• 设为首页
  • 点击收藏
  • 手机版
    手机扫一扫访问
    迪恩网络手机版
  • 关注官方公众号
    微信扫一扫关注
    公众号

Python sympy.harmonic函数代码示例

原作者: [db:作者] 来自: [db:来源] 收藏 邀请

本文整理汇总了Python中sympy.harmonic函数的典型用法代码示例。如果您正苦于以下问题:Python harmonic函数的具体用法?Python harmonic怎么用?Python harmonic使用的例子?那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。



在下文中一共展示了harmonic函数的15个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于我们的系统推荐出更棒的Python代码示例。

示例1: test_harmonic_rewrite_sum_fail

def test_harmonic_rewrite_sum_fail():
    n = Symbol("n")
    m = Symbol("m")

    _k = Dummy("k")
    assert harmonic(n).rewrite(Sum) == Sum(1/_k, (_k, 1, n))
    assert harmonic(n, m).rewrite(Sum) == Sum(_k**(-m), (_k, 1, n))
开发者ID:B-Rich,项目名称:sympy,代码行数:7,代码来源:test_comb_numbers.py


示例2: test_harmonic_rewrite_sum

def test_harmonic_rewrite_sum():
    n = Symbol("n")
    m = Symbol("m")

    _k = Dummy("k")
    assert replace_dummy(harmonic(n).rewrite(Sum), _k) == Sum(1/_k, (_k, 1, n))
    assert replace_dummy(harmonic(n, m).rewrite(Sum), _k) == Sum(_k**(-m), (_k, 1, n))
开发者ID:B-Rich,项目名称:sympy,代码行数:7,代码来源:test_comb_numbers.py


示例3: test_harmonic

def test_harmonic():
    assert harmonic(1, 1) == 1
    assert harmonic(2, 1) == Rational(3, 2)
    assert harmonic(3, 1) == Rational(11, 6)
    assert harmonic(4, 1) == Rational(25, 12)
    assert harmonic(3, 1) == harmonic(3)
    assert harmonic(3, 5) == 1 + Rational(1, 2**5) + Rational(1, 3**5)
    assert harmonic(10, 0) == 10
    assert harmonic(oo, 1) == zoo
    assert harmonic(oo, 2) == (pi**2)/6
开发者ID:Jeyatharsini,项目名称:sympy,代码行数:10,代码来源:test_comb_numbers.py


示例4: test_limit_seq_fail

def test_limit_seq_fail():
    # improve Summation algorithm or add ad-hoc criteria
    e = (harmonic(n)**3 * Sum(1/harmonic(k), (k, 1, n)) /
         (n * Sum(harmonic(k)/k, (k, 1, n))))
    assert limit_seq(e, n) == 2

    # No unique dominant term
    e = (Sum(2**k * binomial(2*k, k) / k**2, (k, 1, n)) /
         (Sum(2**k/k*2, (k, 1, n)) * Sum(binomial(2*k, k), (k, 1, n))))
    assert limit_seq(e, n) == S(3) / 7

    # Simplifications of summations needs to be improved.
    e = n**3*Sum(2**k/k**2, (k, 1, n))**2 / (2**n * Sum(2**k/k, (k, 1, n)))
    assert limit_seq(e, n) == 2

    e = (harmonic(n) * Sum(2**k/k, (k, 1, n)) /
         (n * Sum(2**k*harmonic(k)/k**2, (k, 1, n))))
    assert limit_seq(e, n) == 1

    e = (Sum(2**k*factorial(k) / k**2, (k, 1, 2*n)) /
         (Sum(4**k/k**2, (k, 1, n)) * Sum(factorial(k), (k, 1, 2*n))))
    assert limit_seq(e, n) == S(3) / 16
开发者ID:KonstantinTogoi,项目名称:sympy,代码行数:22,代码来源:test_limitseq.py


