Random(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) ])

#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
#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()

#Creating the Part Sets for each graph


Pg = Set (G.vertices() + G.edges(labels=False)); 


Ph = Set (H.vertices() + H.edges(labels=False)); 

X = FiniteSetMaps(Pg, Ph); 

Z = Set(X)

HomS = Set([]); 

for f in Z:
    s = True

#Checking whether f is a graph morphism (vertices)

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


#Checking whether f is a graph morphism (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

#Adds f to HomS if f is a morphism
    if s==True:
        HomS = HomS + Set([f])

#Picking Random Morphisms

Homfg = FiniteEnumeratedSet(HomS)

f = Homfg.random_element()
print("\n\n Morphism f \n\n")
f
g = Homfg.random_element()
print("\n\n Morphism g \n\n")
g





#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()