def pow_to_mul(expr):
if expr.is_Atom or expr.is_Indexed:
return expr
elif expr.is_Pow:
base, exp = expr.as_base_exp()
if exp <= 0 or not exp.is_integer:
# Cannot handle powers containing non-integer non-positive exponents
return expr
else:
return sympy.Mul(*[base] * exp, evaluate=False)
else:
return expr.func(*[pow_to_mul(i) for i in expr.args], evaluate=False)
def my_sympify(expr, normphase=False, matrix=False, abcsym=False, do_qubit=False, symtab=None):
# make all lowercase real?
if symtab:
varset = symtab
else:
varset = {'p': sympy.Symbol('p'),
'g': sympy.Symbol('g'),
'e': sympy.E, # for exp
'i': sympy.I, # lowercase i is also sqrt(-1)
'Q': sympy.Symbol('Q'), # otherwise it is a sympy "ask key"
'I': sympy.Symbol('I'), # otherwise it is sqrt(-1)
'N': sympy.Symbol('N'), # or it is some kind of sympy function
#'X':sympy.sympify('Matrix([[0,1],[1,0]])'),
#'Y':sympy.sympify('Matrix([[0,-I],[I,0]])'),
#'Z':sympy.sympify('Matrix([[1,0],[0,-1]])'),
'ZZ': sympy.Symbol('ZZ'), # otherwise it is the PythonIntegerRing
'XI': sympy.Symbol('XI'), # otherwise it is the capital \XI
'hat': sympy.Function('hat'), # for unit vectors (8.02)
}
if do_qubit: # turn qubit(...) into Qubit instance
varset.update({'qubit': sympy.physics.quantum.qubit.Qubit,
'Ket': sympy.physics.quantum.state.Ket,
'dot': dot,
'bit': sympy.Function('bit'),
})
if abcsym: # consider all lowercase letters as real symbols, in the parsing
for letter in string.lowercase:
if letter in varset: # exclude those already done
continue
varset.update({letter: sympy.Symbol(letter, real=True)})
sexpr = sympify(expr, locals=varset)
if normphase: # remove overall phase if sexpr is a list
if type(sexpr) == list:
if sexpr[0].is_number:
ophase = sympy.sympify('exp(-I*arg(%s))' % sexpr[0])
sexpr = [sympy.Mul(x, ophase) for x in sexpr]
def to_matrix(x): # if x is a list of lists, and is rectangular, then return Matrix(x)
if not type(x) == list:
return x
for row in x:
if (not type(row) == list):
return x
rdim = len(x[0])
for row in x:
if not len(row) == rdim:
return x
return sympy.Matrix(x)
if matrix:
sexpr = to_matrix(sexpr)
return sexpr
def convert_mp(mp):
if hasattr(mp, 'mp'):
mp_left = mp.mp(0)
mp_right = mp.mp(1)
else:
mp_left = mp.mp_nofunc(0)
mp_right = mp.mp_nofunc(1)
if mp.MUL() or mp.CMD_TIMES() or mp.CMD_CDOT():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, rh, evaluate=False)
elif mp.DIV() or mp.CMD_DIV() or mp.COLON():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, sympy.Pow(rh, -1, evaluate=False), evaluate=False)
else:
if hasattr(mp, 'unary'):
return convert_unary(mp.unary())
else:
return convert_unary(mp.unary_nofunc())
def element_to_sympy(elem):
if isinstance(elem, formula.Frac):
return sympy.Mul(elementlist_to_sympy(elem.numerator),
sympy.Pow(elementlist_to_sympy(elem.denominator), -1))
elif isinstance(elem, formula.Abs):
return sympy.Abs(elementlist_to_sympy(elem.argument))
elif isinstance(elem, formula.Radical):
index = elementlist_to_sympy(elem.index) or 2
return sympy.Pow(elementlist_to_sympy(elem.radicand),
sympy.Pow(index, -1))
else:
raise NotImplementedError
def expand_mul(expr):
assert isinstance(expr, sp.Mul)
commutative, other = split_commutative(expr)
commutative = [(apply_characteristic(v) if isinstance(v, sp.Number) else v)
for v in commutative]
commutative = sp.Mul(*commutative)
if commutative == 0:
return S.Zero
terms = [expand_with_transformers_impl(term) for term in other]
for tr in config['mul']:
terms = apply_transformer_termwise(terms, tr)
def catch_zeros(expr):
s = str(expr)
for z in zeros_mul:
if z in s:
return S.Zero
for z in zeros_pow:
if z in s:
return S.Zero
return expr
def postprocess(expr):
