Find maximum and minimum of multivariable function in sympy - sympy

Question

I have the following function:
f = x**2 + y**2
I would like to use sympy to find the maximum of and minimum value in the unit square [0,1] in x and [0,1] in y.
The expected outcome would be 0 for point [0,0] and 2 for point [1,1]
Can this be achieved?

Answer 1

I did something clunky, but appears to work [although not fast]:
def findMaxMin(f):
# find stationary points:
stationary_points = sym.solve([f.diff(x), f.diff(y)], [x, y], dict=True)
# Append boundary points
stationary_points.append({x:0, y:0})
stationary_points.append({x:1, y:0})
stationary_points.append({x:1, y:1})
stationary_points.append({x:0, y:1})
# store results after evaluation
results = []
# iteration counter
j = -1
for i in range(len(stationary_points)):
j = j+1
x1 = stationary_points[j].get(x)
y1 = stationary_points[j].get(y)
# If point is in the domain evalute and append it
if (0 <= x1 <= 1) and ( 0 <= y1 <= 1):
tmp = f.subs({x:x1, y:y1})
results.append(tmp)
else:
# else remove the point
stationary_points.pop(j)
j = j-1
# Variables to store info
returnMax = []
returnMin = []
# Get the maximum value
maximum = max(results)
# Get the position of all the maximum values
maxpos = [i for i,j in enumerate(results) if j==maximum]
# Append only unique points
append = False
for item in maxpos:
for i in returnMax:
if (stationary_points[item] in i.values()):
append = True
if (not(append)):
returnMax.append({maximum: stationary_points[item]})
# Get the minimum value
minimum = min(results)
# Get the position of all the minimum values
minpos = [i for i,j in enumerate(results) if j==minimum ]
# Append only unique points
append = False
for item in minpos:
for i in returnMin:
if (stationary_points[item] in i.values()):
append = True
if (not(append)):
returnMin.append({minimum: stationary_points[item]})
return [returnMax, returnMin]