示例5: test_limit_seq

def test_limit_seq():
    e = binomial(2*n, n) / Sum(binomial(2*k, k), (k, 1, n))
    assert limit_seq(e) == S(3) / 4
    assert limit_seq(e, m) == e

    e = (5*n**3 + 3*n**2 + 4) / (3*n**3 + 4*n - 5)
    assert limit_seq(e, n) == S(5) / 3

    e = (harmonic(n) * Sum(harmonic(k), (k, 1, n))) / (n * harmonic(2*n)**2)
    assert limit_seq(e, n) == 1

    e = Sum(k**2 * Sum(2**m/m, (m, 1, k)), (k, 1, n)) / (2**n*n)
    assert limit_seq(e, n) == 4

    e = (Sum(binomial(3*k, k) * binomial(5*k, k), (k, 1, n)) /
         (binomial(3*n, n) * binomial(5*n, n)))
    assert limit_seq(e, n) == S(84375) / 83351

    e = Sum(harmonic(k)**2/k, (k, 1, 2*n)) / harmonic(n)**3
    assert limit_seq(e, n) == S(1) / 3

    raises(ValueError, lambda: limit_seq(e * m))
开发者ID:KonstantinTogoi,项目名称:sympy,代码行数:22,代码来源:test_limitseq.py


示例6: test_difference_delta__Sum

def test_difference_delta__Sum():
    e = Sum(1/k, (k, 1, n))
    assert dd(e, n) == 1/(n + 1)
    assert dd(e, n, 5) == Add(*[1/(i + n + 1) for i in range(5)])

    e = Sum(1/k, (k, 1, 3*n))
    assert dd(e, n) == Add(*[1/(i + 3*n + 1) for i in range(3)])

    e = n * Sum(1/k, (k, 1, n))
    assert dd(e, n) == 1 + Sum(1/k, (k, 1, n))

    e = Sum(1/k, (k, 1, n), (m, 1, n))
    assert dd(e, n) == harmonic(n)
开发者ID:KonstantinTogoi,项目名称:sympy,代码行数:13,代码来源:test_limitseq.py


示例7: test_difference_delta__Sum

def test_difference_delta__Sum():
    e = Sum(1/k, (k, 1, n))
    assert dd(e, n) == 1/(n + 1)
    assert dd(e, n, 5) == Sum(1/k, (k, n + 1, n + 5))

    e = Sum(1/k, (k, 1, 3*n))
    assert dd(e, n) == Sum(1/k, (k, 3*n + 1, 3*n + 3))

    e = n * Sum(1/k, (k, 1, n))
    assert dd(e, n) == 1 + Sum(1/k, (k, 1, n))

    e = Sum(1/k, (k, 1, n), (m, 1, n))
    assert dd(e, n) == harmonic(n)
开发者ID:atreyv,项目名称:sympy,代码行数:13,代码来源:test_limitseq.py


示例8: test_harmonic_sums

def test_harmonic_sums():
    assert summation(1/k, (k, 0, n)) == Sum(1/k, (k, 0, n))
    assert summation(1/k, (k, 1, n)) == harmonic(n)
    assert summation(n/k, (k, 1, n)) == n*harmonic(n)
    assert summation(1/k, (k, 5, n)) == harmonic(n) - harmonic(4)
开发者ID:Maihj,项目名称:sympy,代码行数:5,代码来源:test_sums_products.py


示例9: test_polygamma

def test_polygamma():
    from sympy import I

    assert polygamma(n, nan) == nan

    assert polygamma(0, oo) == oo
    assert polygamma(0, -oo) == oo
    assert polygamma(0, I*oo) == oo
    assert polygamma(0, -I*oo) == oo
    assert polygamma(1, oo) == 0
    assert polygamma(5, oo) == 0

    assert polygamma(0, -9) == zoo

    assert polygamma(0, -9) == zoo
    assert polygamma(0, -1) == zoo

    assert polygamma(0, 0) == zoo

    assert polygamma(0, 1) == -EulerGamma
    assert polygamma(0, 7) == Rational(49, 20) - EulerGamma

    assert polygamma(1, 1) == pi**2/6
    assert polygamma(1, 2) == pi**2/6 - 1
    assert polygamma(1, 3) == pi**2/6 - Rational(5, 4)
    assert polygamma(3, 1) == pi**4 / 15
    assert polygamma(3, 5) == 6*(Rational(-22369, 20736) + pi**4/90)
    assert polygamma(5, 1) == 8 * pi**6 / 63

