lcm = SparsePolynomial.lcm([sp1,sp2])
print("Expected: \t", "x**2*y**3 + x**3*y**2")
print("Actual: \t", lcm)
print("--- Division Test ---------------------------------------------------")
sp1 = SparsePolynomial.from_string("x**2 - 1", ['x'])
sp2 = SparsePolynomial.from_string("x - 1", ['x'])
quo = sp1//sp2
print("Expected: \t", "x + 1")
print("Actual: \t", quo)
sp = SparsePolynomial.from_string("1",['x'])
assert sp.is_unitary()
sp = SparsePolynomial(['x'])
assert sp.is_zero()
rf = RationalFunction.from_string("(PI3KInactive**3*boundEGFReceptor**2*kPI3K + PI3KInactive**3*RasActive**2*kPI3KRas + KmPI3K*PI3KInactive**2*RasActive**2*kPI3KRas + KmPI3KRas*PI3KInactive**2*boundEGFReceptor**2*kPI3K)/(PI3KInactive**2 + KmPI3K*KmPI3KRas + KmPI3K*PI3KInactive + KmPI3KRas*PI3KInactive)",
['PI3KInactive',
'boundEGFReceptor',
'kPI3K',
'RasActive',
'kPI3KRas',
'KmPI3K',
'KmPI3KRas',
])
print(rf)
rf.simplify()
print(rf)
def perform_change_of_variables(self, rhs, new_vars_name='y'):
"""
Restrict a system of ODEs with the rhs given by
rhs (SparsePolynomial or RationalFunction) to the subspace
new_vars_name (optional) - the name for variables in the lumped polynomials
"""
old_vars = rhs[0].gens
domain = rhs[0].domain
new_vars = [new_vars_name + str(i) for i in range(self.dim())]
pivots = set(self.parametrizing_coordinates())
lpivots = sorted(pivots)
basis = self.basis()
logging.debug("Constructing new rhs")
if isinstance(rhs[0], SparsePolynomial):
new_rhs = [
SparsePolynomial(old_vars, domain) for _ in range(self.dim())
]
elif isinstance(rhs[0], RationalFunction):
new_rhs = [
RationalFunction(
SparsePolynomial(old_vars, domain),
SparsePolynomial.from_string("1", old_vars, domain))
for _ in range(self.dim())
]
for i, vec in enumerate(basis):
logging.debug(f" Equation number {i}")
for j in vec.nonzero_iter():
# ordering is important due to the implementation of
# multiplication for SparsePolynomial
new_rhs[i] += rhs[j] * vec._data[j]
logging.debug("Plugging zero to nonpivot coordinates")
if isinstance(rhs[0], SparsePolynomial):
shrinked_polys = []
for p in new_rhs:
filtered_dict = dict()
for monom, coef in p.dataiter():
new_monom = []
skip = False
for var, exp in monom:
if var not in pivots:
skip = True
break
else:
new_monom.append((lpivots.index(var), exp))
if not skip:
new_monom = tuple(new_monom)
filtered_dict[new_monom] = coef
shrinked_polys.append(
SparsePolynomial(new_vars, domain, filtered_dict))
return shrinked_polys
elif isinstance(rhs[0], RationalFunction):
# plugging all nonpivot variables with zeros
shrinked_rfs = []
for rf in new_rhs:
num_filtered_dict = dict()
for monom, coef in rf.num.dataiter():
new_monom = []
skip = False
for var, exp in monom:
if var not in pivots:
skip = True
break
else:
new_monom.append((lpivots.index(var), exp))
if not skip:
new_monom = tuple(new_monom)
num_filtered_dict[new_monom] = coef
new_num = SparsePolynomial(new_vars, domain, num_filtered_dict)
denom_filtered_dict = dict()
for monom, coef in rf.denom.dataiter():
new_monom = []
skip = False
for var, exp in monom:
if var not in pivots:
skip = True
break
else:
new_monom.append((lpivots.index(var), exp))
if not skip:
new_monom = tuple(new_monom)
denom_filtered_dict[new_monom] = coef
new_denom = SparsePolynomial(new_vars, domain,
denom_filtered_dict)
if new_denom.is_zero() and False:
print()
print("Before plugging all nonpivot variables with zeros:")
print('\t', rf)
print()
print("After plugging all nonpivot variables with zeros:")
print('\t', f"({new_num})/({new_denom})")
print()
raise ZeroDivisionError
shrinked_rfs.append(RationalFunction(new_num, new_denom))
return shrinked_rfs