def constrained_by(self):
"""
returns a list of parameters that constrain this parameter
"""
if self._is_constraint is None:
return []
params = []
for var in self.is_constraint._vars:
param = var.get_parameter()
if param.uniqueid != self.uniqueid:
params.append(param)
return params
#~ @property
#~ def in_constraints(self):
#~ """
#~ returns a list the labels of the constraints in which this parameter constrains another
#~
#~ you can then access all of the parameters of a given constraint via bundle.get_constraint(constraint)
#~ """
#~ return [param.uniquetwig for param in self.in_constraints_expressions]
python类var()的实例源码
def related_to(self):
"""
returns a list of all parameters that are either constrained by or constrain this parameter
"""
params = []
constraints = self.in_constraints
if self.is_constraint is not None:
constraints.append(self.is_constraint)
for constraint in constraints:
for var in constraint._vars:
param = var.get_parameter()
if param not in params and param.uniqueid != self.uniqueid:
params.append(param)
return params
# def sin(self):
# return np.sin(self.get_value(unit=u.rad))
def test_sylvester():
x = var('x')
assert sylvester(x**3 -7, 0, x) == sylvester(x**3 -7, 0, x, 1) == Matrix([[0]])
assert sylvester(0, x**3 -7, x) == sylvester(0, x**3 -7, x, 1) == Matrix([[0]])
assert sylvester(x**3 -7, 0, x, 2) == Matrix([[0]])
assert sylvester(0, x**3 -7, x, 2) == Matrix([[0]])
assert sylvester(x**3 -7, 7, x).det() == sylvester(x**3 -7, 7, x, 1).det() == 343
assert sylvester(7, x**3 -7, x).det() == sylvester(7, x**3 -7, x, 1).det() == 343
assert sylvester(x**3 -7, 7, x, 2).det() == -343
assert sylvester(7, x**3 -7, x, 2).det() == 343
assert sylvester(3, 7, x).det() == sylvester(3, 7, x, 1).det() == sylvester(3, 7, x, 2).det() == 1
assert sylvester(3, 0, x).det() == sylvester(3, 0, x, 1).det() == sylvester(3, 0, x, 2).det() == 1
assert sylvester(x - 3, x - 8, x) == sylvester(x - 3, x - 8, x, 1) == sylvester(x - 3, x - 8, x, 2) == Matrix([[1, -3], [1, -8]])
assert sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x) == sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x, 1) == Matrix([[1, 0, -7, 7, 0], [0, 1, 0, -7, 7], [3, 0, -7, 0, 0], [0, 3, 0, -7, 0], [0, 0, 3, 0, -7]])
assert sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x, 2) == Matrix([
[1, 0, -7, 7, 0, 0], [0, 3, 0, -7, 0, 0], [0, 1, 0, -7, 7, 0], [0, 0, 3, 0, -7, 0], [0, 0, 1, 0, -7, 7], [0, 0, 0, 3, 0, -7]])
def test_print_as_full():
xvar = sympy.var('xvar')
yvar = sympy.var('yvar')
res1 = '''
# m
# m_num=2
m[0, 0] += 1
m[0, 1] += 2*xvar + (yvar*yvar*yvar)
'''
res1 = res1.strip()
m = sympy.Matrix([[1, 2*xvar + yvar**3]])
assert print_as_full(m, 'm') == res1
res2 = '''
# subs
# yvar = xvar
# m
# m_num=2
m[0, 0] += 1
m[0, 1] += (yvar*yvar*yvar) + 2*yvar
'''
res2 = res2.strip()
assert print_as_full(m, 'm', subs={xvar: yvar}) == res2
def _make_z1():
var("z1")
# make z2 with call-depth = 2
def __make_z2():
var("z2")
def test_var():
var("a")
assert a == Symbol("a")
var("b bb cc zz _x")
assert b == Symbol("b")
assert bb == Symbol("bb")
assert cc == Symbol("cc")
assert zz == Symbol("zz")
assert _x == Symbol("_x")
v = var(['d', 'e', 'fg'])
assert d == Symbol('d')
assert e == Symbol('e')
assert fg == Symbol('fg')
# check return value
assert v == [d, e, fg]
# see if var() really injects into global namespace
raises(NameError, lambda: z1)
_make_z1()
assert z1 == Symbol("z1")
raises(NameError, lambda: z2)
_make_z2()
assert z2 == Symbol("z2")
def test_var_return():
raises(ValueError, lambda: var(''))
v2 = var('q')
v3 = var('q p')
assert v2 == Symbol('q')
assert v3 == (Symbol('q'), Symbol('p'))
def test_var_accepts_comma():
v1 = var('x y z')
v2 = var('x,y,z')
v3 = var('x,y z')
assert v1 == v2
assert v1 == v3
def test_var_cls():
f = var('f', cls=Function)
assert isinstance(f, FunctionClass)
g, h = var('g,h', cls=Function)
assert isinstance(g, FunctionClass)
assert isinstance(h, FunctionClass)
def check_expression(expr, var_symbols):
"""Does eval(expr) both in Sage and SymPy and does other checks."""
