The Symbolic Engine

In addition to performing numerical calculations with PTC Mathcad, you can also perform operations on symbolic expressions that contain variables or mathematical symbols. PTC Mathcad returns the results in symbolic form.

In symbolic calculation, expressions are evaluated using the symbolic evaluation operator → rather than the numerical evaluation operator =. You can evaluate all of the standard PTC Mathcad operators and many built-in functions symbolically.

<region id="ID0EDUGLB" actualWidth="197.32933364629747" actualHeight="99.890667054653179" top="192.00000000000003" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="11">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <minus />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
          <id xml:space="preserve">x</id>
        </apply>
        <real>1</real>
      </apply>
      <command>
        <id xml:space="preserve">solve</id>
      </command>
      <symResult>
        <matrix rows="2" cols="1">
          <apply>
            <div />
            <apply>
              <plus />
              <apply>
                <nthRoot />
                <placeholder />
                <real>5</real>
              </apply>
              <real>1</real>
            </apply>
            <real>2</real>
          </apply>
          <apply>
            <div />
            <apply>
              <plus />
              <apply>
                <neg />
                <apply>
                  <nthRoot />
                  <placeholder />
                  <real>5</real>
                </apply>
              </apply>
              <real>1</real>
            </apply>
            <real>2</real>
          </apply>
        </matrix>
      </symResult>
    </symEval>
  </math>
</region>

The first result, which is evaluated with the equal sign, is a numerical approximation of the result of adding the two fractions. The number of displayed digits is dependent on the current setting of Display Precision. The second result, which is evaluated with the symbolic evaluation operator, is exact. While the difference in this case is insignificant, in other problems, symbolic results can be substantially more accurate than results evaluated with the equal sign.

In PTC Mathcad, the constant π is an approximation to π and not its exact value. Therefore, the numeric evaluation of sin(π) is using that approximation and the result is, in fact, its sin. That isn’t a bug in sin, it’s an artifact of what happens when you approximate a real number.