parserImplicitPlane.pl - Implement implicit planes.

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NAME

parserImplicitPlane.pl - Implement implicit planes.

DESCRIPTION

This is a Parser class that implements implicit planes as a subclass of the Formula class. The standard ->cmp routine will work for this, provided we define the compare() function needed by the overloaded ==. We assign the special precedence so that overloaded operations will be promoted to the ones below.

Use ImplicitPlane(point,vector), ImplicitPlane(point,number) or ImplicitPlane(formula) to create an ImplicitPlane object. The first form uses the point as a point on the plane and the vector as the normal for the plane. The second form uses the point as the coefficients of the variables and the number as the value that the formula must equal. The third form uses the formula directly.

The number of variables in the Context determines the dimension of the "plane" being defined. If there are only two, the formula produces an implicit line, but if there are four variables, it will be a hyperplane in four-space. You can specify the variables you want to use by supplying an additional parameter, which is a reference to an array of variable names.

Usage examples:

        $P = ImplicitPlane(Point(1,0,2),Vector(-1,1,3)); #  -x+y+3z = 5
        $P = ImplicitPlane([1,0,2],[-1,1,3]);            #  -x+y+3z = 5
        $P = ImplicitPlane([1,0,2],4);                   #  x+2z = 4
        $P = ImplicitPlane("x+2y-z=5");
        Context()->variables->are(x=>'Real',y=>'Real',z=>'Real',w=>'Real');
        $P = ImplicitPlane([1,0,2,-1],10);               # w+2y-z = 10 (alphabetical order)
        $P = ImplicitPlane([3,-1,2,4],5,['x','y','z','w']);  # 3x-y+2z+4w = 5
        $P = ImplicitPlane([3,-1,2],5,['y','z','w']);  # 3y-z+2w = 5

Then use

        ANS($P->cmp);

to get the answer checker for $P.