# Source code for crnt4sbml.low_deficiency_approach

```
import re
[docs]class LowDeficiencyApproach:
"""
Class for testing the Deficiency Zero and One Theorems.
"""
[docs] def __init__(self, cgraph):
"""
Initialization of LowDeficiency Approach class.
See also
---------
crnt4sbml.CRNT.get_low_deficiency_approach()
"""
self.__satisfies_deficiency_zero_theorem = False
self.__satisfies_deficiency_one_theorem = False
self.__satisfies_relaxed_deficiency_one_theorem = False
# key conditions
self.__cond1 = cgraph.get_if_cgraph_weakly_reversible()
cond2 = cgraph.get_deficiency() == 0
lcd = cgraph.get_linkage_classes_deficiencies()
cond3 = all([i < 2 for i in lcd])
cond4 = sum(lcd) == cgraph.get_deficiency()
tlc = cgraph.get_number_of_terminal_strong_lc_per_lc()
cond5 = all([i < 2 for i in tlc])
# decision tree for low deficiency theorems
if cond2:
# deficiency zero theorem
self.__satisfies_deficiency_zero_theorem = True
elif self.__cond1 and cond3 and cond4:
# deficiency one theorem
self.__satisfies_deficiency_one_theorem = True
elif cond5 and cond3 and cond4:
# deficiency one theorem with relaxed criteria
self.__satisfies_relaxed_deficiency_one_theorem = True
[docs] def does_satisfy_any_low_deficiency_theorem(self):
"""
Function to see if the network satisfies the Deficiency Zero or One Theorem. Returns True if the network
satisfies the Deficiency Zero or One Theorem, False otherwise.
:download:`Fig1Ci.xml <../../sbml_files/Fig1Ci.xml>` for the provided
example.
Example
--------
>>> import crnt4sbml
>>> network = crnt4sbml.CRNT("path/to/Fig1Ci.xml")
>>> approach = network.get_low_deficiency_approach()
>>> print(approach.does_satisfy_any_low_deficiency_theorem())
False
"""
return (self.__satisfies_deficiency_zero_theorem or
self.__satisfies_deficiency_one_theorem or
self.__satisfies_relaxed_deficiency_one_theorem)
[docs] def does_satisfy_deficiency_zero_theorem(self):
"""
Function to see if the network satisfies the Deficiency Zero Theorem. Returns True if the network
satisfies the Deficiency Zero Theorem, False otherwise.
:download:`Fig1Ci.xml <../../sbml_files/Fig1Ci.xml>` for the provided
example.
Example
--------
>>> import crnt4sbml
>>> network = crnt4sbml.CRNT("path/to/Fig1Ci.xml")
>>> approach = network.get_low_deficiency_approach()
>>> print(approach.does_satisfy_deficiency_zero_theorem())
False
"""
return self.__satisfies_deficiency_zero_theorem
[docs] def does_satisfy_deficiency_one_theorem(self):
"""
Function to see if the network satisfies the Deficiency One Theorem. Returns True if the network
satisfies the Deficiency One Theorem, False otherwise.
:download:`Fig1Ci.xml <../../sbml_files/Fig1Ci.xml>` for the provided
example.
Example
--------
>>> import crnt4sbml
>>> network = crnt4sbml.CRNT("path/to/Fig1Ci.xml")
>>> approach = network.get_low_deficiency_approach()
>>> print(approach.does_satisfy_deficiency_one_theorem())
False
"""
return (self.__satisfies_deficiency_one_theorem or
self.__satisfies_relaxed_deficiency_one_theorem)
[docs] def report_deficiency_zero_theorem(self):
"""
Prints out the applicability of the Deficiency Zero Theorem for the provided network.
Possible output:
"By the Deficiency Zero Theorem, the differential equations
cannot admit a positive equilibrium or a cyclic composition
trajectory containing a positive composition. Thus, multiple
equilibria cannot exist for the network."
or
"By the Deficiency Zero Theorem, there exists within each positive
stoichiometric compatibility class precisely one equilibrium.
Thus, multiple equilibria cannot exist for the network."
or
"The network does not satisfy the Deficiency Zero Theorem, multistability cannot be excluded."
:download:`Fig1Ci.xml <../../sbml_files/Fig1Ci.xml>` for the provided
example.
Example
--------
>>> import crnt4sbml
>>> network = crnt4sbml.CRNT("path/to/Fig1Ci.xml")
>>> approach = network.get_low_deficiency_approach()
>>> print(approach.report_deficiency_zero_theorem())
The network does not satisfy the Deficiency Zero Theorem, multistability cannot be excluded.
"""
if self.__satisfies_deficiency_zero_theorem and not self.__cond1:
report = ("""
By the Deficiency Zero Theorem, the differential equations
cannot admit a positive equilibrium or a cyclic composition
trajectory containing a positive composition. Thus, multiple
equilibria cannot exist for the network.
""")
print(re.sub(r"^\s+", "", report, flags=re.MULTILINE))
elif self.__satisfies_deficiency_zero_theorem and self.__cond1:
report = ("""
By the Deficiency Zero Theorem, there exists within each positive
stoichiometric compatibility class precisely one equilibrium.
Thus, multiple equilibria cannot exist for the network.
""")
print(re.sub(r"^\s+", "", report, flags=re.MULTILINE))
else:
print("The network does not satisfy the Deficiency Zero Theorem, multistability cannot be excluded.")
[docs] def report_deficiency_one_theorem(self):
"""
Prints out the applicability of the Deficiency One Theorem for the provided network.
Possible output:
"By the Deficiency One Theorem, the differential equations
admit precisely one equilibrium in each positive stoichiometric
compatibility class. Thus, multiple equilibria cannot exist
for the network."
or
"The network satisfies relaxed Deficiency One Theorem. That is it
is not weakly reversable, but each linkage class contains no more
than one terminal linkage class. There can exist within a positive
stoichiometric compatibility class at most one equilibrium.
Thus, multiple equilibria cannot exist for the network."
or
"The network does not satisfy the Deficiency One Theorem, multistability cannot be excluded."
:download:`Fig1Ci.xml <../../sbml_files/Fig1Ci.xml>` for the provided
example.
Example
--------
>>> import crnt4sbml
>>> network = crnt4sbml.CRNT("path/to/Fig1Ci.xml")
>>> approach = network.get_low_deficiency_approach()
>>> print(approach.report_deficiency_zero_theorem())
The network does not satisfy the Deficiency One Theorem, multistability cannot be excluded.
"""
if self.__satisfies_deficiency_one_theorem:
report = ("""
By the Deficiency One Theorem, the differential equations
admit precisely one equilibrium in each positive stoichiometric
compatibility class. Thus, multiple equilibria cannot exist
for the network.
""")
print(re.sub(r"^\s+", "", report, flags=re.MULTILINE))
elif self.__satisfies_relaxed_deficiency_one_theorem:
report = ("""
The network satisfies relaxed Deficiency One Theorem. That is it
is not weakly reversable, but each linkage class contains no more
than one terminal linkage class. There can exist within a positive
stoichiometric compatibility class at most one equilibrium.
Thus, multiple equilibria cannot exist for the network.
""")
print(re.sub(r"^\s+", "", report, flags=re.MULTILINE))
else:
print("The network does not satisfy the Deficiency One Theorem, multistability cannot be excluded.")
```