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<h3>Exercises</h3>
<ol>
<li>Create a top level <var>Calculator</var> object and make appropriate changes to lower level components.</li>
<p>
<li>Add two new built in functions to the calculator, <var>sqr</var> and <var>cube</var>. <var>Sqr</var> squares its argument and <var>cube</var> cubes it (raises to the third power).</li>
<p>
<li>Add the recognition of unary plus to the calculator. Make necessary modifications to the scanner and the parser. Add a new node, <var>UPlusNode</var>. The calculator should be able to deal correctly with such expressions as</li>
<p>
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<pre>x = +2
2 * + 7
1 / (+1 - 2)
</pre></table><!-- End Code -->
<p>
<li>Add powers to the calculator according to the following productions</li>
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<pre><b>Factor</b> is <b>SimpleFactor ^ Factor</b> // a ^ b (a to the power of b)
or <b>SimpleFactor</b>
<b>SimpleFactor</b> is <b>( Expression )</b> // parenthesized expression
or <b>Number</b> // literal floating point number
or <b>Identifier ( Expression )</b>// function call
or <b>Identifier</b>// symbolic variable
or <b>- Factor</b> // unary minus</pre>
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<p>
<li>To all nodes in the parse tree add virtual method <var>Print()</var>. When <var>Print()</var> is called on the root of the tree, the whole tree should be displayed in some readable form. Use varying indentation (by printing a number of spaces at the beginning of every line) to distinguish between different levels of the tree. For instance</li>
<p>
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<pre>void AddNode::Print (int indent) const
{
_pLeft->Print (indent + 2);
Indent (indent);
cout << "+" << endl;
_pRight->Print (indent + 2);
cout << endl;
}
</pre></table><!-- End Code --><p>where <var>Indent</var> prints as many spaces as is the value of its argument.
<p>
<li>Derivatives of some of the built-in functions are, respectively</li>
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<pre>sin(x) -> cos(x)
cos(x) -> -sin(x)
exp(x) -> exp(x)
log(x) -> 1/x
sqrt(x) -> 1/(2 * sqrt(x))
</pre></table><!-- End Code --><p>The derivative of a sum is a sum of derivatives, the derivative a product is given by the formula
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<pre>(f(x) * g(x))⌨️ 快捷键说明
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