    def t(m, n):
        x = S(m)/n
        r = polygamma(0, x)
        if r.has(polygamma):
            return False
        return abs(polygamma(0, x.n()).n() - r.n()).n() < 1e-10
    assert t(1, 2)
    assert t(3, 2)
    assert t(-1, 2)
    assert t(1, 4)
    assert t(-3, 4)
    assert t(1, 3)
    assert t(4, 3)
    assert t(3, 4)
    assert t(2, 3)

    assert polygamma(0, x).rewrite(zeta) == polygamma(0, x)
    assert polygamma(1, x).rewrite(zeta) == zeta(2, x)
    assert polygamma(2, x).rewrite(zeta) == -2*zeta(3, x)

    assert polygamma(3, 7*x).diff(x) == 7*polygamma(4, 7*x)

    assert polygamma(0, x).rewrite(harmonic) == harmonic(x - 1) - EulerGamma
    assert polygamma(2, x).rewrite(harmonic) == 2*harmonic(x - 1, 3) - 2*zeta(3)
    ni = Symbol("n", integer=True)
    assert polygamma(ni, x).rewrite(harmonic) == (-1)**(ni + 1)*(-harmonic(x - 1, ni + 1)
                                                                 + zeta(ni + 1))*factorial(ni)

    # Polygamma of non-negative integer order is unbranched:
    from sympy import exp_polar
    k = Symbol('n', integer=True, nonnegative=True)
    assert polygamma(k, exp_polar(2*I*pi)*x) == polygamma(k, x)

    # but negative integers are branched!
    k = Symbol('n', integer=True)
    assert polygamma(k, exp_polar(2*I*pi)*x).args == (k, exp_polar(2*I*pi)*x)

    # Polygamma of order -1 is loggamma:
    assert polygamma(-1, x) == loggamma(x)

    # But smaller orders are iterated integrals and don't have a special name
    assert polygamma(-2, x).func is polygamma

    # Test a bug
    assert polygamma(0, -x).expand(func=True) == polygamma(0, -x)
开发者ID:A-turing-machine,项目名称:sympy,代码行数:74,代码来源:test_gamma_functions.py


示例10: test_harmonic

def test_harmonic():
    n = Symbol("n")

    assert harmonic(n, 0) == n
    assert harmonic(n, 1) == harmonic(n)

    assert harmonic(0, 1) == 0
    assert harmonic(1, 1) == 1
    assert harmonic(2, 1) == Rational(3, 2)
    assert harmonic(3, 1) == Rational(11, 6)
    assert harmonic(4, 1) == Rational(25, 12)
    assert harmonic(0, 2) == 0
    assert harmonic(1, 2) == 1
    assert harmonic(2, 2) == Rational(5, 4)
    assert harmonic(3, 2) == Rational(49, 36)
    assert harmonic(4, 2) == Rational(205, 144)
    assert harmonic(0, 3) == 0
    assert harmonic(1, 3) == 1
    assert harmonic(2, 3) == Rational(9, 8)
    assert harmonic(3, 3) == Rational(251, 216)
    assert harmonic(4, 3) == Rational(2035, 1728)

    assert harmonic(oo, -1) == S.NaN
    assert harmonic(oo, 0) == oo
    assert harmonic(oo, S.Half) == oo
    assert harmonic(oo, 1) == oo
    assert harmonic(oo, 2) == (pi**2)/6
    assert harmonic(oo, 3) == zeta(3)
开发者ID:B-Rich,项目名称:sympy,代码行数:28,代码来源:test_comb_numbers.py


示例11: test_harmonic_limit_fail

def test_harmonic_limit_fail():
    n = Symbol("n")
    m = Symbol("m")
    # For m > 1:
    assert limit(harmonic(n, m), n, oo) == zeta(m)
开发者ID:B-Rich,项目名称:sympy,代码行数:5,代码来源:test_comb_numbers.py