# TODO: are these actually needed?
# expr = sp.powsimp(expr)
# expr = sp.expand_mul(expr)
# TODO: get rid of this
expr = catch_zeros(expr)
return expr
# FIXME: THIS COULD BE A BUG if one of the transformers yielded something
# like an Add whose part could be matched by catch_zeros and thus the whole
# expression would be marked as zero, which it is not. Currently there are no
# such transformers in mul, but there may be.
# Anyway, catch_zeros is evil and should be abandoned.
return commutative * postprocess(sp.Mul(*terms))
def out_add_f(expr01, cof_list, cof_dict, vector_add):
if isinstance(expr01, sympy.Add):
wiss = [sympy.Symbol("W%s" % i) for i, j in enumerate(expr01.args)]
args_new = [(wi, sympy.Mul(wi, ei)) if not ei.is_number else (None, ei) for ei, wi in
zip(expr01.args, wiss)]
wis, we = zip(*args_new)
cof_list.extend([wi for wi in wis if wi is not None])
argss = sympy.Add(*we)
expr01 = argss
elif isinstance(expr01, M3):
exprin1 = expr01.args[0]
conu = expr01.conu
if isinstance(exprin1, sympy.Add):
wiss = [sympy.Symbol("W%s" % i) for i, j in enumerate(exprin1.args)]
args_new = [(wi, sympy.Mul(wi, ei)) if not ei.is_number else (None, ei) for ei, wi in
zip(exprin1.args, wiss)]
wis, we = zip(*args_new)
cof_list.extend([wi for wi in wis if wi is not None])
argss = sympy.Add(*we)
expr01 = expr01.func(argss)
if vector_add:
if conu > 1:
Wi = sympy.Symbol("V")
arg = expr01.args[0]
expr02 = expr01.func(sympy.Mul(Wi, arg))
cof_dict[Wi] = conu
expr01 = expr02
else:
A = sympy.Symbol("A")
expr01 = sympy.Mul(expr01, A)
cof_list.append(A)
else:
A = sympy.Symbol("A")
expr01 = sympy.Mul(expr01, A)
cof_list.append(A)
return expr01
def eval(cls, A, B):
if not A != B:
return sp.S.Zero
if A.is_commutative or B.is_commutative:
return sp.S.Zero
if isinstance(A, sp.Add):
sargs = []
for term in A.args:
sargs.append(Corxet(term, B))
return sp.Add(*sargs)
if isinstance(B, sp.Add):
sargs = []
for term in B.args:
sargs.append(Corxet(A, term))
return sp.Add(*sargs)
cA, ncA = A.args_cnc()
cB, ncB = B.args_cnc()
c_part = cA + cB
if c_part:
return sp.Mul(sp.Mul(*c_part),
cls(sp.Mul._from_args(ncA), sp.Mul._from_args(ncB)))
if A.compare(B) == 1:
return sp.S.NegativeOne * cls.eval(cls, B, A)
i, j, k, l = A.i, A.j, B.i, B.j
if A.t != B.t:
printe("Els objectes %s i %s no pertanyen a la mateixa base." %
(A, B))
exit(-1)
if A.t == "E":
ll = rl.corxetErel(i, j, k, l)
elif A.t == "Z":
ll = rl.corxetZrel(i, j, k, l)
else:
printe("No hi ha cap base definida amb %s." % (A.t))
exit(-1)
args = []
for it in ll:
elem = sp.Mul(sp.Rational(it[0], it[1]), Eel(it[2], it[3], A.t))
args.append(elem)
return sp.Add(*args)
def _arg_func_from_proto(
func: v2.program_pb2.ArgFunction,
*,
arg_function_language: str,
required_arg_name: Optional[str] = None,
) -> Optional[ARG_LIKE]:
supported = SUPPORTED_FUNCTIONS_FOR_LANGUAGE.get(arg_function_language)
if supported is None:
raise ValueError(f'Unrecognized arg_function_language: {arg_function_language!r}')
if func.type not in supported:
raise ValueError(
f'Unrecognized function type {func.type!r} '
f'for arg_function_language={arg_function_language!r}'
)
if func.type == 'add':
return sympy.Add(
