How to formulate summation in z3py - z3

Question

I am very new to z3py.
I am trying to code the following 2 expressions in z3py
and
More information on the problem can be found here
I did search stackoverflow a lot and came across a similar question
But unfortunately I could not get a satisfactory enough answer.
I tried coding the first one in SMT, in following way:
#InputGroup, BlockGroup, OutputGroup contain some integer values to represent blocks
InputGroup = [0,1,2]
BlockGroup = [2,3,4,5,6]
OutputGroup = [7,8,9]
Groups = [InputGroup, BlockGroup, OutputGroup]
NumberOfTasks = len(InputGroup)+ len(BlockGroup)+ len(OutputGroup)
M = Function('M', Intsort(), Intsort())
Task = Function('Task', Intsort(), Intsort(), Intsort())
summation1 = Int('summation1')
# each group from the Groups is represented by its index number
for r, g in enumerate(Groups):
for m in range(0, NumberOfTasks):
if(m in g):
s.add(summation1 == summation1+ M(Task(r,m)))
and the second expression in SMT the following way:
NumberOfInputs = len(InputGroup)
NumberOfBlocks = len(BlockGroup)
NumberOfOutputs = len(OutputGroup)
Node = Function('Node', Intsort(), Intsort(), Intsort())
f = Function('f', Intsort(), Intsort(), Intsort())
for r, g in enumerate(Groups):
if(r != Groups.index(InputGroup) and r != Groups.index(OutputGroup)):
for i in range(0,(NumberOfInputs+NumberOfBlocks+NumberOfOutputs)):
summation2 = Int('summation2')
for m in range(0, (NumberOfTasks)):
if(m in g and i in g):
s.add(summation2 == summation2+ f(Node(r,i), Task(r,m)))
s.add(summation2 == 1)
Although I get satisfactory result from the above equations, the model I get from it is kind of questionable.
I just want to know if I am representing this correctly or not.

Answer 1

I think you want to change:
# each group from the Groups is represented by its index number
for r, g in enumerate(Groups):
for m in range(0, NumberOfTasks):
if(m in g):
s.add(summation1 == summation1+ M(Task(r,m)))
to something like this:
# each group from the Groups is represented by its index number
sumTerms = [M(Task(r,m))
for r, g in enumerate(Groups):
for m in range(0, NumberOfTasks):
if(m in g)]
s.add(summation1 == Sum(sumTerms))
and similarly for the second example.