示例12: test_harmonic_rewrite_polygamma

def test_harmonic_rewrite_polygamma():
    n = Symbol("n")
    m = Symbol("m")

    assert harmonic(n).rewrite(digamma) == polygamma(0, n + 1) + EulerGamma
    assert harmonic(n).rewrite(trigamma) ==  polygamma(0, n + 1) + EulerGamma
    assert harmonic(n).rewrite(polygamma) ==  polygamma(0, n + 1) + EulerGamma

    assert harmonic(n,3).rewrite(polygamma) == polygamma(2, n + 1)/2 - polygamma(2, 1)/2
    assert harmonic(n,m).rewrite(polygamma) == (-1)**m*(polygamma(m - 1, 1) - polygamma(m - 1, n + 1))/factorial(m - 1)

    assert expand_func(harmonic(n+4)) == harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1)
    assert expand_func(harmonic(n-4)) == harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n

    assert harmonic(n, m).rewrite("tractable") == harmonic(n, m).rewrite(polygamma)
开发者ID:B-Rich,项目名称:sympy,代码行数:15,代码来源:test_comb_numbers.py


示例13: test_harmonic_rational

def test_harmonic_rational():
    ne = S(6)
    no = S(5)
    pe = S(8)
    po = S(9)
    qe = S(10)
    qo = S(13)

    Heee = harmonic(ne + pe/qe)
    Aeee = (-log(10) + 2*(-1/S(4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 - 1/S(4))*log(sqrt(sqrt(5)/8 + 5/S(8)))
             + pi*(1/S(4) + sqrt(5)/4)/(2*sqrt(-sqrt(5)/8 + 5/S(8)))
             + 13944145/S(4720968))

    Heeo = harmonic(ne + pe/qo)
    Aeeo = (-log(26) + 2*log(sin(3*pi/13))*cos(4*pi/13) + 2*log(sin(2*pi/13))*cos(32*pi/13)
             + 2*log(sin(5*pi/13))*cos(80*pi/13) - 2*log(sin(6*pi/13))*cos(5*pi/13)
             - 2*log(sin(4*pi/13))*cos(pi/13) + pi*cot(5*pi/13)/2 - 2*log(sin(pi/13))*cos(3*pi/13)
             + 2422020029/S(702257080))

    Heoe = harmonic(ne + po/qe)
    Aeoe = (-log(20) + 2*(1/S(4) + sqrt(5)/4)*log(-1/S(4) + sqrt(5)/4)
             + 2*(-1/S(4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 - 1/S(4))*log(sqrt(sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 + 1/S(4))*log(1/S(4) + sqrt(5)/4)
             + 11818877030/S(4286604231) - pi*sqrt(sqrt(5)/8 + 5/S(8))/(-sqrt(5)/2 + 1/S(2)) )


    Heoo = harmonic(ne + po/qo)
    Aeoo = (-log(26) + 2*log(sin(3*pi/13))*cos(54*pi/13) + 2*log(sin(4*pi/13))*cos(6*pi/13)
             + 2*log(sin(6*pi/13))*cos(108*pi/13) - 2*log(sin(5*pi/13))*cos(pi/13)
             - 2*log(sin(pi/13))*cos(5*pi/13) + pi*cot(4*pi/13)/2
             - 2*log(sin(2*pi/13))*cos(3*pi/13) + 11669332571/S(3628714320))

    Hoee = harmonic(no + pe/qe)
    Aoee = (-log(10) + 2*(-1/S(4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 - 1/S(4))*log(sqrt(sqrt(5)/8 + 5/S(8)))
             + pi*(1/S(4) + sqrt(5)/4)/(2*sqrt(-sqrt(5)/8 + 5/S(8)))
             + 779405/S(277704))

    Hoeo = harmonic(no + pe/qo)
    Aoeo = (-log(26) + 2*log(sin(3*pi/13))*cos(4*pi/13) + 2*log(sin(2*pi/13))*cos(32*pi/13)
             + 2*log(sin(5*pi/13))*cos(80*pi/13) - 2*log(sin(6*pi/13))*cos(5*pi/13)
             - 2*log(sin(4*pi/13))*cos(pi/13) + pi*cot(5*pi/13)/2
             - 2*log(sin(pi/13))*cos(3*pi/13) + 53857323/S(16331560))

