def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_x")
f = function_symbol("f", 2*x)
assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), [_x]), [_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), [x]), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), [x]), [y, x], [x, _x])
def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_xi_1")
f = function_symbol("f", 2*x)
assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), [_x]), [_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), [x]), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), [x]), [y, x], [x, _x])
def test_conv8():
e1 = function_symbol("f", Symbol("x"))
e2 = function_symbol("g", Symbol("x"), Symbol("y"))
assert e1._sympy_() == sympy.Function("f")(sympy.Symbol("x"))
assert e2._sympy_() != sympy.Function("f")(sympy.Symbol("x"))
assert e2._sympy_() == sympy.Function("g")(sympy.Symbol("x"), sympy.Symbol("y"))
e3 = function_symbol("q", Symbol("t"))
assert e3._sympy_() == sympy.Function("q")(sympy.Symbol("t"))
assert e3._sympy_() != sympy.Function("f")(sympy.Symbol("t"))
assert e3._sympy_() != sympy.Function("q")(sympy.Symbol("t"), sympy.Symbol("t"))
def test_conv8():
e1 = function_symbol("f", Symbol("x"))
e2 = function_symbol("g", Symbol("x"), Symbol("y"))
assert e1._sympy_() == sympy.Function("f")(sympy.Symbol("x"))
assert e2._sympy_() != sympy.Function("f")(sympy.Symbol("x"))
assert (e2._sympy_() == sympy.Function("g")(sympy.Symbol("x"),
sympy.Symbol("y")))
e3 = function_symbol("q", Symbol("t"))
assert e3._sympy_() == sympy.Function("q")(sympy.Symbol("t"))
assert e3._sympy_() != sympy.Function("f")(sympy.Symbol("t"))
assert (e3._sympy_() != sympy.Function("q")(sympy.Symbol("t"),
sympy.Symbol("t")))
def test_conv11():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
x1 = Symbol("x")
y1 = Symbol("y")
e1 = sympy.Subs(sympy.Derivative(sympy.Function("f")(x, y), x), [x, y], [y, y])
e2 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [x1, y1], [y1, y1])
e3 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [y1, x1], [x1, y1])
assert sympify(e1) == e2
assert sympify(e1) != e3
assert e2._sympy_() == e1
assert e3._sympy_() != e1
def test_conv10():
A = DenseMatrix(1, 4, [Integer(1), Integer(2), Integer(3), Integer(4)])
assert (A._sympy_() == sympy.Matrix(1, 4, [
sympy.Integer(1),
sympy.Integer(2),
sympy.Integer(3),
sympy.Integer(4)
]))
B = DenseMatrix(4, 1, [Symbol("x"), Symbol("y"), Symbol("z"), Symbol("t")])
assert (B._sympy_() == sympy.Matrix(4, 1, [
sympy.Symbol("x"),
sympy.Symbol("y"),
sympy.Symbol("z"),
sympy.Symbol("t")
]))
C = DenseMatrix(
2, 2,
[Integer(5),
Symbol("x"),
function_symbol("f", Symbol("x")), 1 + I])
assert (C._sympy_() == sympy.Matrix(
[[5, sympy.Symbol("x")],
[sympy.Function("f")(sympy.Symbol("x")), 1 + sympy.I]]))
def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_xi_1")
f = function_symbol("f", 2*x)
assert str(f.diff(x)) == "2*Subs(Derivative(f(_xi_1), _xi_1), (_xi_1), (2*x))"
# TODO: fix me
# assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), _x), [_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), x), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), x), [y, x], [x, _x])
s = f.diff(x)/2
