139.sagews

# Create a bunch of variables with the same prefix
# Example:
#       makevars('x',3)
# creates variables x1, x2, x3 in the global namespace.
# Return value: a tuple containing the variables.
def makevars(prefix, n):
    return var(' '.join([prefix+str(i) for i in range(n)]))

x = makevars('x',5); x

(x0, x1, x2, x3, x4)

# Defining an expression:
fexpr = sum(sin(v)^2 for v in x); fexpr

sin(x4)^2 + sin(x3)^2 + sin(x2)^2 + sin(x1)^2 + sin(x0)^2

# Defining a function
f(tuple(x)) = sum( sum(sin(v)-cos(w) for w in x if w!=v) for v in x); f

(x0, x1, x2, x3, x4) |--> 4*sin(x4) - 4*cos(x4) + 4*sin(x3) - 4*cos(x3) + 4*sin(x2) - 4*cos(x2) + 4*sin(x1) - 4*cos(x1) + 4*sin(x0) - 4*cos(x0)

# Computing partial derivatives, for example:
diff(fexpr,x1)

2*cos(x1)*sin(x1)

# Some computations with the function
print f(0,0,0,0,x4)
print diff(f(2,-1,x2,4,x4),x4)
plot (f(2,-1,3,x3,0),-2*pi,2*pi)

4 sin(x4) - 4 cos(x4) - 16 4 sin(x4) + 4 cos(x4)