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Python functions.harmonic函数代码示例

本文整理汇总了Python中sympy.functions.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10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,您的评价将有助于系统推荐出更棒的Python代码示例。

示例1: 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:DVNSarma,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_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:DVNSarma,项目名称:sympy,代码行数:7,代码来源:test_comb_numbers.py

示例3: test_Function

def test_Function():
    assert mcode(sin(x) ** cos(x)) == "sin(x).^cos(x)"
    assert mcode(sign(x)) == "sign(x)"
    assert mcode(exp(x)) == "exp(x)"
    assert mcode(log(x)) == "log(x)"
    assert mcode(factorial(x)) == "factorial(x)"
    assert mcode(floor(x)) == "floor(x)"
    assert mcode(atan2(y, x)) == "atan2(y, x)"
    assert mcode(beta(x, y)) == 'beta(x, y)'
    assert mcode(polylog(x, y)) == 'polylog(x, y)'
    assert mcode(harmonic(x)) == 'harmonic(x)'
    assert mcode(bernoulli(x)) == "bernoulli(x)"
    assert mcode(bernoulli(x, y)) == "bernoulli(x, y)"
开发者ID:Lenqth,项目名称:sympy,代码行数:13,代码来源:test_octave.py

示例4: eval_sum_symbolic

def eval_sum_symbolic(f, limits):
    from sympy.functions import harmonic, bernoulli

    f_orig = f
    (i, a, b) = limits
    if not f.has(i):
        return f*(b - a + 1)

    # Linearity
    if f.is_Mul:
        L, R = f.as_two_terms()

        if not L.has(i):
            sR = eval_sum_symbolic(R, (i, a, b))
            if sR:
                return L*sR

        if not R.has(i):
            sL = eval_sum_symbolic(L, (i, a, b))
            if sL:
                return R*sL

        try:
            f = apart(f, i)  # see if it becomes an Add
        except PolynomialError:
            pass

    if f.is_Add:
        L, R = f.as_two_terms()
        lrsum = telescopic(L, R, (i, a, b))

        if lrsum:
            return lrsum

        lsum = eval_sum_symbolic(L, (i, a, b))
        rsum = eval_sum_symbolic(R, (i, a, b))

        if None not in (lsum, rsum):
            r = lsum + rsum
            if not r is S.NaN:
                return r

    # Polynomial terms with Faulhaber's formula
    n = Wild('n')
    result = f.match(i**n)

    if result is not None:
        n = result[n]

        if n.is_Integer:
            if n >= 0:
                if (b is S.Infinity and not a is S.NegativeInfinity) or \
                   (a is S.NegativeInfinity and not b is S.Infinity):
                    return S.Infinity
                return ((bernoulli(n + 1, b + 1) - bernoulli(n + 1, a))/(n + 1)).expand()
            elif a.is_Integer and a >= 1:
                if n == -1:
                    return harmonic(b) - harmonic(a - 1)
                else:
                    return harmonic(b, abs(n)) - harmonic(a - 1, abs(n))

    if not (a.has(S.Infinity, S.NegativeInfinity) or
            b.has(S.Infinity, S.NegativeInfinity)):
        # Geometric terms
        c1 = Wild('c1', exclude=[i])
        c2 = Wild('c2', exclude=[i])
        c3 = Wild('c3', exclude=[i])
        wexp = Wild('wexp')

        # Here we first attempt powsimp on f for easier matching with the
        # exponential pattern, and attempt expansion on the exponent for easier
        # matching with the linear pattern.
        e = f.powsimp().match(c1 ** wexp)
        if e is not None:
            e_exp = e.pop(wexp).expand().match(c2*i + c3)
            if e_exp is not None:
                e.update(e_exp)

        if e is not None:
            p = (c1**c3).subs(e)
            q = (c1**c2).subs(e)

            r = p*(q**a - q**(b + 1))/(1 - q)
            l = p*(b - a + 1)

            return Piecewise((l, Eq(q, S.One)), (r, True))

        r = gosper_sum(f, (i, a, b))

        if not r in (None, S.NaN):
            return r

    return eval_sum_hyper(f_orig, (i, a, b))
开发者ID:carstimon,项目名称:sympy,代码行数:93,代码来源:summations.py