_xi_1 = Symbol("_xi_1")
assert s.expr == Derivative(function_symbol("f", _xi_1), _xi_1)
assert s.variables == (_xi_1,)
assert s.point == (2*x,)
def test_conv11():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
x1 = Symbol("x")
y1 = Symbol("y")
e1 = sympy.Subs(sympy.Derivative(sympy.Function("f")(x, y), x), [x, y],
[y, y])
e2 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [x1, y1],
[y1, y1])
e3 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [y1, x1],
[x1, y1])
assert sympify(e1) == e2
assert sympify(e1) != e3
assert e2._sympy_() == e1
assert e3._sympy_() != e1
def test_conv10b():
A = sympy.Matrix([[sympy.Symbol("x"), sympy.Symbol("y")],
[sympy.Symbol("z"), sympy.Symbol("t")]])
assert sympify(A) == densematrix(2, 2, [Symbol("x"), Symbol("y"),
Symbol("z"), Symbol("t")])
B = sympy.Matrix([[1, 2], [3, 4]])
assert sympify(B) == densematrix(2, 2, [Integer(1), Integer(2), Integer(3),
Integer(4)])
C = sympy.Matrix([[7, sympy.Symbol("y")],
[sympy.Function("g")(sympy.Symbol("z")), 3 + 2*sympy.I]])
assert sympify(C) == densematrix(2, 2, [Integer(7), Symbol("y"),
function_symbol("g", Symbol("z")), 3 + 2*I])
def test_conv10():
A = densematrix(1, 4, [Integer(1), Integer(2), Integer(3), Integer(4)])
assert A._sympy_() == sympy.Matrix(1, 4, [sympy.Integer(1), sympy.Integer(2),
sympy.Integer(3), sympy.Integer(4)])
B = densematrix(4, 1, [Symbol("x"), Symbol("y"), Symbol("z"), Symbol("t")])
assert B._sympy_() == sympy.Matrix(4, 1, [sympy.Symbol("x"), sympy.Symbol("y"),
sympy.Symbol("z"), sympy.Symbol("t")])
C = densematrix(2, 2,
[Integer(5), Symbol("x"), function_symbol("f", Symbol("x")), 1 + I])
assert C._sympy_() == sympy.Matrix([[5, sympy.Symbol("x")],
[sympy.Function("f")(sympy.Symbol("x")), 1 + sympy.I]])
def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
assert f.diff(x).args == (f, x)
assert f.diff(x).diff(x).args == (f, x, x)
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
f = function_symbol("f", x, y)
assert f.diff(x).diff(y) == function_symbol("f", x, y).diff(x).diff(y)
assert f.diff(Symbol("z")) == 0
def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
assert f.diff(x).args == (f, x)
assert f.diff(x).diff(x).args == (f, x, x)
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
f = function_symbol("f", x, y)
assert f.diff(x).diff(y) == function_symbol("f", x, y).diff(x).diff(y)
assert f.diff(Symbol("z")) == 0
def test_conv10b():
A = sympy.Matrix([[sympy.Symbol("x"), sympy.Symbol("y")],
[sympy.Symbol("z"), sympy.Symbol("t")]])
assert sympify(A) == DenseMatrix(2, 2, [Symbol("x"), Symbol("y"),
Symbol("z"), Symbol("t")])
B = sympy.Matrix([[1, 2], [3, 4]])
assert sympify(B) == DenseMatrix(2, 2, [Integer(1), Integer(2), Integer(3),
Integer(4)])
C = sympy.Matrix([[7, sympy.Symbol("y")],
[sympy.Function("g")(sympy.Symbol("z")), 3 + 2*sympy.I]])
assert sympify(C) == DenseMatrix(2, 2, [Integer(7), Symbol("y"),
function_symbol("g",
Symbol("z")),
3 + 2*I])
def test_conv8b():
e1 = sympy.Function("f")(sympy.Symbol("x"))
e2 = sympy.Function("g")(sympy.Symbol("x"), sympy.Symbol("y"))
