Transformações Lineares.sagews

v1=3
v2=2
vector_v=vector(QQ,(v1,v2))

def rotatevector(u,a): #Vetor u e ângulo a
    v1=u[0]
    v2=u[1]
    vec=vector((v1*cos(a)-v2*sin(a),v1*sin(a)+v2*cos(a)))
    return vec
def multivector(u,a): #Vetor u e multiplicidade a
    v1=u[0]
    v2=u[1]
    vec=vector((a*v1,a*v2))
    return vec

def reflectvectorx(u): #Reflete u no eixo x
    v1=u[0]
    v2=u[1]
    vec=vector((v1,-v2))
    return vec
def reflectvectory(u): #Reflete u no eixo y
    v1=u[0]
    v2=u[1]
    vec=vector((-v1,v2))
    return vec
def projx(u): #Projeta u em x
    v1=u[0]
    v2=u[1]
    vec=vector((v1,0))
    return vec

def projy(u): #Projeta u em y
    v1=u[0]
    v2=u[1]
    vec=vector((0,v2))
    return vec

P=plot(vector_v,color='black',aspect_ratio=1)
# P+=plot(reflectvectorx(vector_v),color='green',aspect_ratio=1)
# P+=plot(reflectvectory(vector_v),color='blue',aspect_ratio=1)
# P+=plot(projx(vector_v),color='red',aspect_ratio=1)
# P+=plot(projy(vector_v),color='brown',aspect_ratio=1)
P+=plot(rotatevector(vector_v,pi/4),color='yellow',aspect_ratio=1)
# P+=plot(multivector(vector_v,-2),color='pink',aspect_ratio=1)
P.show()