Hello,
I am doing a vector calculus problem that uses:
$VForm = Formula("(x^2/2) + (y^2/2) + (z^2/2)");
However, I want to evaluate this at two different points (it's used as an antiderivative). Is there a way of essentially doing the following:
$Pt1 = Point(1,2,3);
$Pt2 = Point(4,5,6);
$Antider = ($VectForm->eval((x,y,z)=>$Pt1)) - ($VectForm->eval((x,y,z)=>$Pt2));
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If not, how can I get the first, second, and third coordinates from a Point object?
Also, what is the syntax for evaluating a vector field at a point using the vector object?
Thank you,
Spyro Roubos
There is no direct way to do this, but there are a couple of approaches to getting the same effect.
The first is to deconstruct the points first, and then use eval:
($x1,$y1,$z1) = $Pt1->value;
($x2,$y2,$z2) = $Pt2->value;
$AntiDir = $VectForm->eval(x=>$x2,y=>$y2,z=>$z2) -
$VectForm->eval(x=>$x1,y=>$y1,z=>$z1);
It's somewhat awkward, but works.
Alternatively, you can create a perl function and pass the coordinates of the point. (Note that the perlFunction's parameters are in alphabetical order unless otherwise specificied.)
$vf = $VectForm->perlFunction;
$AntiDir = &$vf($Pt2->value) - &$vf($Pt1->value);
Finally, you could make a named function:
$VectForm->perlFunction('VF');
$AntiDir = VF($Pt2->value) - VF($Pt1->value);
Hope one of these works for you.
Davide
To get the coordinates of a vector, you can do either
($x,$y,$z) = $v->value;
as in the example above, or you can get individual coordinates (by number) as
$x = $v->extract(1);
$y = $v->extract(2);
$z = $v->extract(3);
Davide