(Co)EqPublic.sagews

import sys
from sage.all import *

#Graphs G and H  G is the Domain, H is the coDomain.
G = Graph([('a', 'b'),('b', 'c'), ('b', 'd')])
H = Graph([(1, 2), (2, 3) ])

##DO NOT EDIT THESE 3 LINES
Pg = Set (G.vertices() + G.edges(labels=False));
Ph = Set (H.vertices() + H.edges(labels=False));
X = FiniteSetMaps(Pg, Ph)
##DO NOT EDIT THE ABOVE 3 LINES


f = X.from_dict({'a':1, 'b':2, 'c':3, 'd':3, ('a', 'b'):(1, 2), ('b', 'c'):(2, 3), ('b', 'd'):(2, 3)}); 


g = X.from_dict({'a':1, 'b':2, 'c':1, 'd':3, ('a', 'b'):(1, 2), ('b', 'c'):(1, 2), ('b', 'd'):(2, 3)}); 



#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
#PLEASE DO NOT EDIT ANYTHING AFTER THIS LINE!
#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

print("\n\n Graph G \n")
G.show()



print("\n\n Graph H \n\n")
H.show()


s = True

#Checking whether f and g are graph morphisms (vertices) It seems like this only checks if f is a graph morphism rather than g. - Dr. C

for j in G.vertices():
    if f(j)in H.vertices():
        s=s and True
    else:
        s=s and False


#Checking whether f and g are graph morphisms (edges).

for i in G.edges(labels=False):
    u=i[0];
    v=i[1];
    if f(u)==f(v) and f(u)==f(i):
        s=s and True
    elif f(i)in H.edges(labels=False):
        z=f(i)
        if (z[0]==f(u) and z[1]==f(v)) or (z[1]==f(u) and z[0]==f(v)):
            s=s and True
        else:
            s=s and False
    else: s=s and False

print("\n\n Are f and g Graph Morphism? (T/F) \n\n"); s


#Breaks the program if it is not a graph morphism

if s == False:
   quit("Not a Morphism")

#Eq is the equalizer graph

Eq = Graph()

#Creating the equalizer


for j in G.vertices():
    if f(j)==g(j):
        Eq.add_vertex(j)


for j in G.edges(labels=False):
    u=j[0]
    v=j[1]
    if f(j)==g(j) and j[0] in Eq.vertices() and j[1] in Eq.vertices():
        Eq.add_edge(j)


print("\n\n Graph Eq \n\n")
Eq.show()


#Coeq is the co-equalizer graph

Coeq = Graph(multiedges=True, loops=True)

Gdone = Set([])
Hdone = Set([])

for p in H.vertices():
    if p not in Hdone:
        Gtemp=Set([])
        Htemp=Set([p])
        s = False
        while s == False:
            Gcheck=Gtemp
            Hcheck=Htemp
            for x in Pg:
                if f(x) in Htemp:
                    Gtemp = Gtemp + Set([x])
                if g(x) in Htemp:
                    Gtemp = Gtemp + Set([x])
            for p in Gtemp:
                Htemp = Htemp + Set([f(p), g(p)])

            if (Gtemp == Gcheck) and (Htemp == Hcheck):
                s = True
                Gdone = Gdone + Gtemp
                Hdone = Hdone + Htemp
                Coeq.add_vertex(Htemp)


for p in H.edges(labels=False):
    if p not in Hdone:
        Gtemp=Set([])
        Htemp=Set([p])
        s = False
        while s == False:
            Gcheck=Gtemp
            Hcheck=Htemp
            for x in Pg:
                if f(x) in Htemp:
                    Gtemp = Gtemp + Set([x])
                if g(x) in Htemp:
                    Gtemp = Gtemp + Set([x])
            for p in Gtemp:
                Htemp = Htemp + Set([f(p), g(p)])

            if (Gtemp == Gcheck) and (Htemp == Hcheck):
                s = True
                Gdone = Gdone + Gtemp
                Hdone = Hdone + Htemp
                e=Htemp[0]
                for v in Coeq.vertices():
                    if e[0] in v:
                        a = v
                    if e[1] in v:
                        b = v
                Coeq.add_edge(a, b, Htemp)


print("\n\n Graph CoEq \n\n")
Coeq.show()