new object $help_obj_math: $help_obj;

var $dmi_data descriptions = #[];
var $has_name name = ['prop, "Math Library", "Math Library"];
var $help_node body = <$ctext_frob, [[<$format, ["subj", [["level", "3"]], ["Vector operations"], 'do_subj]>, <$format, ["dl", [], [<$format, ["dt", [], [".", <$format, ["method", [["math.add", 1]], ["add"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Vector addition. It adds two floating-point lists, element-by-element."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.sub", 1]], ["sub"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Vector substraction."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.dot", 1]], ["dot"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Dot product of two vectors."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.cross", 1]], ["cross"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Cross product of 3-dimensional vectors."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.distance", 1]], ["distance"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Euclidean distance between the two vectors."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.scale", 1]], ["scale"], 'do_method]>, "(", <$format, ["var", [], ["x"], 'do_var]>, ",", <$format, ["var", [], ["v"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Scales the vector ", <$format, ["var", [], ["v"], 'do_var]>, " by scalar ", <$format, ["var", [], ["x"], 'do_var]>, "."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.minor", 1]], ["minor"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Calculates element-by-element minimum of the two lists. Used for boxes."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.major", 1]], ["major"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Calculates element-by-element maximum."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.is_lower", 1]], ["is_lower"], 'do_method]>, "(", <$format, ["var", [], ["v1"], 'do_var]>, ",", <$format, ["var", [], ["v2"], 'do_var]>, ") native"], 'do_dt]>, <$format, ["dd", [], ["Returns true if every element of ", <$format, ["var", [], ["v1"], 'do_var]>, " is lesser or equal than corresponding element of ", <$format, ["var", [], ["v2"], 'do_var]>, "."], 'do_dd]>], 'do_dl]>, <$format, ["subj", [["level", "3"]], ["Coordinate operations"], 'do_subj]>, <$format, ["dl", [], [<$format, ["dt", [], [".", <$format, ["method", [["math.pi", 1]], ["pi"], 'do_method]>, "()"], 'do_dt]>, <$format, ["dd", [], ["Returns pi."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.pi2", 1]], ["pi2"], 'do_method]>, "()"], 'do_dt]>, <$format, ["dd", [], ["Returns 2*pi."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.deg_rad", 1]], ["deg_rad"], 'do_method]>, "(", <$format, ["var", [], ["angle"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Converts the ", <$format, ["var", [], ["angle"], 'do_var]>, " from degrees to radians."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rad_deg", 1]], ["rad_deg"], 'do_method]>, "(", <$format, ["var", [], ["angle"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Converts the ", <$format, ["var", [], ["angle"], 'do_var]>, " from radians to degrees."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.polar_rectangular", 1]], ["polar_rectangular"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Transforms pair [distance, angle] into [x,y]."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rectangular_polar", 1]], ["rectangular_polar"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Inverse of the above."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.cylindrical_rectangular", 1]], ["cylindrical_rectangular"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Transforms [r, angle, z] into [x,y,z]."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rectangular_cylindrical", 1]], ["rectangular_cylindrical"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Inverse of the above."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.spherical_rectangular", 1]], ["spherical_rectangular"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Transform [r, phi, theta] into [x,y,z]."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rectangular_spherical", 1]], ["rectangular_spherical"], 'do_method]>, "(", <$format, ["var", [], ["coords"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Inverse of the above."], 'do_dd]>], 'do_dl]>, <$format, ["subj", [["level", "3"]], ["Matrix operations"], 'do_subj]>, <$format, ["dl", [], [<$format, ["dt", [], [".", <$format, ["method", [["math.matrix_add", 1]], ["matrix_add"], 'do_method]>, "(", <$format, ["var", [], ["m1"], 'do_var]>, ",", <$format, ["var", [], ["m2"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Add two matrices."