def test4():
str_=r"""T \ar[bend left]{drrr}{u} \ar[bend right]{ddr}{v} & & & \\
& Z \times_Y (X \times_B Y) \ar{r}{f} \ar{d}{h} & Y \times_B X \ar{r}{g} \ar{d}{i} & X \ar{d}{j} \\
& Z \ar{r}{k} & Y \ar{r}{l} & B\\
"""
D=diagBuild(str_) #construct a diagram D from this input
#Also, tell the program about the following assumptions:
Commute(D['k']*D['h'],D['i']*D['f'])
Commute(D['l']*D['i'],D['j']*D['g'])
FibreProductProperty(D['h'],D['f'],D['k'],D['i'])
FibreProductProperty(D['i'],D['g'],D['l'],D['j'])
Commute(D['l']*D['k']*D['v'],D['j']*D['u'])
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)
# RM = RuleMaster(D,Rules = [FibreProductRuleUnique,FibreProductRule,ComposeRule])
#
# RM.rule_exhaustively()
# print latexDiag(D)
return D
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 test3():
str_=r"""P_1 \ar{r}{i1} & P_1 \oplus P_2 \ar[bend left]{dd}{f} & P_2 \ar{l}{i2}\\
& A \ar{d}{\pi} & \\
& B &"""
D=diagBuild(str_) #construct a diagram D from this input
#Also, tell the program about the following assumptions:
Projective(D['P_1']) #the object of D named 'P_1' is projective
Projective(D['P_2']) #the object of D named 'P_2' is projective
Epimorphism(D[r'\pi']) #the morphism named '\pi' is an epimorphism
CoProductProperty(D['i1'],D['i2']) #P_1 \oplus P_2 is a coproduct with canonical embeddings i1,i2
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