def main2():
t, n = var('t, n')
G = symbolic_expression(t**n * (t - Integer(1))**n /
factorial(n) * e**t).function(t)
T = symbolic_expression(G.integral(t, Integer(0), Integer(1))).function(n)
print([T(j) for j in range(Integer(10))])
print([T(j).n() for j in range(Integer(10))])
def __init__(self, fx, fy):
x, y = var('x,y')
fx = EnsurephyFunction(fx)
fy = EnsurephyFunction(fy)
self.fx = symbolic_expression(fx.sage).function(x, y)
self.fy = symbolic_expression(fy.sage).function(x, y)
# g=[fx,fy]
# for i in [0,1]:
# if isinstance(g[i],phyFunction):
# g[i]=g[i].sage
# self.fx=g[0]
# self.fy=g[1]
self.vector_field = self
def divergence(self):
"""
return the divergence of the vector field.
OUTPUT:
a two-variable function
EXAMPLES::
sage: from yanntricks.BasicGeometricObjects import *
sage: x,y=var('x,y')
sage: F = GeometricVectorField( x , y )
sage: F.divergence()
(x, y) |--> 2
The divergence of the gravitational field vanishes::
sage: G=GeometricVectorField(x/(x**2+y**2),y/(x**2+y**2))
sage: G.divergence().simplify_full()
0
The divergence is a function::
sage: a,b=var('a,b')
sage: H=GeometricVectorField( x**2,y**3 )
sage: H.divergence()(a,b)
3*b^2 + 2*a
"""
x, y = var('x,y')
formula = self.fx.diff(x) + self.fy.diff(y)
divergence = symbolic_expression(formula).function(x, y)
return divergence
def phyFunction(fun, mx=None, Mx=None):
"""
Represent a function.
INPUT:
- ``fun`` - a function.
- ``mx,Mx`` - initial and final value of the argument.
EXAMPLES::
sage: from phystricks import *
sage: f=phyFunction(cos(x))
sage: f(pi/2)
0
sage: g=phyFunction(2*f,0,pi)
sage: g(pi)
-2
One can deal with probability distributions :
sage: C=RealDistribution('chisquared',10).distribution_function
sage: f=phyFunction(C)
sage: f(4)
0.0451117610789
EXAMPLES with function for which one don't know analytic form
.. literalinclude:: phystricksChiSquared.py
.. image:: Picture_FIGLabelFigChiSquaredPICTChiSquared-for_eps.png
OTHER EXAMPLE
.. literalinclude:: phystricksNonAnalyticOne.py
.. image:: Picture_FIGLabelFigNonAnalyticOnePICTNonAnalyticOne-for_eps.png
"""
from phystricks.src.phyFunctionGraph import phyFunctionGraph
# The first try is that the given expression is already a phyFunction.
try:
return fun.graph(mx, Mx)
except (AttributeError, TypeError):
pass
# The second try is that `fun` is something that Sage knows.
try:
sy = symbolic_expression(fun)
except TypeError: # Happens with probability distributions.
return phyFunctionGraph(fun, mx, Mx)
x = var('x')
return phyFunctionGraph(sy.function(x), mx, Mx)
def grade(self, guess, data):
try:
from sage.all import symbolic_expression, var
except:
raise ImportError('could not import from sage.all')
output = {
'score': 0,
'max_score': 1,
'data': {
'info': 'incorrect expression'
}
}
for v in data['variable_names']:
var(v)
try:
guess_expression = symbolic_expression(guess)
except:
output.update({
'data': {
'info': 'could not convert input into a valid expression'
}
})
return output
answer = symbolic_expression(data['answer_string'])
if data['method'] == 'identity':
if (guess_expression - answer).is_zero():
output.update({'score': 1, 'data': {}})
else:
pass
return output
else:
raise ValueError('Unknown method in ExpressionInput')
def __init__(self, convection_field, forcing_function):
self._forcing_function = forcing_function
self._convection_field = convection_field
dx0 = sg.diff(convection_field[0], x)
dx1 = sg.diff(convection_field[1], x)
dy0 = sg.diff(convection_field[0], y)
dy1 = sg.diff(convection_field[1], y)
to_ccode = lambda u: sp.ccode(
sympy.sympify(sg.symbolic_expression(u)._sympy_()))
self._forcing_code = _forcing_template.format(
**{'forcing_expr': to_ccode(forcing_function)})
self._convection_code = _convection_template.format(**
{'value0_expr': to_ccode(convection_field[0]),
'value1_expr': to_ccode(convection_field[1]),
'dx0_expr': to_ccode(dx0),
'dx1_expr': to_ccode(dx1),
'dy0_expr': to_ccode(dy0),
'dy1_expr': to_ccode(dy1)})
self.so_folder = tf.mkdtemp(prefix="cfem_") + os.sep
# even if the object is not instantiated, we can still clean it up at
# exit.
atexit.register(lambda folder=self.so_folder: shutil.rmtree(folder))
shutil.copy(_module_path + "makefile", self.so_folder)
shutil.copy(_module_path + "cfem.h", self.so_folder)
with open(self.so_folder + "funcs.c", 'w') as fhandle:
fhandle.write("#include <math.h>\n")
fhandle.write("#include \"cfem.h\"\n")
fhandle.write(self._forcing_code)
fhandle.write(self._convection_code)
current_directory = os.getcwd()
try:
os.chdir(self.so_folder)
util.run_make(command="autogenerated_functions")
self.so = np.ctypeslib.load_library("libfuncs.so", "./")
self.so.cf_forcing.restype = ct.c_double
self.so.cf_forcing.argtypes = [ct.c_double, ct.c_double,
ct.c_double]
self.so.cf_convection.restype = CConvection
self.so.cf_convection.argtypes = [ct.c_double, ct.c_double]
finally:
os.chdir(current_directory)
