Numerical Tolerance

Explains the difference in tolerance type and numerical tolerance.

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Complete Code

Download file: NumericalTolerance.pg

See Also

PG problem file

Explanation

DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');

Preamble

These standard macros need to be loaded. 
$ans1 = Compute('1.5708')->cmp(
    tolType   => 'absolute',
    tolerance => .0001,
);

$ans2 = Compute('1.5708');

Context('Numeric')->flags->set(
    tolerance => 0.0001,
    tolType   => 'absolute',
);

$ans3 = Compute('1.5708');

Setup

This shows three different ways of setting the toltype and tolerance of the answer. The tolType can be absolute (specifying a decimal distance from the correct answer that will be allowed) or relative (specifying a percent error that will be allowed).

Thus if the correct answer is 17, a tolerance of 0.01 will mean that the student answer must be in the interval (16.99,17.01) if the tolType is absolute, and in the interval (16.83,17.17) if tolType is relative (which is the default).

  1. The cmp method is called directly on the MathObject returned by the Compute call, and the tolerance and tolType are passed as options to the cmp call. Note that this answer is in the current context which in this case would be the default Numeric context since no other context has been specified.

  2. The cmp call is called on the MathObject returned by the Compute call, expect that is done when the answer is specified in the PGML problem statement. Note that this answer is also in the current default Numeric context. Also note that this is really the same as the first case. It is just a different time that the cmp call is made.

  3. The tolerance and toltype context flags are set. This is useful if the desired toltype or tolerance are the same for many answers. Typically this would be done at the beginning of the setup section. However, note that calling Context('Numeric') as is done in this example creates a new copy of the unmodified default Numeric context (not a copy of any Numeric contexts previously created and used in the problem). So the context flags specified here do not apply to any answers created before this. Hence it is also useful to do this later in the setup for unrelated answers.

BEGIN_PGML
For each of the following Enter your answer accurate to four decimal places .

1. Enter [``\frac{\pi}{2} =``] [____]{$ans1}

2. Enter [``\frac{\pi}{2} =``] [____]{$ans2->cmp(
    tolType   => 'absolute',
    tolerance => .0001,
)}

3. Enter [``\frac{\pi}{2} =``] [____]{$ans3}
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.