*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='An addition argument',
)
for a in func.args
]
)
if func.type == 'mul':
return sympy.Mul(
*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='A multiplication argument',
)
for a in func.args
]
)
if func.type == 'pow':
return sympy.Pow(
*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='A power argument',
)
for a in func.args
]
)
return None
def get_spontaneous_decay_rate(self,
z=sp.Symbol('Z', real=True),
mu=sp.Symbol('mu', real=True),
algo="auto"):
"""
Get the spontaneous decay rate of the transition
:param z: atomic number (int)
:param mu: reduced mass (float)
:return: the spontaneous decay rate (float)
"""
# check if spontaneous_decay_rate is already calculated
if self.spontaneous_decay_rate is not None:
return self.spontaneous_decay_rate
elif self.repr_without_spin(
) in Transition.n_ell_m_ell_state_to_rs.keys():
self.spontaneous_decay_rate = Transition.n_ell_m_ell_state_to_rs[
self.repr_without_spin()]
return self.spontaneous_decay_rate
r, theta, phi = sp.Symbol("r", real=True, positive=True), sp.Symbol("theta", real=True),\
sp.Symbol("phi", real=True)
coeff = (4 * const.alpha *
(self.get_delta_energy(z, mu)**3)) / (3 * (const.hbar**3) *
(const.c**2))
psi = self._initial_quantum_state.get_wave_function(z, mu)
psi_prime = self._ending_quantum_state.get_wave_function(z, mu)
if algo == "auto":
if self._initial_quantum_state.hydrogen and self._ending_quantum_state.hydrogen:
algo = "sympy_ns"
else:
algo = "scipy_nquad"
# \Vec{r} = x + y + z
r_operator = r * (sp.sin(theta) * sp.cos(phi) +
sp.sin(theta) * sp.sin(phi) + sp.cos(theta))
# Process the integral with algo
bracket_product = QuantumFactory.bracket_product(
psi, psi_prime, r_operator, algo)
bracket_product_norm_square = sp.Mul(sp.conjugate(bracket_product),
bracket_product).evalf()
# print(bracket_product_norm_square)
self.spontaneous_decay_rate = sp.Float(coeff *
bracket_product_norm_square)
# updating Transition static attribute
Transition.n_ell_m_ell_state_to_rs[
self.repr_without_spin()] = self.spontaneous_decay_rate
return self.spontaneous_decay_rate
def f1(x, xT, P, A):
"""
:param x: matrix
:param xT: transpose of x
:param P: matrix
:param A: matrix
:return: x^T (A^T P + P A) x
"""
AT = sp.Transpose(A)
e0 = sp.Mul(AT, P, evaluate=False)
e1 = sp.Mul(P, A, evaluate=False)
e2 = sp.Add(e0, e1, evaluate=False)
e = sp.Mul(xT, e2, evaluate=False)
e = sp.Mul(e, x, evaluate=False)
m = {
str(P[r, c]): P[r, c]
for r in range(P.shape[0]) for c in range(P.shape[0])
}
m.update({str(x): x for x in x})
e = parse_expr(str(e), local_dict=m)
# res = sp.expand((xT * (AT * P + P * A) * x)[0])
return sp.expand(e[0])
def pow_to_mul(expr):
if expr.is_Atom or expr.is_Indexed:
return expr
elif expr.is_Pow:
base, exp = expr.as_base_exp()
if exp > 10 or exp < -10 or int(exp) != exp or exp == 0:
# Large and non-integer powers remain untouched
return expr
elif exp == -1:
# Reciprocals also remain untouched, but we traverse the base
# looking for other Pows
return expr.func(pow_to_mul(base), exp, evaluate=False)
elif exp > 0:
return sympy.Mul(*[base]*int(exp), evaluate=False)
else:
# SymPy represents 1/x as Pow(x,-1). Also, it represents
# 2/x as Mul(2, Pow(x, -1)). So we shouldn't end up here,
# but just in case SymPy changes its internal conventions...
posexpr = sympy.Mul(*[base]*(-int(exp)), evaluate=False)
return sympy.Pow(posexpr, -1, evaluate=False)
else:
return expr.func(*[pow_to_mul(i) for i in expr.args], evaluate=False)
def convert_add(add):
if add.ADD():
lh = convert_add(add.additive(0))
rh = convert_add(add.additive(1))
return sympy.Add(lh, rh, evaluate=False)
elif add.SUB():
lh = convert_add(add.additive(0))
rh = convert_add(add.additive(1))
# return sympy.Add(lh, -1 * rh, evaluate=False)
# just keep the origin expression, don't simplify
return sympy.Add(lh, sympy.Mul(-1, rh, evaluate=False), evaluate=False)
else:
return convert_mp(add.mp())
def ma(self):
"""Return the mass action monomial associated to the complex.
:Example:
>>> c1 = Complex({'S': 2, 'E': 1})
>>> c1.ma()
E*S**2
:rtype: sympy expression.
"""
if self == {}: return 1
return sp.Mul(*(sp.Symbol(r)**self[r] for r in self))
def hack_simplify_sum(expr):
# https://stackoverflow.com/questions/62679575/why-cant-sympy-simplify-these-sum-expressions-of-indexed-variables
# https://github.com/sympy/sympy/issues/19685
if expr.func is sym.concrete.summations.Sum:
body, (idx, lower, upper) = expr.args
if idx not in body.free_symbols:
factor = (upper + 1) - lower
return factor * body
else:
if body.func is sym.Mul:
factor_out = []
factor_in = []
for sub_arg in body.args:
if idx in sub_arg.free_symbols:
factor_in.append(sub_arg)
else:
factor_out.append(sub_arg)
outer = sym.Mul(*factor_out)
return outer * sym.summation(sym.Mul(*factor_in),
(idx, lower, upper))
return expr
def residue(self, pole, poles):
"""Determine residue for given pole."""
expr = self.expr
var = self.var
# Remove occurrence of pole; sym.cancel
# doesn't always work, for example, for complex poles.
occurrences = []
for p in poles:
occurrences += [p.n - 1 if p.expr == pole else p.n]
numer, denom = expr.as_numer_denom()
Dpoly = sym.Poly(denom, var)
K = Dpoly.LC()
D = [(var - p.expr)**o for p, o in zip(poles, occurrences)]
denom = sym.Mul(K, *D)
# Could calculate all residues simultaneously using
# system of linear equations.
def method1(numer, denom, var, pole):
d = sym.limit(denom, var, pole)
if d != 0:
tmp = (numer / denom).simplify()
# Sometimes this takes ages...
return sym.limit(tmp, var, pole)
# Use l'Hopital's rule
tmp = numer / denom
tmp = sym.diff(tmp, var)
return sym.limit(tmp, var, pole)
def method2(numer, denom, var, pole):
d = denom.subs(var, pole)
n = numer.subs(var, pole)
if d != 0:
return n / d
ddenom = sym.diff(denom, var)
return n / ddenom.subs(pole)
m2 = method2(numer, denom, var, pole)
return m2.cancel()
def _parse_reaction(model, line, reaction_cache):
"""Parse a 'reaction' line from a BNGL net file."""
