PreTeXt Sample Book Abstract Algebra (SAMPLE ONLY)

<exercises xml:id="runestone-hodgepodge">

                      <title>Hodgepodge</title>

                      <exercise label="multifile-program-2">

                        <statement>

                          <p>
This is a test of accessing program resources across pages by relying on what is in the database.
                          </p>

                        </statement>

                        <program interactive="activecode" add-files="addh-v1 addcpp-v1" compile-also="addcpp-v1" language="cpp">

                
                #include "add.h"
                #include &lt;iostream&gt;
                using namespace std;
                int main() {
                    int a = 1;
                    int b = 2;
                    cout &lt;&lt; "The sum of " &lt;&lt; a &lt;&lt; " and " &lt;&lt; b &lt;&lt; " is " &lt;&lt; add(a, b) &lt;&lt; endl;
                }
                        </program>

                      </exercise>

                      <exercise label="true-false-exercise-with-tasks-in-exercises">

                        <title>With Tasks in an Exercises Division</title>

                        <introduction>

                          <p>
Structured with task, recycled earlier from earlier, to make sure that the tasks do not get counted as Runestone reading activities (since they are inside an <tag>exercise</tag> inside of an <tag>exercises</tag> division.
                          </p>

                        </introduction>

                        <task label="true-false-task-in-exercises">

                          <title>True/False</title>

                          <idx>vector space</idx>

                          <statement correct="no">

                            <p>
Every vector space has finite dimension.
                            </p>

                          </statement>

                          <feedback>

                            <p>
The vector space of all polynomials with finite degree has a basis, <m>B = \{1,x,x^2,x^3,\dots\}</m>, which is infinte.
                            </p>

                          </feedback>

                          <hint>

                            <p>

                              <m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>, has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws"/>.  [Cross-reference is just a demo, content is not relevant.]  What happens if we relax the defintion and remove the parameter <m>n</m>?

                            </p>

                          </hint>

                        </task>

                        <task label="short-answer-task-in-exercises">

                          <statement>

                            <p>
Explain your reasoning in the previous question.
                            </p>

                          </statement>

                          <response/>

                        </task>

                        <conclusion>

                          <p>
A sequence of <tag>task</tag> can have a <tag>conclusion</tag>, like this one, even if they do not see much use in practice.
                          </p>

                        </conclusion>

                      </exercise>

                      </exercises>