Vectors over callable symbolic rings#
AUTHOR:
Jason Grout (2010)
EXAMPLES:
sage: f(r, theta, z) = (r*cos(theta), r*sin(theta), z)
sage: f.parent()
Vector space of dimension 3 over Callable function ring with arguments (r, theta, z)
sage: f
(r, theta, z) |--> (r*cos(theta), r*sin(theta), z)
sage: f[0]
(r, theta, z) |--> r*cos(theta)
sage: f+f
(r, theta, z) |--> (2*r*cos(theta), 2*r*sin(theta), 2*z)
sage: 3*f
(r, theta, z) |--> (3*r*cos(theta), 3*r*sin(theta), 3*z)
sage: f*f # dot product
(r, theta, z) |--> r^2*cos(theta)^2 + r^2*sin(theta)^2 + z^2
sage: f.diff()(0,1,2) # the matrix derivative
[cos(1) 0 0]
[sin(1) 0 0]
[ 0 0 1]
>>> from sage.all import *
>>> __tmp__=var("r,theta,z"); f = symbolic_expression((r*cos(theta), r*sin(theta), z)).function(r,theta,z)
>>> f.parent()
Vector space of dimension 3 over Callable function ring with arguments (r, theta, z)
>>> f
(r, theta, z) |--> (r*cos(theta), r*sin(theta), z)
>>> f[Integer(0)]
(r, theta, z) |--> r*cos(theta)
>>> f+f
(r, theta, z) |--> (2*r*cos(theta), 2*r*sin(theta), 2*z)
>>> Integer(3)*f
(r, theta, z) |--> (3*r*cos(theta), 3*r*sin(theta), 3*z)
>>> f*f # dot product
(r, theta, z) |--> r^2*cos(theta)^2 + r^2*sin(theta)^2 + z^2
>>> f.diff()(Integer(0),Integer(1),Integer(2)) # the matrix derivative
[cos(1) 0 0]
[sin(1) 0 0]
[ 0 0 1]