(number, reactants, products, rate, rule) = line.strip().split(' ', 4)
# the -1 is to switch from one-based to zero-based indexing
reactants = tuple(int(r) - 1 for r in reactants.split(',') if r != '0')
products = tuple(int(p) - 1 for p in products.split(',') if p != '0')
rate = rate.rsplit('*')
(rule_list, unit_conversion) = re.match(
r'#([\w,\(\)]+)(?: unit_conversion=(.*))?\s*$', rule).groups()
rule_list = rule_list.split(',') # BNG lists all rules that generate a rxn
# Support new (BNG 2.2.6-stable or greater) and old BNG naming convention
# for reverse rules
rule_name, is_reverse = zip(
*[re.subn('^_reverse_|\(reverse\)$', '', r) for r in rule_list])
is_reverse = tuple(bool(i) for i in is_reverse)
r_names = ['__s%d' % r for r in reactants]
rate_param = [
model.parameters.get(r) or model.expressions.get(r)
or model._derived_parameters.get(r)
or model._derived_expressions.get(r) or float(r) for r in rate
]
combined_rate = sympy.Mul(*[sympy.S(t) for t in r_names + rate_param])
reaction = {
'reactants': reactants,
'products': products,
'rate': combined_rate,
'rule': rule_name,
'reverse': is_reverse,
}
model.reactions.append(reaction)
# bidirectional reactions
key = (reactants, products)
key_reverse = (products, reactants)
if key in reaction_cache:
reaction_bd = reaction_cache.get(key)
reaction_bd['rate'] += combined_rate
reaction_bd['rule'] += tuple(r for r in rule_name
if r not in reaction_bd['rule'])
elif key_reverse in reaction_cache:
reaction_bd = reaction_cache.get(key_reverse)
reaction_bd['reversible'] = True
reaction_bd['rate'] -= combined_rate
reaction_bd['rule'] += tuple(r for r in rule_name
if r not in reaction_bd['rule'])
else:
# make a copy of the reaction dict
reaction_bd = dict(reaction)
# default to false until we find a matching reverse reaction
reaction_bd['reversible'] = False
reaction_cache[key] = reaction_bd
model.reactions_bidirectional.append(reaction_bd)
def std_latex_array(self, out_var=None):
l_scalar, r_scalar = self.get_scalar()
l_part = []
r_part = [sympy.latex(r_scalar)]
for variable in self.variables:
l_coeff, r_coeff = self.get_coeff(variable)
substitution = self.substitutions.get(variable, variable)
if l_coeff != 0:
l_part.append(sympy.latex(sympy.Mul(l_coeff, substitution, evaluate=False)))
if r_coeff < 0:
r_part.append("-")
r_part.append(sympy.latex(sympy.Mul(-r_coeff, substitution, evaluate=False)))
elif r_coeff > 0:
r_part.append("+")
r_part.append(sympy.latex(sympy.Mul(r_coeff, substitution, evaluate=False)))
elif out_var:
if variable in out_var:
r_part += ["", ""]
else:
pass
else:
r_part += ["", ""]
l_part = " & ".join(l_part)
r_part = " & ".join(r_part)
comp = {
'LEQ' : r"""\leq""",
'EQ' : r"""=""",
'GEQ' : r"""\geq""",
}[self.comp]
return l_part + " & " + comp + " & " + r_part + r"""\\"""
def parse_term(self, expr):
syms = []
cons = []
if type(expr) == sy.Symbol:
syms.append(expr)
cons.append(1)
elif type(expr) == sy.Pow:
var, exponent = expr.args
if type(var) == sy.Symbol:
syms.append(expr)
cons.append(1)
else:
cons.append(expr)
else:
for arg in expr.args:
if type(arg) == sy.Symbol:
syms.append(arg)
elif type(arg) == sy.Pow:
var, exponent = arg.args
if type(var) == sy.Symbol:
syms.append(arg)
else:
cons.append(arg)
else:
cons.append(arg)
const_term = 1
syms_term = None
if len(cons) == 1:
const_term = cons[0]
elif len(cons) > 1:
const_term = sy.Mul(*cons)
if len(syms) == 1:
syms_term = syms[0]
elif len(syms) > 0:
syms_term = sy.Mul(*syms)
return const_term, syms_term
def add_coefficient(expr01, inter_add=True, inner_add=False, vector_add=False, out_add=False, flat_add=False):
"""
Try add the placeholder coefficient to sympy expression.
