<pl-card header="An example in which complex numbers are not allowed (<code>allow-complex="false"</code>)">
<pl-question-panel>
<p>Suppose $$y = a x + b.$$ Assuming that $a \neq 0$, solve for $x$.</p>
<p>The attribute <code>initial-value</code> pre-fills the input the first time it is rendered so students can begin from a suggested expression.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Symbolic expression for x" answers-name="x" variables="a, b, y" label="$x=$" initial-value="(y - b)/a"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which complex numbers are allowed (<code>allow-complex="true"</code>)">
<pl-question-panel>
<p>Write an expression for the complex number $z$ whose argument is $a$ (in radians) and whose modulus is $m$.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="z" variables="a, m" allow-complex="true" label="$z=$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which the correct answer is specified as a string in <code>server.py</code>">
<pl-question-panel>
<p>Write an expression for the current $I$ in a resistor if the voltage is $V$ and the resistance is $R$.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="I" variables="V, R" label="$I=$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which we specify a different imaginary unit for display (<code>imaginary-unit-for-display="j"</code>)">
<pl-question-panel>
<p>Write an expression for the complex number $c$ whose real part is $a$ and whose imaginary part is $b$.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="c" variables="a, b" allow-complex="true" imaginary-unit-for-display="j" label="$c=$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which we specify the use of ln rather than log for display (<code>display-log-as-ln="true"</code>)">
<pl-question-panel>
<p>Write an expression for the derivative of $ln(x)*x$.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="lnx" variables="x" display-log-as-ln="true" label="$\dfrac{d}{dx} ln(x)*x =$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example that uses the formula editor input">
<pl-question-panel>
<p>Submit $\displaystyle {\rm test}\left(\sqrt{\frac{e^x}{x^2}}\right)$</p>
</pl-question-panel>
<pl-symbolic-input label="$y = $" aria-label="Function expression" formula-editor="true" answers-name="formula_editor" variables="x" show-score="false" custom-functions="test"></pl-symbolic-input>
</pl-card>
<pl-card header="An example that uses the formula editor with an initial value">
<pl-question-panel>
<p>Suppose $$y = a x + b.$$ Assuming that $a \neq 0$, solve for $x$.</p>
<p>The <code>initial-value</code> attribute works with the formula editor. The sympy expression is automatically converted to LaTeX for the editor display.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Symbolic expression for x" formula-editor="true" answers-name="formula_editor_initial" variables="a, b, y" label="$x=$" initial-value="(y - b)/a"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which we disable the display of simplified student submissions (<code>display-simplified-expression="false"</code>)">
<pl-question-panel>
<p>Write the expression $sin(atan(x))$.</p>
<p>Note that this expression will be simplified to $\frac{x}{\sqrt{x^2+1}}$ if <code>display-simplified-expression</code> is not disabled.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="nosimplify" variables="x" display-simplified-expression="false" label="$y =$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which we change display attributes">
<pl-question-panel>
<p>The size of the input box can be set with the attribute <code>size</code>, and the attribute <code>show-help-text="false"</code> removes the button for the help popup.
The attribute <code>placeholder</code> can be used to set the placeholder text. This box below has <code>size=5</code> instead of the default <code>size=35</code>.
</p>
<p>Write an expression for the first derivative of $\frac{1}{2} x^2$.</p>
</pl-question-panel>
<pl-symbolic-input answers-name="dx" variables="x" size="5" show-help-text="false" placeholder="" label="$\dfrac{d}{dx} \frac{1}{2}x^2 =$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which we allow a blank answer">
<pl-question-panel>
<p>The <code>allow-blank</code> attribute allows an expression to be left blank by the user and still be considered valid. By default a blank expression is equivalent to the expression <code>0</code>, unless the <code>blank-value</code> is used. The <code>placeholder</code> attribute allows setting custom placeholder text.</p>
<p>Simplify the expression $x^2+x+1$, or leave it blank if the expression cannot be simplified further.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Simplified expression for x" answers-name="simplify" variables="x" allow-blank="true" blank-value="x^2+x+1" placeholder="symbolic expression (blank is allowed)"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which a blank answer is the only correct answer">
<pl-question-panel>
<p>When <code>allow-blank="true"</code> is set, truly empty answers are also supported by setting <code>blank-value=""</code> (and potentially <code>correct-answer=""</code>).</p>
