Python Integral.as_sum示例

示例#1

文件： test_integrals.py 项目： baoqchau/sympy

def test_as_sum_raises():
    e = Integral((x + y)**2, (x, 0, 1))
    raises(ValueError, lambda: e.as_sum(-1))
    raises(ValueError, lambda: e.as_sum(0))
    raises(ValueError, lambda: Integral(x).as_sum(3))
    raises(NotImplementedError, lambda: e.as_sum(oo))
    raises(NotImplementedError, lambda: e.as_sum(3, method='xxxx2'))

示例#2

def test_as_sum_raises():
    e = Integral((x + y)**2, (x, 0, 1))
    raises(ValueError, lambda: e.as_sum(-1))
    raises(ValueError, lambda: e.as_sum(0))
    raises(ValueError, lambda: Integral(x).as_sum(3))
    raises(NotImplementedError, lambda: e.as_sum(oo))
    raises(NotImplementedError, lambda: e.as_sum(3, method='xxxx2'))

示例#3

文件： test_integrals.py 项目： normalhuman/sympy

def test_as_sum_right():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="right").expand() == 1 + 2*y + y**2
    assert e.as_sum(2, method="right").expand() == S(5)/8 + 3*y/2 + y**2
    assert e.as_sum(3, method="right").expand() == S(14)/27 + 4*y/3 + y**2
    assert e.as_sum(4, method="right").expand() == S(15)/32 + 5*y/4 + y**2
    assert e.as_sum(n, method="right").expand() == \
        y**2 + y + S(1)/3 + y/n + 1/(2*n) + 1/(6*n**2)

示例#4

def test_as_sum_right():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="right").expand() == 1 + 2 * y + y**2
    assert e.as_sum(2, method="right").expand() == S(5) / 8 + 3 * y / 2 + y**2
    assert e.as_sum(3,
                    method="right").expand() == S(14) / 27 + 4 * y / 3 + y**2
    assert e.as_sum(4,
                    method="right").expand() == S(15) / 32 + 5 * y / 4 + y**2

示例#5

文件： test_integrals.py 项目： tapaseid/sympy

def test_as_sum_trapezoid():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="trapezoid").expand() == y**2 + y + S(1)/2
    assert e.as_sum(2, method="trapezoid").expand() == y**2 + y + S(3)/8
    assert e.as_sum(3, method="trapezoid").expand() == y**2 + y + S(19)/54
    assert e.as_sum(4, method="trapezoid").expand() == y**2 + y + S(11)/32
    assert e.as_sum(n, method="trapezoid").expand() == \
        y**2 + y + S(1)/3 + 1/(6*n**2)
    assert Integral(sign(x), (x, 0, 1)).as_sum(1, 'trapezoid') == S(1)/2

示例#6

文件： test_integrals.py 项目： tapaseid/sympy

def test_as_sum_left():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="left").expand() == y**2
    assert e.as_sum(2, method="left").expand() == S(1)/8 + y/2 + y**2
    assert e.as_sum(3, method="left").expand() == S(5)/27 + 2*y/3 + y**2
    assert e.as_sum(4, method="left").expand() == S(7)/32 + 3*y/4 + y**2
    assert e.as_sum(n, method="left").expand() == \
        y**2 + y + S(1)/3 - y/n - 1/(2*n) + 1/(6*n**2)
    assert e.as_sum(10, method="left", evaluate=False).has(Sum)

示例#7

文件： test_integrals.py 项目： tapaseid/sympy

def test_as_sum_midpoint2():
    e = Integral((x + y)**2, (x, 0, 1))
    n = Symbol('n', positive=True, integer=True)
    assert e.as_sum(1, method="midpoint").expand() == S(1)/4 + y + y**2
    assert e.as_sum(2, method="midpoint").expand() == S(5)/16 + y + y**2
    assert e.as_sum(3, method="midpoint").expand() == S(35)/108 + y + y**2
    assert e.as_sum(4, method="midpoint").expand() == S(21)/64 + y + y**2
    assert e.as_sum(n, method="midpoint").expand() == \
        y**2 + y + 1/3 - 1/(12*n**2)