示例5: 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:DVNSarma,项目名称:sympy,代码行数:28,代码来源:test_comb_numbers.py

示例6: 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:DVNSarma,项目名称:sympy,代码行数:5,代码来源:test_comb_numbers.py

示例7: 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:DVNSarma,项目名称:sympy,代码行数:15,代码来源:test_comb_numbers.py

示例8: 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:DVNSarma,项目名称:sympy,代码行数:3,代码来源:test_comb_numbers.py

示例9: 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:DVNSarma,项目名称:sympy,代码行数:66,代码来源:test_comb_numbers.py

示例10: eval_sum_symbolic

def eval_sum_symbolic(f, limits):
    from sympy.functions import harmonic, bernoulli

    f_orig = f
    (i, a, b) = limits
    if not f.has(i):
        return f*(b - a + 1)

    # Linearity
    if f.is_Mul:
        L, R = f.as_two_terms()

        if not L.has(i):
            sR = eval_sum_symbolic(R, (i, a, b))
            if sR:
                return L*sR

        if not R.has(i):
            sL = eval_sum_symbolic(L, (i, a, b))
            if sL:
                return R*sL

        try:
            f = apart(f, i)  # see if it becomes an Add
        except PolynomialError:
            pass

    if f.is_Add:
        L, R = f.as_two_terms()
        lrsum = telescopic(L, R, (i, a, b))

        if lrsum:
            return lrsum

        lsum = eval_sum_symbolic(L, (i, a, b))
        rsum = eval_sum_symbolic(R, (i, a, b))

        if None not in (lsum, rsum):
            r = lsum + rsum
            if not r is S.NaN:
                return r

    # Polynomial terms with Faulhaber's formula
    n = Wild('n')
    result = f.match(i**n)

    if result is not None:
        n = result[n]

        if n.is_Integer:
            if n >= 0:
                if (b is S.Infinity and not a is S.NegativeInfinity) or \
                   (a is S.NegativeInfinity and not b is S.Infinity):
                    return S.Infinity
                return ((bernoulli(n + 1, b + 1) - bernoulli(n + 1, a))/(n + 1)).expand()
            elif a.is_Integer and a >= 1:
                if n == -1:
                    return harmonic(b) - harmonic(a - 1)
                else:
                    return harmonic(b, abs(n)) - harmonic(a - 1, abs(n))

    if not (a.has(S.Infinity, S.NegativeInfinity) or
            b.has(S.Infinity, S.NegativeInfinity)):
        # Geometric terms
        c1 = Wild('c1', exclude=[i])
        c2 = Wild('c2', exclude=[i])
        c3 = Wild('c3', exclude=[i])
        wexp = Wild('wexp')

        # Here we first attempt powsimp on f for easier matching with the
        # exponential pattern, and attempt expansion on the exponent for easier
        # matching with the linear pattern.
        e = f.powsimp().match(c1 ** wexp)
        if e is not None:
            e_exp = e.pop(wexp).expand().match(c2*i + c3)
            if e_exp is not None:
                e.update(e_exp)

        if e is not None:
            p = (c1**c3).subs(e)
            q = (c1**c2).subs(e)

            r = p*(q**a - q**(b + 1))/(1 - q)
            l = p*(b - a + 1)

            return Piecewise((l, Eq(q, S.One)), (r, True))

        r = gosper_sum(f, (i, a, b))

        if isinstance(r, (Mul,Add)):
            from sympy import ordered, Tuple
            non_limit = r.free_symbols - Tuple(*limits[1:]).free_symbols
            den = denom(together(r))
            den_sym = non_limit & den.free_symbols
            args = []
            for v in ordered(den_sym):
                try:
                    s = solve(den, v)
                    m = Eq(v, s[0]) if s else S.false
                    if m != False:
#.........这里部分代码省略.........
开发者ID:cklb,项目名称:sympy,代码行数:101,代码来源:summations.py


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