1. Add Wi,A,B normal coefficients to expression.
2. Add V, Vi vector coefficients to expression, for this type of coefficient ,
there should be with expr01.conu for Function("MAdd"), Function("MSub").
more details can be found in ..translate.simple
Parameters
----------
expr01: Expr
sympy expressions
inter_add: bool
bool
inner_add: bool
bool
vector_add:bool
bool
flat_add:bool
bool
out_add:bool
bool
Returns
-------
expr
"""
cof_list = []
cof_dict = {}
assert len([i for i in [inner_add, out_add, flat_add] if i is True]) <= 1, \
"For the 'out_add','flat_add'and 'out_add', you should just choose one of them."
if out_add: # out layer
expr01 = out_add_f(expr01, cof_list, cof_dict, vector_add)
elif inner_add: # out and inner layer each add and Madd...
expr01 = inner_add_f(expr01, cof_list, cof_dict, vector_add)
elif flat_add: # out and inner layer each add and Madd... just open by add.
expr01 = flatten_add_f(expr01, cof_list, cof_dict, vector_add)
else:
A = sympy.Symbol("A")
expr01 = sympy.Mul(expr01, A)
cof_list.append(A)
if inter_add: # intercept
B = sympy.Symbol("B")
expr01 = sympy.Add(expr01, B)
cof_list.append(B)
return expr01, cof_list, cof_dict
def oneEpsAsDeltas(eps, **tempOverride):
'''Takes an instance of Eps and rewrites it as Deltas'''
dim, indexRange = delta.getTempDimAndIndexRange(**tempOverride)
if not isinstance(eps, Eps):
raise TypeError('Error: input must be an Eps(*indecis)')
if not len(eps.index) == dim:
raise TypeError('Error: Eps must have dim number of indices')
termList = []
for perm in permute_all(eps.index):
factorList = [perm['parity']]
for (pos, index) in enumerate(perm['perm']):
factorList.append(delta.Delta(pos + 1, index))
termList.append(sympy.Mul(*factorList))
return sympy.Add(*termList)
def _print_Pow(self, expr):
result = self._scalarFallback('_print_Pow', expr)
if result:
return result
one = self.instruction_set['makeVecConst'].format(1.0, **self._kwargs)
if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
elif expr.exp == -1:
one = self.instruction_set['makeVecConst'].format(1.0, **self._kwargs)
return self.instruction_set['/'].format(one, self._print(expr.base), **self._kwargs)
elif expr.exp == 0.5:
return self.instruction_set['sqrt'].format(self._print(expr.base), **self._kwargs)
elif expr.exp == -0.5:
root = self.instruction_set['sqrt'].format(self._print(expr.base), **self._kwargs)
return self.instruction_set['/'].format(one, root, **self._kwargs)
elif expr.exp.is_integer and expr.exp.is_number and - 8 < expr.exp < 0:
return self.instruction_set['/'].format(one,
self._print(sp.Mul(*[expr.base] * (-expr.exp), evaluate=False)),
**self._kwargs)
else:
raise ValueError("Generic exponential not supported: " + str(expr))
def pow_to_mul(expr):
"""
Convert integer powers in an expression to Muls, like a**2 => a*a.
"""
pows = list(expr.atoms(sympy.Pow))
if any(not e.is_Integer for b, e in (i.as_base_exp() for i in pows)):
raise ValueError("A power contains a non-integer exponent")
print(pows)
for b, e in (i.as_base_exp() for i in pows):
print(b, e)
repl = zip(pows, (sympy.Mul(*[b] * e, evaluate=False)
for b, e in (i.as_base_exp() for i in pows)))
#print repl
return expr.subs(repl)
def zeros_to_coeffs(*z_list, **kwargs):
"""
calculates the coeffs corresponding to a poly with provided zeros
"""
s = sp.Symbol("s")
p = sp.Mul(*[s-s0 for s0 in z_list])
real_coeffs = kwargs.get("real_coeffs", True)
c = np.array(coeffs(p, s), dtype=np.float)
if real_coeffs:
c = np.real(c)
return c
def distribute(e, x):
"""Helper method to apply distributive multiplication.
