Vectors have important applications in physics and engineering. Vectors are used to represent position, velocity, angular momentum, electromagnetic fields, and so on. Let's see how to perform some basic operations with vectors in Sage. You can enter the following code in an input cell in a worksheet, or enter it line by line in the interactive shell. You can also enter the code into a plain text file, save it with a .sage
extension, and run it from the Sage command line as
described in the previous chapter:
R3 = VectorSpace(QQ, 3) (b1, b2, b3) = R3.basis() print("Basis for space:") print b1 print b2 print b3 vector1 = R3([-1, 2, 7]) # define some vectors vector2 = R3([4, -9, 2]) print("Linear combinations:") var('a b') print(a * vector1 + b * vector2) print("Norm of vector 1:") print(sqrt(vector1 * vector1)) # definition print(vector1.norm()) # using norm method print("Scalar multiplication:") print(2 * vector1) print("Scalar (dot) products...