assert sympify(e1) == function_symbol("f", Symbol("x"))
assert sympify(e2) != function_symbol("f", Symbol("x"))
assert sympify(e2) == function_symbol("g", Symbol("x"), Symbol("y"))
e3 = sympy.Function("q")(sympy.Symbol("t"))
assert sympify(e3) == function_symbol("q", Symbol("t"))
assert sympify(e3) != function_symbol("f", Symbol("t"))
assert sympify(e3) != function_symbol("q", Symbol("t"), Symbol("t"))
def test_conv8b():
e1 = sympy.Function("f")(sympy.Symbol("x"))
e2 = sympy.Function("g")(sympy.Symbol("x"), sympy.Symbol("y"))
assert sympify(e1) == function_symbol("f", Symbol("x"))
assert sympify(e2) != function_symbol("f", Symbol("x"))
assert sympify(e2) == function_symbol("g", Symbol("x"), Symbol("y"))
e3 = sympy.Function("q")(sympy.Symbol("t"))
assert sympify(e3) == function_symbol("q", Symbol("t"))
assert sympify(e3) != function_symbol("f", Symbol("t"))
assert sympify(e3) != function_symbol("q", Symbol("t"), Symbol("t"))
def test_f():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f.subs({function_symbol("f", x): function_symbol("g", x)}) == g
assert (f+g).subs({function_symbol("f", x): function_symbol("g", x)}) == 2*g
e = (f+x)**3
assert e.subs({f: y}) == (x+y)**3
e = e.expand()
assert e.subs({f: y}) == ((x+y)**3).expand()
def test_f():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f != g
f = function_symbol("f", x)
g = function_symbol("f", x)
assert f == g
f = function_symbol("f", x, y)
g = function_symbol("f", y, x)
assert f != g
f = function_symbol("f", x, y)
g = function_symbol("f", x, y)
assert f == g
def test_f():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f != g
f = function_symbol("f", x)
g = function_symbol("f", x)
assert f == g
f = function_symbol("f", x, y)
g = function_symbol("f", y, x)
assert f != g
f = function_symbol("f", x, y)
g = function_symbol("f", x, y)
assert f == g
def test_f():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f.subs({function_symbol("f", x): function_symbol("g", x)}) == g
assert ((f + g).subs({function_symbol("f", x):
function_symbol("g", x)}) == 2 * g)
e = (f + x)**3
assert e.subs({f: y}) == (x + y)**3
e = e.expand()
assert e.subs({f: y}) == ((x + y)**3).expand()
def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
assert f.diff(x).args == (f, x)
assert f.diff(x).diff(x).args == (f, x, x)
assert f.diff(x, 0) == f
assert f.diff(x, 0) == Derivative(function_symbol("f", x), x, 0)
raises(ValueError, lambda: f.diff(0))
raises(ValueError, lambda: f.diff(x, 0, 0))
raises(ValueError, lambda: f.diff(x, y, 0, 0, x))
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
f = function_symbol("f", x, y)
assert f.diff(x).diff(y) == function_symbol("f", x, y).diff(x).diff(y)
assert f.diff(Symbol("z")) == 0
s = Derivative(function_symbol("f", x), x)
assert s.expr == function_symbol("f", x)
assert s.variables == (x, )
fxy = Function("f")(x, y)
g = Derivative(Function("f")(x, y), x, 2, y, 1)
assert g == fxy.diff(x, x, y)
assert g == fxy.diff(y, 1, x, 2)
assert g == fxy.diff(y, x, 2)
h = Derivative(Function("f")(x, y), x, 0, y, 1)
assert h == fxy.diff(x, 0, y)