# evaluate the expression in the context of Sage:
if var_symbols:
sage.var(var_symbols)
a = globals().copy()
# safety checks...
assert not "sin" in a
a.update(sage.__dict__)
assert "sin" in a
e_sage = eval(expr, a)
assert not isinstance(e_sage, sympy.Basic)
# evaluate the expression in the context of SymPy:
if var_symbols:
sympy.var(var_symbols)
b = globals().copy()
assert not "sin" in b
b.update(sympy.__dict__)
assert "sin" in b
b.update(sympy.__dict__)
e_sympy = eval(expr, b)
assert isinstance(e_sympy, sympy.Basic)
# Do the actual checks:
assert sympy.S(e_sage) == e_sympy
assert e_sage == sage.SR(e_sympy)
def test_issue_4023():
sage.var("a x")
log = sage.log
i = sympy.integrate(log(x)/a, (x, a, a + 1))
i2 = sympy.simplify(i)
s = sage.SR(i2)
assert s == (a*log(1 + a) - a*log(a) + log(1 + a) - 1)/a
# This string contains Sage doctests, that execute all the functions above.
# When you add a new function, please add it here as well.
def energy_corrections(perturbation, n, a=10, mass=0.5):
"""
Calculating first two order corrections due to perturbation theory and
returns tuple where zero element is unperturbated energy, and two second
is corrections
``n``
the "nodal" quantum number. Corresponds to the number of nodes in the
wavefunction. n >= 0
``a``
width of the well. a > 0
``mass``
mass.
"""
x, _a = var("x _a")
Vnm = lambda n, m, a: Integral(X_n(n, a, x) * X_n(m, a, x)
* perturbation.subs({_a: a}), (x, 0, a)).n()
# As we know from theory for V0*r/a we will just V(n, n-1) and V(n, n+1)
# wouldn't equals zero
return (E_n(n, a, mass).evalf(),
Vnm(n, n, a).evalf(),
(Vnm(n, n - 1, a)**2/(E_n(n, a, mass) - E_n(n - 1, a, mass))
+ Vnm(n, n + 1, a)**2/(E_n(n, a, mass) - E_n(n + 1, a, mass))).evalf())
def main():
print()
print("Applying perturbation theory to calculate the ground state energy")
print("of the infinite 1D box of width ``a`` with a perturbation")
print("which is linear in ``x``, up to second order in perturbation.")
print()
x, _a = var("x _a")
perturbation = .1 * x / _a
E1 = energy_corrections(perturbation, 1)
print("Energy for first term (n=1):")
print("E_1^{(0)} = ", E1[0])
print("E_1^{(1)} = ", E1[1])
print("E_1^{(2)} = ", E1[2])
print()
E2 = energy_corrections(perturbation, 2)
print("Energy for second term (n=2):")
print("E_2^{(0)} = ", E2[0])
print("E_2^{(1)} = ", E2[1])
print("E_2^{(2)} = ", E2[2])
print()
E3 = energy_corrections(perturbation, 3)
print("Energy for third term (n=3):")
print("E_3^{(0)} = ", E3[0])
print("E_3^{(1)} = ", E3[1])
print("E_3^{(2)} = ", E3[2])
print()
def constrains(self):
"""
returns a list of parameters that are constrained by this parameter
"""
params = []
for constraint in self.in_constraints:
for var in constraint._vars:
param = var.get_parameter()
if param.component == constraint.component and param.qualifier == constraint.qualifier:
if param not in params and param.uniqueid != self.uniqueid:
params.append(param)
return params
def vars(self):
"""
return all the variables in a PS
"""
return ParameterSet([var.get_parameter() for var in self._vars])
def _get_var(self, param=None, **kwargs):
if not isinstance(param, Parameter):
if isinstance(param, str) and 'twig' not in kwargs.keys():
kwargs['twig'] = param
param = self.get_parameter(**kwargs)
varids = [var.unique_label for var in self._vars]
if param.uniqueid not in varids:
raise KeyError("{} was not found in expression".format(param.uniquetwig))
return self._vars[varids.index(param.uniqueid)]
def set_value(self, value, **kwargs):
"""
kwargs are passed on to filter
"""
_orig_value = deepcopy(self.get_value())
if self._bundle is None:
raise ValueError("ConstraintParameters must be attached from the bundle, and cannot be standalone")
value = str(value) # <-- in case unicode
# if the user wants to see the expression, we'll replace all
# var.safe_label with var.curly_label
self._value, self._vars = self._parse_expr(value)
#~ print "***", self.uniquetwig, self.uniqueid
self._add_history(redo_func='set_value', redo_kwargs={'value': value, 'uniqueid': self.uniqueid}, undo_func='set_value', undo_kwargs={'value': _orig_value, 'uniqueid': self.uniqueid})
def _update_bookkeeping(self):
# do bookkeeping on parameters
self._remove_bookkeeping()
for var in self._vars:
param = var.get_parameter()
if param.qualifier == self.qualifier and param.component == self.component:
# then this is the currently constrained parameter
param._is_constraint = self.uniqueid
if param.uniqueid in param._in_constraints:
param._in_constraints.remove(self.uniqueid)
else:
# then this is a constraining parameter
if self.uniqueid not in param._in_constraints:
param._in_constraints.append(self.uniqueid)
def _remove_bookkeeping(self):
for var in self._vars:
param = var.get_parameter()
if param._is_constraint == self.uniqueid:
param._is_constraint = None
if self.uniqueid in param._in_constraints:
param._in_constraints.remove(self.uniqueid)
def get_value(self):
"""
"""
# for access to the sympy-safe expr, just use self._expr
expr = self._value
for var in self._vars:
# update to current unique twig
var.update_user_label() # update curly label
#~ print "***", expr, var.safe_label, var.curly_label
expr = expr.replace(str(var.safe_label), str(var.curly_label))
return expr
def PSC(F, G, x):
"""PSC(F, G, x) returns a set with the non-zero principal subresultant
coefficients (psc) of the two polynomials F and G with respect to the
variable x.
