def conclude(self,CD):
A = CD["A"]
B = CD["B"]
AxB = Object(CD,"AxB")
AxB.namescheme=('{}x{}',('A','B')) #this should be a pair (format string,tuple of names in chardiag), names from main diagram will be substitued when rule is implemented
AxB.latexscheme=('{} \\times {}',('A','B'))
pi1 = Morphism(AxB,A,"pi1")
pi2 = Morphism(AxB,B,"pi2")
pi1.latexscheme=('',()) #suppress morphism name display
pi2.latexscheme=('',()) #suppress morphism name display
ProductProperty(pi1,pi2)
def implement(self):
'''carry out the pushout of the Extension Meta-Diagram'''
#Extend hom to a lift of the extension to the main Diagram
lift = self.hom*self.rule.partialInverse #inefficient
for obj in self.rule.newObjects:
try:
names=[]
for s in obj.namescheme[1]:
obj_item = self.charDiag[s]
if isinstance(obj_item,Object):
names.append(self.hom[self.charDiag[s]].name)
else:#morphism
names.append(self.hom.get_edge_image(self.charDiag[s]).representative.name)
newname=obj.namescheme[0].format(*names)
newobj = Object(self.mainDiag,newname) #try naming according to scheme
except:
try:
newobj=Object(self.mainDiag,self.mainDiag.giveName(mode=newname)) #append a number to name if this failed
except:
newobj = Object(self.mainDiag) #give a generic name if everything fails
latexlist=[]
try:
for s in obj.latexscheme[1]:
try:
try:
latexlist.append(self.hom[self.charDiag[s]].latex)
except:
latexlist.append(self.hom[self.charDiag[s]].name)
except:
try:
latexlist.append(self.hom.edgeMap[self.charDiag.Morphisms[s]].latex)
except:
latexlist.append(self.hom.edgeMap[self.charDiag.Morphisms[s]].name)
newobj.latex=obj.latexscheme[0].format(*latexlist) #set LaTeX display string
except:
newobj.latex=newobj.name
lift.set_node_image(obj,newobj)
for morphi in self.rule.newMorphisms:
source = lift[morphi.source]
target = lift[morphi.target]
if isinstance(morphi,Identity):
newmorphi = getIdentity(source)
elif isMorphismZero(morphi):
newmorphi = GiveZeroMorphism(source,target)
else:
newmorphi = Morphism(source,target) #do not implement nameschemes for morphisms for now
latexlist=[]
try:
for s in morphi.latexscheme[1]:
try:
try:
latexlist.append(self.hom[self.charDiag[s]].latex)
except:
latexlist.append(self.hom[self.charDiag[s]].name)
except:
try:
latexlist.append(self.hom.edgeMap[self.charDiag[s]].representative.latex)
except:
latexlist.append(self.hom.edgeMap[self.charDiag[s]].representative.name)
newmorphi.latex=morphi.latexscheme[0].format(*latexlist) #set LaTeX display string
except:
pass
lift.set_edge_image(morphi,self.mainDiag.CommutativityQuotient.get_edge_image(newmorphi))
#compose characteristic homomorphism of property with lift to get
#characteristic homomorphism in the extended main Diagram
#for commutativity classes, just choose an arbitrary section
for prop in self.rule.newProperties:
prop.push_forward(lift)
def test2():
D=Diagram()
P1=Object(D,'P1')
P1.latex='P_1'
P2=Object(D,'P2')
P1.latex='P_1'
id1=Identity(P1)
id2=Identity(P2)
P1xP2=Object(D,'P1xP2')
P1xP2.latex="P_1 \oplus P_2"
idprod=Identity(P1xP2)
i1=Morphism(P1,P1xP2,'i1')
i2=Morphism(P2,P1xP2,'i2')
CoProductProperty(i1,i2)
B=Object(D,'B')
C=Object(D,'C')
pi=Morphism(B,C)
f=Morphism(P1xP2,C)
Epimorphism(pi)
pi.latex=r"\pi"
f.latex=r"\varphi"
Projective(P1)
Projective(P2)
P1.gridpos=(0,0)
P2.gridpos=(0,2)
P1xP2.gridpos=(0,1)
B.gridpos=(1,1)
C.gridpos=(2,1)
P1.latex='P_1'
P2.latex='P_2'
P1xP2.latex='P_1 \oplus P_2'
B.latex='B'
C.latex='C'
SRM = SimpleRuleMaster(D,maxMorphisms=1)
diagSequence=[]
while(True):
result=SRM(numberOfExtensions=10,verbose=False,printlatex=True)
if (result==False):
break
diagSequence.append(result)
print processDiagSequence(diagSequence)
return D
def __init__(self,diagram):
Object.__init__(self,diagram,"0")
InitialObject(self)
FinalObject(self)