assert h == fxy.diff(y, x, 0)
i = Derivative(Function("f")(x, y), x, 0, y, 1, x, 1)
assert i == fxy.diff(x, 0, y, x, 1)
assert i == fxy.diff(x, 0, y, x)
assert i == fxy.diff(y, x)
assert i == fxy.diff(y, 1, x, 1)
assert i == fxy.diff(y, 1, x)
def test_sage_conversions():
try:
import sage.all as sage
except ImportError:
return
x, y = sage.SR.var('x y')
x1, y1 = symbols('x, y')
# Symbol
assert x1._sage_() == x
assert x1 == sympify(x)
# Integer
assert Integer(12)._sage_() == sage.Integer(12)
assert Integer(12) == sympify(sage.Integer(12))
# Rational
assert (Integer(1) / 2)._sage_() == sage.Integer(1) / 2
assert Integer(1) / 2 == sympify(sage.Integer(1) / 2)
# Operators
assert x1 + y == x1 + y1
assert x1 * y == x1 * y1
assert x1**y == x1**y1
assert x1 - y == x1 - y1
assert x1 / y == x1 / y1
assert x + y1 == x + y
assert x * y1 == x * y
# Doesn't work in Sage 6.1.1ubuntu2
# assert x ** y1 == x ** y
assert x - y1 == x - y
assert x / y1 == x / y
# Conversions
assert (x1 + y1)._sage_() == x + y
assert (x1 * y1)._sage_() == x * y
assert (x1**y1)._sage_() == x**y
assert (x1 - y1)._sage_() == x - y
assert (x1 / y1)._sage_() == x / y
assert x1 + y1 == sympify(x + y)
assert x1 * y1 == sympify(x * y)
assert x1**y1 == sympify(x**y)
assert x1 - y1 == sympify(x - y)
assert x1 / y1 == sympify(x / y)
# Functions
assert sin(x1) == sin(x)
assert sin(x1)._sage_() == sage.sin(x)
assert sin(x1) == sympify(sage.sin(x))
assert cos(x1) == cos(x)
assert cos(x1)._sage_() == sage.cos(x)
assert cos(x1) == sympify(sage.cos(x))
assert function_symbol('f', x1, y1)._sage_() == sage.function('f', x, y)
assert function_symbol('f', 2 * x1,
x1 + y1).diff(x1)._sage_() == sage.function(
'f', 2 * x, x + y).diff(x)
# For the following test, sage needs to be modified
# assert sage.sin(x) == sage.sin(x1)
# Constants
assert pi._sage_() == sage.pi
assert E._sage_() == sage.e
assert I._sage_() == sage.I
assert pi == sympify(sage.pi)
assert E == sympify(sage.e)
# SympyConverter does not support converting the following
# assert I == sympify(sage.I)
# Matrix
assert DenseMatrix(1, 2, [x1, y1])._sage_() == sage.matrix([[x, y]])
# SympyConverter does not support converting the following
# assert DenseMatrix(1, 2, [x1, y1]) == sympify(sage.matrix([[x, y]]))
# Sage Number
a = sage.Mod(2, 7)
b = PyNumber(a, sage_module)
a = a + 8
b = b + 8
assert isinstance(b, PyNumber)
assert b._sage_() == a
a = a + x
b = b + x
assert isinstance(b, Add)
assert b._sage_() == a
# Sage Function
e = x1 + wrap_sage_function(sage.log_gamma(x))
assert str(e) == "x + log_gamma(x)"
assert isinstance(e, Add)
assert e + wrap_sage_function(
sage.log_gamma(x)) == x1 + 2 * wrap_sage_function(sage.log_gamma(x))
f = e.subs({x1: 10})
assert f == 10 + log(362880)
f = e.subs({x1: 2})
assert f == 2
f = e.subs({x1: 100})
v = f.n(53, real=True)
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x1)
from timeit import default_timer as clock
from symengine import var, sympify, function_symbol, Symbol
import sympy
s = open("expr.txt").read()
print "Converting to SymPy..."
e = sympy.sympify(s)
print "Converting to SymEngine..."
ce = sympify(e)
print " Done."