This helps by allowing the use of 'subs' instead of 'limit'
in special circumstances
"""
# traverse the operations graph
if e.is_Add:
return sp.Add(*[distribute(a, x) for a in e.args])
elif e.is_Mul:
o = sp.Integer(1)
done = False
for a in e.args:
if x in a.atoms() and not done:
# prefer multiply where x is found
# seek for simplification
o = sp.Mul(o, distribute(a, x))
done = True
else:
o = sp.Mul(o, a)
return o if done else sp.Mul(o, x)
else:
return sp.Mul(e, x)
def _interpolate_Function(expr):
path = 'None'
factor = 'None'
change = False
summand_0 = 'None'
summand_1 = 'None'
res = expr
for i in np.arange(len(expr.args)):
argument = sympy.expand(expr.args[i])
if argument.func == sympy.Add:
for j in np.arange(len(argument.args)):
summand = argument.args[j]
if summand.func == sympy.Mul:
for k in np.arange(len(summand.args)):
temp = 0
if summand.args[k] == sympy.Symbol('a'):
temp = sympy.Mul(sympy.Mul(*summand.args[:k]),
sympy.Mul(*summand.args[k + 1:]))
#print(temp)
if not temp == int(temp):
#print('found one')
factor = (temp)
path = np.array([i, j, k])
if not factor == 'None':
change = True
sign = np.sign(factor)
offsets = np.array([int(factor), sign * (int(sign * factor) + 1)])
weights = 1 / np.abs(offsets - factor)
weights = weights / np.sum(weights)
res = (weights[0] *
_interchange(expr, offsets[0] * sympy.Symbol('a'), path[:-1]) +
weights[1] *
_interchange(expr, offsets[1] * sympy.Symbol('a'), path[:-1]))
return sympy.expand(res), change
def expected(expr):
cls = expr.__class__
if cls == sp.Add:
return sp.Add(*[expected(elem) for elem in expr.args])
if cls == sp.Mul:
return sp.Mul(*[expected(elem) for elem in expr.args])
if cls == sp.Pow and isinstance(expr.args[0],RandomVar):
if (not expr.args[1].is_integer):
raise Exception("Can't do expected values of non-integer powers")
if expr.args[1]<0:
raise Exception("Can't do expected values of negative powers (including division)")
return moment(expr.args[0], expr.args[1])
if isinstance(expr, RandomVar):
return moment(expr, 1)
return expr
def expand_tp(expr):
l, r = expr.args
l = expand_with_transformers_impl(l)
r = expand_with_transformers_impl(r)
if l == 0 or r == 0:
return S.Zero
if isinstance(l, sp.Add):
expr = sp.Add(*[TP(arg, r) for arg in l.args])
return expand_with_transformers_impl(expr)
if isinstance(r, sp.Add):
expr = sp.Add(*[TP(l, arg) for arg in r.args])
return expand_with_transformers_impl(expr)
lc, lnc = split_commutative(l) if isinstance(l, sp.Mul) else ([S.One], [l])
rc, rnc = split_commutative(r) if isinstance(r, sp.Mul) else ([S.One], [r])
lnc = sp.Mul(*lnc)
rnc = sp.Mul(*rnc)
commutative = sp.Mul(*(lc + rc))
tp = TP(lnc, rnc)
return commutative * tp
def convert_frac(frac):
diff_op = False
partial_op = False
lower_itv = frac.lower.getSourceInterval()
lower_itv_len = lower_itv[1] - lower_itv[0] + 1
if (frac.lower.start == frac.lower.stop
and frac.lower.start.type == PSLexer.DIFFERENTIAL):
wrt = get_differential_var_str(frac.lower.start.text)
diff_op = True
elif (lower_itv_len == 2 and frac.lower.start.type == PSLexer.SYMBOL
and frac.lower.start.text == '\\partial'
and (frac.lower.stop.type == PSLexer.LETTER_NO_E
or frac.lower.stop.type == PSLexer.SYMBOL)):
partial_op = True
wrt = frac.lower.stop.text
if frac.lower.stop.type == PSLexer.SYMBOL:
wrt = wrt[1:]