示例#8

文件： test_integrals.py 项目： normalhuman/sympy

def test_as_sum_trapezoid():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="trapezoid").expand() == y**2 + y + S(1)/2
    assert e.as_sum(2, method="trapezoid").expand() == y**2 + y + S(3)/8
    assert e.as_sum(3, method="trapezoid").expand() == y**2 + y + S(19)/54
    assert e.as_sum(4, method="trapezoid").expand() == y**2 + y + S(11)/32
    assert e.as_sum(n, method="trapezoid").expand() == \
        y**2 + y + S(1)/3 + 1/(6*n**2)
    assert Integral(sign(x), (x, 0, 1)).as_sum(1, 'trapezoid') == S(1)/2

示例#9

文件： test_integrals.py 项目： normalhuman/sympy

def test_as_sum_left():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="left").expand() == y**2
    assert e.as_sum(2, method="left").expand() == S(1)/8 + y/2 + y**2
    assert e.as_sum(3, method="left").expand() == S(5)/27 + 2*y/3 + y**2
    assert e.as_sum(4, method="left").expand() == S(7)/32 + 3*y/4 + y**2
    assert e.as_sum(n, method="left").expand() == \
        y**2 + y + S(1)/3 - y/n - 1/(2*n) + 1/(6*n**2)
    assert e.as_sum(10, method="left", evaluate=False).has(Sum)

示例#10

文件： test_integrals.py 项目： normalhuman/sympy

def test_as_sum_midpoint2():
    e = Integral((x + y)**2, (x, 0, 1))
    n = Symbol('n', positive=True, integer=True)
    assert e.as_sum(1, method="midpoint").expand() == S(1)/4 + y + y**2
    assert e.as_sum(2, method="midpoint").expand() == S(5)/16 + y + y**2
    assert e.as_sum(3, method="midpoint").expand() == S(35)/108 + y + y**2
    assert e.as_sum(4, method="midpoint").expand() == S(21)/64 + y + y**2
    assert e.as_sum(n, method="midpoint").expand() == \
        y**2 + y + 1/3 - 1/(12*n**2)

示例#11

文件： test_integrals.py 项目： arunenigma/sympy

def test_as_sum_midpoint1():
    e = Integral(sqrt(x ** 3 + 1), (x, 2, 10))
    assert e.as_sum(1, method="midpoint") == 8 * sqrt(217)
    assert e.as_sum(2, method="midpoint") == 4 * sqrt(65) + 12 * sqrt(57)
    assert e.as_sum(3, method="midpoint") == 8 * sqrt(217) / 3 + 8 * sqrt(3081) / 27 + 8 * sqrt(52809) / 27
    assert e.as_sum(4, method="midpoint") == 2 * sqrt(730) + 4 * sqrt(7) + 4 * sqrt(86) + 6 * sqrt(14)
    assert abs(e.as_sum(4, method="midpoint").n() - e.n()) < 0.5

    e = Integral(sqrt(x ** 3 + y ** 3), (x, 2, 10), (y, 0, 10))
    raises(NotImplementedError, "e.as_sum(4)")

示例#12

def test_as_sum_midpoint1():
    e = Integral(sqrt(x**3 + 1), (x, 2, 10))
    assert e.as_sum(1, method="midpoint") == 8 * sqrt(217)
    assert e.as_sum(2, method="midpoint") == 4 * sqrt(65) + 12 * sqrt(57)
    assert e.as_sum(3, method="midpoint") == 8*sqrt(217)/3 + \
        8*sqrt(3081)/27 + 8*sqrt(52809)/27
    assert e.as_sum(4, method="midpoint") == 2*sqrt(730) + \
        4*sqrt(7) + 4*sqrt(86) + 6*sqrt(14)
    assert abs(e.as_sum(4, method="midpoint").n() - e.n()) < 0.5

    e = Integral(sqrt(x**3 + y**3), (x, 2, 10), (y, 0, 10))
    raises(NotImplementedError, lambda: e.as_sum(4))