print "SymPy subs:"
t1 = clock()
f = e.subs(sympy.Function("q5")(sympy.Symbol("t")), sympy.Symbol("sq5"))
t2 = clock()
print "Total time:", t2 - t1, "s"
print "SymEngine subs:"
t1 = clock()
cf = ce.subs(function_symbol("q5", Symbol("t")), Symbol("sq5"))
t2 = clock()
print "Total time:", t2 - t1, "s"
print "SymPy diff:"
t1 = clock()
g = f.diff(sympy.Symbol("sq5"))
t2 = clock()
print "Total time:", t2 - t1, "s"
print "SymEngine diff:"
t1 = clock()
cg = cf.diff(Symbol("sq5"))
t2 = clock()
print "Total time:", t2 - t1, "s"
def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
assert f.diff(x).args == (f, x)
assert f.diff(x).diff(x).args == (f, x, x)
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
f = function_symbol("f", x, y)
assert f.diff(x).diff(y) == function_symbol("f", x, y).diff(x).diff(y)
assert f.diff(Symbol("z")) == 0
s = Derivative(function_symbol("f", x), x)
assert s.expr == function_symbol("f", x)
assert s.variables == (x, )
def test_sage_conversions():
x, y = sage.SR.var('x y')
x1, y1 = symbols('x, y')
# Symbol
assert x1._sage_() == x
assert x1 == sympify(x)
# Integer
assert Integer(12)._sage_() == sage.Integer(12)
assert Integer(12) == sympify(sage.Integer(12))
# Rational
assert (Integer(1) / 2)._sage_() == sage.Integer(1) / 2
assert Integer(1) / 2 == sympify(sage.Integer(1) / 2)
# Operators
assert x1 + y == x1 + y1
assert x1 * y == x1 * y1
assert x1**y == x1**y1
assert x1 - y == x1 - y1
assert x1 / y == x1 / y1
assert x + y1 == x + y
assert x * y1 == x * y
# Doesn't work in Sage 6.1.1ubuntu2
# assert x ** y1 == x ** y
assert x - y1 == x - y
assert x / y1 == x / y
# Conversions
assert (x1 + y1)._sage_() == x + y
assert (x1 * y1)._sage_() == x * y
assert (x1**y1)._sage_() == x**y
assert (x1 - y1)._sage_() == x - y
assert (x1 / y1)._sage_() == x / y
assert x1 + y1 == sympify(x + y)
assert x1 * y1 == sympify(x * y)
assert x1**y1 == sympify(x**y)
assert x1 - y1 == sympify(x - y)
assert x1 / y1 == sympify(x / y)
# Functions
assert sin(x1) == sin(x)
assert sin(x1)._sage_() == sage.sin(x)
assert sin(x1) == sympify(sage.sin(x))
assert cos(x1) == cos(x)
assert cos(x1)._sage_() == sage.cos(x)
assert cos(x1) == sympify(sage.cos(x))
assert function_symbol('f', x1, y1)._sage_() == sage.function('f')(x, y)
assert (function_symbol('f', 2 * x1,
x1 + y1).diff(x1)._sage_() == sage.function('f')(
2 * x, x + y).diff(x))
assert LambertW(x1) == LambertW(x)
assert LambertW(x1)._sage_() == sage.lambert_w(x)
assert KroneckerDelta(x1, y1) == KroneckerDelta(x, y)
assert KroneckerDelta(x1, y1)._sage_() == sage.kronecker_delta(x, y)
assert erf(x1) == erf(x)
assert erf(x1)._sage_() == sage.erf(x)
assert lowergamma(x1, y1) == lowergamma(x, y)
assert lowergamma(x1, y1)._sage_() == sage.gamma_inc_lower(x, y)
assert uppergamma(x1, y1) == uppergamma(x, y)
assert uppergamma(x1, y1)._sage_() == sage.gamma_inc(x, y)
assert loggamma(x1) == loggamma(x)
assert loggamma(x1)._sage_() == sage.log_gamma(x)
assert beta(x1, y1) == beta(x, y)
assert beta(x1, y1)._sage_() == sage.beta(x, y)
assert floor(x1) == floor(x)
assert floor(x1)._sage_() == sage.floor(x)
assert ceiling(x1) == ceiling(x)
assert ceiling(x1)._sage_() == sage.ceil(x)
assert conjugate(x1) == conjugate(x)
assert conjugate(x1)._sage_() == sage.conjugate(x)
