Eval Versus Substitute

Shows the difference between eval and substitute for MathObject Formulas

Complete Code

PG problem file

Explanation

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

Preamble

These standard macros need to be loaded.

$f  = Compute("sqrt(3x + 1)");
$f1 = $f->eval(x => "3");
$f2 = $f->substitute(x => "3");

Context()->variables->add(y => 'Real');
$g = Compute('7xy');
# This next line is an error.
# $g1 = $g->eval(x => '3');
$g2 = $g->substitute(x => '3');
$g3 = $g->eval(x => 3, y => -1);

Context()->flags->set(reduceConstants => 0);
$f3 = $f->eval(x => 3);
$f4 = $f->substitute(x => 3);

Context()->flags->set(reduceConstantFunctions => 0, reduceConstants => 1);
$f5 = $f->substitute(x => 3);

Setup

First, we start with a formula using Compute.

eval returns a number, which is a Value::Real
substitute returns a Formula which is a Value::Formula

The ref command is a perl command to determine the reference type. In these cases they are MathObjects with type Value::Real and Value::Formula

For the function $g, the line $g->eval(x => '3'); throws an error because it is expected to return a number (Value::Real).

The next section shows the effect of changing reduceConstants to 0 (false). Notice that there is no effect on eval, the result is the same number as before, however with substitute the value 3 is substituted in but left within the formula, which is not reduced.

Lastly, to show the effect of reduceConstantFunctions, if we set reduceConstants back to 1 and reduceConstantFunctions to 0, we see that the inside of the square root is reduced (because they are constants), but the square root remains.

BEGIN_PGML
This shows the difference between [|eval|] and [|substitute|].  First, we start
with a function [`[$f]`]:

* [|$f->eval(x=>'3')|] returns [$f1] and the type is [@ ref $f1@]
* [|$f->substitute(x=>'3')|] returns [$f2] and the type is [@ ref $f2 @]

Next, we do the same with the function [`[$g]`]

* [|$g->eval(x=>'3')|] throws an error.
* [|$g->substitute(x=>'3')|] returns [$g2] and the type is [@ ref $g2 @]
* [|$g->eval(x=>'3', y => -1)|] returns [$g3] and the type is [@ ref $g3 @]

If [|reduceConstants|] is set to 0 (False) in the flags, we get

* [|$f->eval(x => 3)|] returns [$f3]
* [|$f->substitute(x => 3)|] returns [$f4]

If [|reducedConstants|] is set back to 1 and [|reduceConstantFunctions|] is
set to 0, then

* [|$f->substitute(x => 3)|] returns [$f5]

END_PGML

ENDDOCUMENT();

Statement

This is the problem statement in PGML.