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 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 test():
'''tests projective property'''
D=Diagram()
P=Object(D,'P')
B=Object(D,'B')
C=Object(D,'C')
pi=Morphism(B,C)
f=Morphism(P,C)
Epimorphism(pi)
pi.latex=r"\pi"
f.latex=r"\varphi"
Projective(P)
f=Morphism(P,B)
SRM = SimpleRuleMaster(D)
for i in xrange(10):
SRM(verbose=True)
return D
def test():
'''constructs and displays all products of two objects'''
D = Diagram()
X = Object(D,"X")
Y = Object(D,"Y")
f1 = Morphism(X,Y,"f1")
f1.name="f1"
f1.latex=r"\phi"
rule=ExistProduct
homs=HomomorphismIterator(rule.CD,D)
ers=[]
for hom in homs:
ers.append(ExtensionRequest(rule,hom))
for ER in ers:
ER.implement()
return D
def conclude(self,D):
phi = Morphism(D["P"],D["N"],"phi")
phi.namescheme=("{} x {}",("f","g"))
phi.latexscheme=("{} \\oplus {}",("f","g"))
Commute(D["f"],phi*D["i1"])
Commute(D["g"],phi*D["i2"])
def conclude(self,D):
ftilde=Morphism(D['B'],D['I'])
ftilde.namescheme=("{}tilde",("f"))
ftilde.latexscheme=("\\tilde\{{}\}",("f"))
Commute(D["f"],ftilde*D['iota'])