示例#13

文件： test_integrals.py 项目： silver1543/sympy

def test_as_sum_midpoint1():
    e = Integral(sqrt(x**3+1), (x, 2, 10))
    assert e.as_sum(1, method="midpoint") == 8*217**(S(1)/2)
    assert e.as_sum(2, method="midpoint") == 4*65**(S(1)/2) + 12*57**(S(1)/2)
    assert e.as_sum(3, method="midpoint") == 8*217**(S(1)/2)/3 + \
            8*3081**(S(1)/2)/27 + 8*52809**(S(1)/2)/27
    assert e.as_sum(4, method="midpoint") == 2*730**(S(1)/2) + \
            4*7**(S(1)/2) + 4*86**(S(1)/2) + 6*14**(S(1)/2)
    assert abs(e.as_sum(4, method="midpoint").n() - e.n()) < 0.5

    e = Integral(sqrt(x**3+y**3), (x, 2, 10), (y, 0, 10))
    raises(NotImplementedError, "e.as_sum(4)")

示例#14

文件： test_integrals.py 项目： wxgeo/sympy

def test_as_sum_midpoint1():
    e = Integral(sqrt(x**3+1), (x, 2, 10))
    assert e.as_sum(1, method="midpoint") == 8*217**(S(1)/2)
    assert e.as_sum(2, method="midpoint") == 4*65**(S(1)/2) + 12*57**(S(1)/2)
    assert e.as_sum(3, method="midpoint") == 8*217**(S(1)/2)/3 + \
            8*3081**(S(1)/2)/27 + 8*52809**(S(1)/2)/27
    assert e.as_sum(4, method="midpoint") == 2*730**(S(1)/2) + \
            4*7**(S(1)/2) + 4*86**(S(1)/2) + 6*14**(S(1)/2)
    assert abs(e.as_sum(4, method="midpoint").n() - e.n()) < 0.5

    e = Integral(sqrt(x**3+y**3), (x, 2, 10), (y, 0, 10))
    raises(NotImplementedError, "e.as_sum(4)")

示例#15

def test_as_sum_left():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="left").expand() == y**2
    assert e.as_sum(2, method="left").expand() == S(1) / 8 + y / 2 + y**2
    assert e.as_sum(3, method="left").expand() == S(5) / 27 + 2 * y / 3 + y**2
    assert e.as_sum(4, method="left").expand() == S(7) / 32 + 3 * y / 4 + y**2

示例#16

def test_as_sum_midpoint2():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="midpoint").expand() == S(1) / 4 + y + y**2
    assert e.as_sum(2, method="midpoint").expand() == S(5) / 16 + y + y**2
    assert e.as_sum(3, method="midpoint").expand() == S(35) / 108 + y + y**2
    assert e.as_sum(4, method="midpoint").expand() == S(21) / 64 + y + y**2

示例#17

文件： test_integrals.py 项目： baoqchau/sympy

def test_as_sum_left():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="left").expand() == y**2
    assert e.as_sum(2, method="left").expand() == S(1)/8 + y/2 + y**2
    assert e.as_sum(3, method="left").expand() == S(5)/27 + 2*y/3 + y**2
    assert e.as_sum(4, method="left").expand() == S(7)/32 + 3*y/4 + y**2

示例#18

文件： test_integrals.py 项目： baoqchau/sympy

def test_as_sum_midpoint2():
    e = Integral((x + y)**2, (x, 0, 1))
    assert e.as_sum(1, method="midpoint").expand() == S(1)/4 + y + y**2
    assert e.as_sum(2, method="midpoint").expand() == S(5)/16 + y + y**2
    assert e.as_sum(3, method="midpoint").expand() == S(35)/108 + y + y**2
    assert e.as_sum(4, method="midpoint").expand() == S(21)/64 + y + y**2