vector-3.sagews

from sympy import *
from sympy import N as Num
from sympy import mpmath
from mpmath import radians as rad

def rot(v,phi_rad):
    """
    actively rotate vector V by phi_deg degrees
    """

    c = cos(phi_rad)
    s = sin(phi_rad)

    # rotation matrix Q:
    Q = Matrix([[c, -s],[s, c]])

    return Q*v

u = Matrix([5, 0])
# set V parallel to u:
V = Matrix([3, 0])

# rotate V by phi_deg:
pie=2*pi

# pc = piece of pie:
pc = pie/12

for phi in [pc * x for x in [1,2,3,4]]:
    v = rot(V,phi)
    pprint("\n\nv:")
    pprint(v)

    vu = v.norm()*cos(phi)
    dotp = u.dot(v)

    # precision:
    p=2

    pprint("\nvu:")
    pprint(vu)
    pprint(Num(vu,p))
    pprint("\nu.v:")
    pprint(dotp)
    pprint(Num(dotp,p))

v: [ ___] [3*\/ 3 ] [-------] [ 2 ] [ ] [ 3/2 ] vu: ___ 3*\/ 3 ------- 2 2.6 u.v: ___ 15*\/ 3 -------- 2 13. v: [ 3/2 ] [ ] [ ___] [3*\/ 3 ] [-------] [ 2 ] vu: 3/2 1.5 u.v: 15/2 7.5 v: [0] [ ] [3] vu: 0 0 u.v: 0 0 v: [ -3/2 ] [ ] [ ___] [3*\/ 3 ] [-------] [ 2 ] vu: -3/2 -1.5 u.v: -15/2 -7.5