# For the following test, sage needs to be modified
# assert sage.sin(x) == sage.sin(x1)
# Constants and Booleans
assert pi._sage_() == sage.pi
assert E._sage_() == sage.e
assert I._sage_() == sage.I
assert GoldenRatio._sage_() == sage.golden_ratio
assert Catalan._sage_() == sage.catalan
assert EulerGamma._sage_() == sage.euler_gamma
assert oo._sage_() == sage.oo
assert zoo._sage_() == sage.unsigned_infinity
assert nan._sage_() == sage.NaN
assert true._sage_() == True
assert false._sage_() == False
assert pi == sympify(sage.pi)
assert E == sympify(sage.e)
assert GoldenRatio == sympify(sage.golden_ratio)
assert Catalan == sympify(sage.catalan)
assert EulerGamma == sympify(sage.euler_gamma)
assert oo == sympify(sage.oo)
assert zoo == sympify(sage.unsigned_infinity)
assert nan == sympify(sage.NaN)
# SympyConverter does not support converting the following
# assert I == sympify(sage.I)
# Matrix
assert DenseMatrix(1, 2, [x1, y1])._sage_() == sage.matrix([[x, y]])
# SympyConverter does not support converting the following
# assert DenseMatrix(1, 2, [x1, y1]) == sympify(sage.matrix([[x, y]]))
# Sage Number
a = sage.Mod(2, 7)
b = PyNumber(a, sage_module)
a = a + 8
b = b + 8
assert isinstance(b, PyNumber)
assert b._sage_() == a
assert str(a) == str(b)
# Sage Function
e = x1 + wrap_sage_function(sage.log_gamma(x))
assert str(e) == "x + log_gamma(x)"
assert isinstance(e, Add)
assert (e + wrap_sage_function(sage.log_gamma(x)) == x1 +
2 * wrap_sage_function(sage.log_gamma(x)))
f = e.subs({x1: 10})
assert f == 10 + log(362880)
f = e.subs({x1: 2})
assert f == 2
f = e.subs({x1: 100})
v = f.n(53, real=True)
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x1)
def test_sage_conversions():
try:
import sage.all as sage
except ImportError:
return
x, y = sage.SR.var('x y')
x1, y1 = symbols('x, y')
# Symbol
assert x1._sage_() == x
assert x1 == sympify(x)
# Integer
assert Integer(12)._sage_() == sage.Integer(12)
assert Integer(12) == sympify(sage.Integer(12))
# Rational
assert (Integer(1) / 2)._sage_() == sage.Integer(1) / 2
assert Integer(1) / 2 == sympify(sage.Integer(1) / 2)
# Operators
assert x1 + y == x1 + y1
assert x1 * y == x1 * y1
assert x1 ** y == x1 ** y1
assert x1 - y == x1 - y1
assert x1 / y == x1 / y1
assert x + y1 == x + y
assert x * y1 == x * y
# Doesn't work in Sage 6.1.1ubuntu2
# assert x ** y1 == x ** y
assert x - y1 == x - y
assert x / y1 == x / y
# Conversions
assert (x1 + y1)._sage_() == x + y
assert (x1 * y1)._sage_() == x * y
assert (x1 ** y1)._sage_() == x ** y
assert (x1 - y1)._sage_() == x - y
assert (x1 / y1)._sage_() == x / y
assert x1 + y1 == sympify(x + y)
assert x1 * y1 == sympify(x * y)
assert x1 ** y1 == sympify(x ** y)
assert x1 - y1 == sympify(x - y)
assert x1 / y1 == sympify(x / y)
# Functions
assert sin(x1) == sin(x)
assert sin(x1)._sage_() == sage.sin(x)
assert sin(x1) == sympify(sage.sin(x))
assert cos(x1) == cos(x)
assert cos(x1)._sage_() == sage.cos(x)
assert cos(x1) == sympify(sage.cos(x))
assert function_symbol('f', x1, y1)._sage_() == sage.function('f', x, y)
assert function_symbol('f', 2 * x1, x1 + y1).diff(x1)._sage_() == sage.function('f', 2 * x, x + y).diff(x)
# For the following test, sage needs to be modified
# assert sage.sin(x) == sage.sin(x1)
# Constants
assert pi._sage_() == sage.pi
