/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 0.8.4 ] */ /* [wxMaxima: comment start ] In the vect1 package, there are a number of useful functions for performing vector operations. Those functions are illustrated here. [wxMaxima: comment end ] */ /* [wxMaxima: comment start ] First save the package file "vect1.mac" to a folder on your computer. Use File --> Load Package... (or Ctrl+L) to find and load the package. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ load("C:/Documents and Settings/Compaq_Owner/My Documents/Maxima/vect1.mac")$ /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (1) The norm() function computes the magnitude of a vector. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ u: [1,-2,3]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ norm( u ); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (2) The normalize() function normalizes a vector. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ v: [4,1,-3]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ normalize( v ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ float(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ norm(%); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (3) The dot() function computes the dot product of two vectors. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ dot( [1,2], [4,-3] ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ u: [1/2,-3,4/3]; v: [-1,2/5,-6]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ dot( u, v ); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (4) The cross() function computes the cross products of two 3D vectors. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ u: [1,-2,1]; v: [3,-2,2]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ cross( u, v ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ cross( v, u ); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (5) The angle() function computes the angle between two vectors. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ angle( [2,3], [1,0] ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ float(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ u: [4,2,1]; v: [0,4,-5]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ angle( u, v ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ float(%*180/%pi); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (6) The allsimp() function attempts to simplify using a variety of techniques. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ cos(1)^2+sin(1)^2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ allsimp(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ 1/sqrt(430); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ allsimp(%); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (7) The nabla() function computes the gradient vector. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ nabla( 2*x^2+4*y^4, [x,y] ); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ nabla( x^3*y^2*z + sin(x*y*z), [x,y,z] ); /* [wxMaxima: input end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"$