##################################################################### # # Some utility routines that are useful in vector problems # sub _parserVectorUtils_init {}; # don't reload this file ################################################## # # formats a vector name (should be used in math mode) # # Vectors will be in bold italics in HTML modes, and # will be overlined in TeX modes. (Bold italic could also work in # TeX modes, but the low resolution on screen made it less easy # to distinguish the difference between bold and regular letters.) # sub Overline { my $v = shift; my$HTML = ''.$v.''; MODES( TeX => "\\overline{$v}", HTML => $HTML, HTML_tth => '\begin{rawhtml}'.$HTML.'\end{rawhtml}', HTML_dpng => "\\overline{$v}", ); } # # This gets a bold letter in TeX as well as HTML modes. # Although \boldsymbol{} works fine on screen in latex2html mode, # the PDF file produces non-bold letters. I haven't been able to # track this down, so used \mathbf{} in TeX mode, which produces # roman bold, not math-italic bold. # sub BoldMath { my$v = shift; my $HTML = ''.$v.''; MODES( TeX => "\\boldsymbol{$v}", # doesn't seem to work in TeX mode # TeX => "\\mathbf{$v}", # gives non-italic bold in TeX mode Latex2HTML => "\\boldsymbol{$v}", HTML =>$HTML, HTML_tth => '\begin{rawhtml}'.$HTML.'\end{rawhtml}', HTML_dpng => "\\boldsymbol{$v}", ); } # # Grad sumbol # $GRAD = '\nabla '; # # Create a non-zero point with the given number of coordinates # with the given random range (which defaults to (-5,5,1)). # # non_zero_point(n,a,b,c) # sub non_zero_point { my$n = shift; my $k =$n; my @v = (); my $a = shift || -5; my$b = shift || $a + 10; my$c = shift || 1; while ($k--) {push(@v,random($a,$b,$c))} if (norm(Point(@v)) == 0) {$v[random(0,$n-1,1)] = non_zero_random($a,$b,$c)} return Point(@v); } sub non_zero_point2D {non_zero_point(2,@_)} sub non_zero_point3D {non_zero_point(3,@_)} # # Same but for Vectors # sub non_zero_vector {Vector(non_zero_point(@_))} sub non_zero_vector2D {non_zero_vector(2,@_)} sub non_zero_vector3D {non_zero_vector(3,@_)} # # Form the vector-parametric form for a line given its point and vector # # Usage: Line(P,V); or Line(P,V,'t'); # # where P is the point and V the direction vector for the line, and # t is the variable to use (default is 't'). # # Ex: Line([1,-3],[2,1]) produces Vector("1+2t","-3+t"). # Ex: Line(Point(1,-3),Vector(2,1)) produces Vector("1+2t","-3+t"). # sub Line { my @p = Point(shift)->value; my @v = Vector(shift)->value; my$t = shift; $t = 't' unless$t; $t = Formula($t); my @coords = (); die "Dimensions of point and vector don't match" unless $#p ==$#v; foreach my $i (0..$#p) {push(@coords,($p[$i]+$v[$i]*$t)->reduce)} return Vector(@coords); } # # Creates a displayable string for a plane given its # normal vector and a point on the plane. (Better to use # the ImplicitPlane class from parserImplicitPlane.pl). # # Usage: Plane(P,N); # sub Plane { my$P = Point(shift); my $N = Vector(shift); my @N =$N->value; my $xyz = shift;$xyz = ['x','y','z'] unless defined($xyz); die "Number of variables doesn't match dimension of normal vector" unless scalar(@N) == scalar(@{$xyz}); my @terms = (); foreach my $i (0..$#N) {push(@terms,$N[$i]->TeX.$xyz->[$i])} Formula(join(' + ',@terms))->reduce->TeX . " = " . ($N.$P)->TeX; } 1;