if diff_op or partial_op:
wrt = sympy.Symbol(wrt, real=True, positive=True)
if (diff_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == PSLexer.LETTER_NO_E
and frac.upper.start.text == 'd'):
return [wrt]
elif (partial_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == PSLexer.SYMBOL
and frac.upper.start.text == '\\partial'):
return [wrt]
upper_text = rule2text(frac.upper)
expr_top = None
if diff_op and upper_text.startswith('d'):
expr_top = process_sympy(upper_text[1:])
elif partial_op and frac.upper.start.text == '\\partial':
expr_top = process_sympy(upper_text[len('\\partial'):])
if expr_top:
return sympy.Derivative(expr_top, wrt)
expr_top = convert_expr(frac.upper)
expr_bot = convert_expr(frac.lower)
if expr_top.is_Matrix or expr_bot.is_Matrix:
return sympy.MatMul(expr_top,
sympy.Pow(expr_bot, -1, evaluate=False),
evaluate=False)
else:
return sympy.Mul(expr_top,
sympy.Pow(expr_bot, -1, evaluate=False),
evaluate=False)
def check_filter_equations(self):
made_changes = False
# Expand, and remove instances of '0 = 0' and 'non-zero number != 0'
len_cl, len_op = len(self.cl_eqs), len(self.op_eqs)
self.cl_eqs = list({ sp.expand(e) for e in self.cl_eqs if e != 0 })
self.op_eqs = list({ sp.expand(e) for e in self.op_eqs if not e.is_complex or e == 0 })
if len(self.cl_eqs) != len_cl or len(self.op_eqs) != len_op:
made_changes = True
# If any equation is of the form 'x = 0', we can solve for x = 0 and continue with the remaining system
for x in [ eq for eq in self.cl_eqs if eq.is_Symbol and eq in self.vars ]:
self.vars = self.vars.difference({x,})
self.cl_eqs = [ e.subs(x, 0) for e in self.cl_eqs ]
self.op_eqs = [ e.subs(x, 0) for e in self.op_eqs ]
made_changes = True
for eq in self.cl_eqs:
eq_factor = sp.factor(eq)
# If any equation is of the form '(...)^n = 0', we can simply substitute with '(...) = 0' (provided n is positive)
if eq_factor.is_Pow:
if eq_factor.args[1] < 0:
return 0
self.cl_eqs = [ eq_factor.args[0] if e == eq else e for e in self.cl_eqs]
# If any equation is a product, we can remove all denominators and all numeric factors. Also, one can remove all higher multiplicities
if eq_factor.is_Mul:
unnecessary_factors = [ a for a in eq_factor.args if a.is_complex or (a.is_Pow and a.args[1] < 0) ]
higher_multiplicity = [ a for a in eq_factor.args if a.is_Pow and a.args[1] > 0 ]
if unnecessary_factors or higher_multiplicity:
replacement = sp.Mul(*( f.args[0] if f in higher_multiplicity else f for f in eq_factor.args if f not in unnecessary_factors ))
self.cl_eqs = [ replacement if e == eq else e for e in self.cl_eqs ]
made_changes = True
for eq in self.op_eqs:
eq_factor = sp.factor(eq)
# If an equation is of the form '(u) * ... * (v) != 0', replace by '(u) != 0 & ... & (v) != 0'
if eq_factor.is_Mul:
self.op_eqs = [ e for e in self.op_eqs if e != eq ] + [ f for f in eq_factor.args if not f.is_complex]
made_changes = True
if made_changes:
return self.compute_class()
return None
def seperate_coeff(big_term):
coefficients = []
terms = []
for term in big_term:
if term.func == sympy.Pow:
coefficients.append(1)
mul2 = [term.args[0]] * term.args[1]
else:
mul2 = []
for arg in term.args:
if arg.is_Integer is True:
coefficients.append(arg)
else:
mul2.append(arg)
terms.append(sympy.Mul(*mul2))
return (terms, coefficients)