<p>Find a value for $x \in \mathbb{R}$ so that $x^2 = -1$. If there is no solution, leave the answer blank.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Simplified expression for x" correct-answer="" answers-name="simplify_blank" variables="x" allow-blank="true" blank-value="" placeholder="symbolic expression (blank is allowed)"></pl-symbolic-input>
</pl-card>
<pl-card header="An example where we use assumptions">
<pl-question-panel>
<p>Sometimes, certain expressions can only be treated as equivalent by sympy if additional assumptions are made. For example, consider that $\sqrt{B^2} = B$ is only true if $B \geq 0$. To use these, assumptions must be set in the <code>server.py</code> file when variables are declared.</p>
<p>Submit an expression equivalent to $\sqrt{B^2}$ when assuming $B > 0$.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Expression for B" answers-name="assumptions" variables="B"></pl-symbolic-input>
</pl-card>
<pl-card header="Another example where we use assumptions">
<pl-question-panel>
<p>Simplify $|C|$ assuming that $C \leq 0$.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Simplified expression for C" answers-name="assumptions_2" variables="C"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which trig functions are not allowed (<code>allow-trig-functions="false"</code>)">
<pl-question-panel>
<p>What is the value of $\cos(\pi) * x$?</p>
</pl-question-panel>
<pl-symbolic-input answers-name="no_trig" allow-trig-functions="false" variables="x" correct-answer="-x" label="$\cos(\pi) * x = $"></pl-symbolic-input>
</pl-card>
<pl-card header="Example using custom functions">
<pl-question-panel>
<p>Submit $f(x) + beef(\alpha)$, where $\alpha$ should be spelled out as <code>alpha</code> in the submission.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Function expression" answers-name="custom_function" variables="x,alpha" custom-functions="f,beef" correct-answer="f(x) + beef(alpha)"></pl-symbolic-input>
</pl-card>
<pl-card header="Another example with custom functions">
<pl-question-panel>
<p>Submit $beef(y) + the(y)$. We set <code>show-score="false"</code> to hide the score badge and <code>suffix="$= \text{where?}$"</code> to set the suffix.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Function expression" answers-name="custom_function_2" variables="y" show-score="false" custom-functions="beef,the" suffix="$= \text{where?}$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example with nested absolute value expressions">
<pl-question-panel>
<p>This example demonstrates handling of nested absolute value expressions. Submit the expression $|x+|-x+1+2+3+4||$.</p>
<p>Note: This tests the symbolic input's ability to handle complex nested absolute value expressions with multiple terms.</p>
</pl-question-panel>
<pl-symbolic-input aria-label="Nested absolute value expression" answers-name="nested_abs" variables="x" label="$y =$"></pl-symbolic-input>
</pl-card>
<pl-card header="An example that times-out.">
<pl-question-panel>
<p>This demonstrates a submission for which sympy takes an indeterminate amount of time to solve, when the answer is wrong.</p>
<p>Submit below $\exp(sin(n)) \cdot (1+ sin(n)^2)^{125}$. The actual answer is $\exp(\sin(n))*(1 + \sin(n)^{10})^{5}$, but the submission will timeout. </p>
</pl-question-panel>
<pl-symbolic-input aria-label="Timeout example" answers-name="timeout" variables="n" correct-answer="exp(sin(n))*(1 + sin(n)**10)**5"></pl-symbolic-input>
<br><br>
</pl-card>
<pl-card header="An example in which interval notation is allowed (<code>allow-sets="true"</code>)">
<pl-question-panel>
<p>Consider $f(x) = x^{-2} - 4$. Using intervals and set unions, find $\{ x | f(x) \leq 0 \}$.</p>
<i>Correct answer: $ (-\infty, -1/2] \cup [1/2, \infty) $</i>
</pl-question-panel>
<pl-symbolic-input formula-editor="true" allow-sets="true" aria-label="Set notation expression" answers-name="interval_notation" correct-answer="(-infty, -1/2] U [1/2, infty)"></pl-symbolic-input>
</pl-card>
<pl-card header="An example in which set notation is allowed (<code>allow-sets="true"</code>)">
<pl-question-panel>
<p>For which values of $\theta \in [0, 2\pi)$ does $\sin(\theta) = \cos(\theta)$? Express your answer as a set.</p>
<i>Correct answer: $\{\pi/4, 5\pi/4\}$</i>
</pl-question-panel>
<pl-symbolic-input formula-editor="true" allow-sets="true" aria-label="Set notation expression" answers-name="set_notation" label="$\theta \in$" correct-answer="{pi/4, 5pi/4}"></pl-symbolic-input>
</pl-card>
<pl-card header="Another example of set notation">
<pl-question-panel>
<p>Set theory defines numerals inductively: $0 = \{ \}$, and $n + 1 = \{ 0, 1, ..., n \}$ where each number is written in set-numeral form. What is the set numeral for 2? (Don't use any numbers!)</p>
<i>Correct answer: $\left\{ \{\}, \left\{ \{\} \right\} \right\}$</i>
</pl-question-panel>
<pl-symbolic-input formula-editor="true" allow-sets="true" aria-label="Set notation expression" answers-name="set_numerals" label="$2 =$" correct-answer="{ {}, { {} } }"></pl-symbolic-input>
</pl-card>