If the degree of the polynomial F is strictly less than the degree of
the polynomial G, then F and G are interchanged.
Extended psc beyond the n-th are not considered, where n is the minimum
of the degrees of F and G with respect to x.
>>> PSC(0, 0, var('x'))
set()
>>> PSC(poly('2*x'), poly('3*y'), var('x'))
{3*y}
>>> PSC(poly('2*x'), poly('3*y + 5*x**2'), var('x')) == {12*var('y'), 2}
True
>>> PSC(poly('x**3'), poly('x**3 + x'), var('x'))
{1}
"""
subs = subresultants(F, G, x)
s = set()
i = len(subs) - 1
if i < 0:
return s
currDeg = degree(subs[i], x)
while i > 0:
nextDeg = degree(subs[i-1], x)
s.add( LC(subs[i], x)**(nextDeg-currDeg) )
currDeg = nextDeg
i -= 1
return s
# Execute doctest when run from the command line
def _make_z1():
var("z1")
# make z2 with call-depth = 2
def __make_z2():
var("z2")
def test_var():
var("a")
assert a == Symbol("a")
var("b bb cc zz _x")
assert b == Symbol("b")
assert bb == Symbol("bb")
assert cc == Symbol("cc")
assert zz == Symbol("zz")
assert _x == Symbol("_x")
v = var(['d', 'e', 'fg'])
assert d == Symbol('d')
assert e == Symbol('e')
assert fg == Symbol('fg')
# check return value
assert v == [d, e, fg]
# see if var() really injects into global namespace
raises(NameError, lambda: z1)
_make_z1()
assert z1 == Symbol("z1")
raises(NameError, lambda: z2)
_make_z2()
assert z2 == Symbol("z2")
def test_var_return():
raises(ValueError, lambda: var(''))
v2 = var('q')
v3 = var('q p')
assert v2 == Symbol('q')
assert v3 == (Symbol('q'), Symbol('p'))
def test_var_accepts_comma():
v1 = var('x y z')
v2 = var('x,y,z')
v3 = var('x,y z')
assert v1 == v2
assert v1 == v3
def test_var_cls():
f = var('f', cls=Function)
assert isinstance(f, FunctionClass)
g, h = var('g,h', cls=Function)
assert isinstance(g, FunctionClass)
assert isinstance(h, FunctionClass)
def check_expression(expr, var_symbols, only_from_sympy=False):
"""
Does eval(expr) both in Sage and SymPy and does other checks.
"""
# evaluate the expression in the context of Sage:
if var_symbols:
sage.var(var_symbols)
a = globals().copy()
# safety checks...
a.update(sage.__dict__)
assert "sin" in a
is_different = False
try:
e_sage = eval(expr, a)
assert not isinstance(e_sage, sympy.Basic)
except (NameError, TypeError):
is_different = True
pass
# evaluate the expression in the context of SymPy:
if var_symbols:
sympy_vars = sympy.var(var_symbols)
b = globals().copy()
b.update(sympy.__dict__)
assert "sin" in b
b.update(sympy.__dict__)
e_sympy = eval(expr, b)
assert isinstance(e_sympy, sympy.Basic)
# Sympy func may have specific _sage_ method
if is_different:
_sage_method = getattr(e_sympy.func, "_sage_")
e_sage = _sage_method(sympy.S(e_sympy))
# Do the actual checks:
if not only_from_sympy:
assert sympy.S(e_sage) == e_sympy
assert e_sage == sage.SR(e_sympy)
def test_issue_4023():
sage.var("a x")
log = sage.log
i = sympy.integrate(log(x)/a, (x, a, a + 1))
i2 = sympy.simplify(i)
s = sage.SR(i2)
assert s == (a*log(1 + a) - a*log(a) + log(1 + a) - 1)/a
