---- |