    Hooe = harmonic(no + po/qe)
    Aooe = (-log(20) + 2*(1/S(4) + sqrt(5)/4)*log(-1/S(4) + sqrt(5)/4)
             + 2*(-1/S(4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 - 1/S(4))*log(sqrt(sqrt(5)/8 + 5/S(8)))
             + 2*(-sqrt(5)/4 + 1/S(4))*log(1/S(4) + sqrt(5)/4)
             + 486853480/S(186374097) - pi*sqrt(sqrt(5)/8 + 5/S(8))/(2*(-sqrt(5)/4 + 1/S(4))))

    Hooo = harmonic(no + po/qo)
    Aooo = (-log(26) + 2*log(sin(3*pi/13))*cos(54*pi/13) + 2*log(sin(4*pi/13))*cos(6*pi/13)
             + 2*log(sin(6*pi/13))*cos(108*pi/13) - 2*log(sin(5*pi/13))*cos(pi/13)
             - 2*log(sin(pi/13))*cos(5*pi/13) + pi*cot(4*pi/13)/2
             - 2*log(sin(2*pi/13))*cos(3*pi/13) + 383693479/S(125128080))

    H = [Heee, Heeo, Heoe, Heoo, Hoee, Hoeo, Hooe, Hooo]
    A = [Aeee, Aeeo, Aeoe, Aeoo, Aoee, Aoeo, Aooe, Aooo]

    for h, a in zip(H, A):
        e = expand_func(h).doit()
        assert cancel(e/a) == 1
        assert h.n() == a.n()
开发者ID:B-Rich,项目名称:sympy,代码行数:66,代码来源:test_comb_numbers.py


示例14: test_harmonic_rewrite_sum_fail

def test_harmonic_rewrite_sum_fail():
    n = Symbol("n")
    m = Symbol("m")

    assert harmonic(n).rewrite(digamma) == polygamma(0, n + 1) + EulerGamma
    assert harmonic(n).rewrite(trigamma) ==  polygamma(0, n + 1) + EulerGamma
    assert harmonic(n).rewrite(polygamma) ==  polygamma(0, n + 1) + EulerGamma

    assert harmonic(n,3).rewrite(polygamma) == polygamma(2, n + 1)/2 - polygamma(2, 1)/2
    assert harmonic(n,m).rewrite(polygamma) == (-1)**m*(polygamma(m - 1, 1) - polygamma(m - 1, n + 1))/factorial(m - 1)

    assert expand_func(harmonic(n+4)) == harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1)
    assert expand_func(harmonic(n-4)) == harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n

    assert harmonic(n, m).rewrite("tractable") == harmonic(n, m).rewrite(polygamma)

    _k = Dummy("k")
    assert harmonic(n).rewrite(Sum) == Sum(1/_k, (_k, 1, n))
    assert harmonic(n, m).rewrite(Sum) == Sum(_k**(-m), (_k, 1, n))
开发者ID:Jeyatharsini,项目名称:sympy,代码行数:19,代码来源:test_comb_numbers.py


示例15: test_harmonic_evalf

def test_harmonic_evalf():
    assert str(harmonic(1.5).evalf(n=10)) == '1.280372306'
    assert str(harmonic(1.5, 2).evalf(n=10)) == '1.154576311'  # issue 7443
开发者ID:Bercio,项目名称:sympy,代码行数:3,代码来源:test_comb_numbers.py



注:本文中的sympy.harmonic函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台,相关代码片段筛选自各路编程大神贡献的开源项目,源码版权归原作者所有,传播和使用请参考对应项目的License;未经允许,请勿转载。


鲜花

握手

雷人

路过

鸡蛋
该文章已有0人参与评论

请发表评论

全部评论

专题导读
上一篇:
Python sympy.hyper函数代码示例发布时间:2022-05-27
下一篇:
Python sympy.gcd函数代码示例发布时间:2022-05-27
热门推荐
阅读排行榜

扫描微信二维码

查看手机版网站

随时了解更新最新资讯

139-2527-9053

在线客服(服务时间 9:00~18:00)

在线QQ客服
地址:深圳市南山区西丽大学城创智工业园
电邮:jeky_zhao#qq.com
移动电话:139-2527-9053

Powered by 互联科技 X3.4© 2001-2213 极客世界.|Sitemap