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.matrix_sub", 1]], ["matrix_sub"], 'do_method]>, "(", <$format, ["var", [], ["m1"], 'do_var]>, ",", <$format, ["var", [], ["m2"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Substract ", <$format, ["var", [], ["m2"], 'do_var]>, " from ", <$format, ["var", [], ["m1"], 'do_var]>], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.matrix_mul", 1]], ["matrix_mul"], 'do_method]>, "(", <$format, ["var", [], ["m1"], 'do_var]>, ",", <$format, ["var", [], ["m2"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Multiply the two matrices (their dimensions must be compatible for multiplication, of course)"], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.matrix_scale", 1]], ["matrix_scale"], 'do_method]>, "(", <$format, ["var", [], ["s"], 'do_var]>, ",", <$format, ["var", [], ["m"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Scale the matrix ", <$format, ["var", [], ["m"], 'do_var]>, " by scalar ", <$format, ["var", [], ["s"], 'do_var]>, "."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.transpose", 1]], ["transpose"], 'do_method]>, "(", <$format, ["var", [], ["m"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Transpose the matrix. This will actually work regardless of the element type, so the operation is useful on lists, as well."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.ident_mat", 1]], ["ident_mat"], 'do_method]>, "(", <$format, ["var", [], ["n"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Returns ", <$format, ["var", [], ["n"], 'do_var]>, "-dimensional identity matrix."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.translation_mat", 1]], ["translation_mat"], 'do_method]>, "(", <$format, ["var", [], ["v"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Constructs the matrix for translation by vector ", <$format, ["var", [], ["v"], 'do_var]>, ". It works for 2d or 3d case."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.tensor", 1]], ["tensor"], 'do_method]>, "(", <$format, ["var", [], ["m1"], 'do_var]>, ",", <$format, ["var", [], ["m2"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Tensor product of the two vectors. This is the matrix ", <$format, ["var", [], ["A"], 'do_var]>, " with the property that Ax=<x,v1>v2."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.skew", 1]], ["skew"], 'do_method]>, "(", <$format, ["var", [], ["v"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Construct a skew operator for the vector ", <$format, ["var", [], ["v"], 'do_var]>, ". That's matrix ", <$format, ["var", [], ["A"], 'do_var]>, " that turns any vector into its cross product with ", <$format, ["var", [], ["v"], 'do_var]>, ". This is used by rotation_mat_3d."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rotation_mat_2d", 1]], ["rotation_mat_2d"], 'do_method]>, "(", <$format, ["var", [], ["angle"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Construct 2d rotation matrix for the given ", <$format, ["var", [], ["angle"], 'do_var]>, "."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.rotation_mat_3d", 1]], ["rotation_mat_3d"], 'do_method]>, "(", <$format, ["var", [], ["axis"], 'do_var]>, ",", <$format, ["var", [], ["angle"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["This is 3d rotation. Valid values for ", <$format, ["var", [], ["axis"], 'do_var]>, " are 'x, 'y, 'z, or a 3d vector. The result is a homogenous matrix."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.scale_mat", 1]], ["scale_mat"], 'do_method]>, "(", <$format, ["var", [], ["scale"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Returns a scaling matrix (nonuniform). Scale is assumed to be 2d or 3d vector."], 'do_dd]>, <$format, ["dt", [], [".", <$format, ["method", [["math.transform_vect", 1]], ["transform_vect"], 'do_method]>, "(", <$format, ["var", [], ["m"], 'do_var]>, ",", <$format, ["var", [], ["v"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["Transform the vector by matrix. This will work for both normal and homogenous matrices (determined by comparing the dimensions of the matrix and vector)."], 'do_dd]>], 'do_dl]>, <$format, ["subj", [["level", "3"]], ["Miscellanous"], 'do_subj]>, <$format, ["dl", [], [<$format, ["dt", [], [".", <$format, ["method", [["math.runge", 1]], ["runge"], 'do_method]>, "(", <$format, ["var", [], ["x"], 'do_var]>, ",", <$format, ["var", [], ["y"], 'do_var]>, ",", <$format, ["var", [], ["h"], 'do_var]>, ",", <$format, ["var", [], ["f"], 'do_var]>, ",", <$format, ["var", [], ["data"], 'do_var]>, ")"], 'do_dt]>, <$format, ["dd", [], ["This is one step in Runge-Kutta method for ordinary differential equations. Scalar ", <$format, ["var", [], ["x"], 'do_var]>, " and vector ", <$format, ["var", [], ["y"], 'do_var]>, " are the current values of independant and dependant variables, ", <$format, ["var", [], ["h"], 'do_var]>, " is the timestep, ", <$format, ["var", [], ["f"], 'do_var]>, " is the method on the sender that accepts ", <$format, ["var", [], ["x"], 'do_var]>, ", ", <$format, ["var", [], ["y"], 'do_var]>, ", and ", <$format, ["var", [], ["data"], 'do_var]>, ", and returns the right-hand-side of the equation."], 'do_dd]>], 'do_dl]>], #[]]>;
var $help_node group = 1;
var $help_node index = $help_index_objects;
var $help_node links = #[];
var $root created_on = 869046674;
var $root flags = ['variables, 'methods, 'code, 'core];
var $root inited = 1;
var $root managed = [$help_obj_math];
var $root manager = $help_obj_math;