assert E._sage_() == sage.e
assert I._sage_() == sage.I
assert pi == sympify(sage.pi)
assert E == sympify(sage.e)
# SympyConverter does not support converting the following
# assert I == sympify(sage.I)
# Matrix
assert DenseMatrix(1, 2, [x1, y1])._sage_() == sage.matrix([[x, y]])
def test_sage_conversions():
try:
import sage.all as sage
except ImportError:
return
x, y = sage.SR.var('x y')
x1, y1 = symbols('x, y')
# Symbol
assert x1._sage_() == x
assert x1 == sympify(x)
# Integer
assert Integer(12)._sage_() == sage.Integer(12)
assert Integer(12) == sympify(sage.Integer(12))
# Rational
assert (Integer(1) / 2)._sage_() == sage.Integer(1) / 2
assert Integer(1) / 2 == sympify(sage.Integer(1) / 2)
# Operators
assert x1 + y == x1 + y1
assert x1 * y == x1 * y1
assert x1 ** y == x1 ** y1
assert x1 - y == x1 - y1
assert x1 / y == x1 / y1
assert x + y1 == x + y
assert x * y1 == x * y
# Doesn't work in Sage 6.1.1ubuntu2
# assert x ** y1 == x ** y
assert x - y1 == x - y
assert x / y1 == x / y
# Conversions
assert (x1 + y1)._sage_() == x + y
assert (x1 * y1)._sage_() == x * y
assert (x1 ** y1)._sage_() == x ** y
assert (x1 - y1)._sage_() == x - y
assert (x1 / y1)._sage_() == x / y
assert x1 + y1 == sympify(x + y)
assert x1 * y1 == sympify(x * y)
assert x1 ** y1 == sympify(x ** y)
assert x1 - y1 == sympify(x - y)
assert x1 / y1 == sympify(x / y)
# Functions
assert sin(x1) == sin(x)
assert sin(x1)._sage_() == sage.sin(x)
assert sin(x1) == sympify(sage.sin(x))
assert cos(x1) == cos(x)
assert cos(x1)._sage_() == sage.cos(x)
assert cos(x1) == sympify(sage.cos(x))
assert function_symbol('f', x1, y1)._sage_() == sage.function('f', x, y)
assert function_symbol('f', 2 * x1, x1 + y1).diff(x1)._sage_() == sage.function('f', 2 * x, x + y).diff(x)
# For the following test, sage needs to be modified
# assert sage.sin(x) == sage.sin(x1)
# Constants
assert pi._sage_() == sage.pi
assert E._sage_() == sage.e
assert I._sage_() == sage.I
assert pi == sympify(sage.pi)
assert E == sympify(sage.e)
# SympyConverter does not support converting the following
# assert I == sympify(sage.I)
# Matrix
assert DenseMatrix(1, 2, [x1, y1])._sage_() == sage.matrix([[x, y]])
# SympyConverter does not support converting the following
# assert DenseMatrix(1, 2, [x1, y1]) == sympify(sage.matrix([[x, y]]))
# Sage Number
a = sage.Mod(2, 7)
b = PyNumber(a, sage_module)
a = a + 8
b = b + 8
assert isinstance(b, PyNumber)
assert b._sage_() == a
a = a + x
b = b + x
assert isinstance(b, Add)
assert b._sage_() == a
# Sage Function
e = x1 + wrap_sage_function(sage.log_gamma(x))
assert str(e) == "x + log_gamma(x)"
assert isinstance(e, Add)
assert e + wrap_sage_function(sage.log_gamma(x)) == x1 + 2*wrap_sage_function(sage.log_gamma(x))
f = e.subs({x1 : 10})
assert f == 10 + log(362880)
f = e.subs({x1 : 2})
assert f == 2
f = e.subs({x1 : 100});
v = f.n(53, real=True);
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x1)
def test_msubs():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.msubs({f: y}) == y
assert f.diff(x).msubs({f: y}) == f.diff(x)
def test_msubs():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.msubs({f: y}) == y
assert f.diff(x).msubs({f: y}) == f.diff(x)
