Exemplo n.º 1
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def test_sequence():
    form = SeqFormula(n**2, (n, 0, 5))
    per = SeqPer((1, 2, 3), (n, 0, 5))
    inter = SeqFormula(n**2)

    assert sequence(n**2, (n, 0, 5)) == form
    assert sequence((1, 2, 3), (n, 0, 5)) == per
    assert sequence(n**2) == inter
Exemplo n.º 2
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def test_sub():
    per = SeqPer((1, 2), (n, 0, oo))
    form = SeqFormula(n**2)

    assert per - (SeqPer((2, 3))) == SeqPer((-1, -1), (n, 0, oo))
    assert form - (SeqFormula(n**3)) == SeqFormula(n**2 - n**3)

    assert per - form == SeqAdd(per, -form)

    raises(TypeError, lambda: per - n)
    raises(TypeError, lambda: n - per)
Exemplo n.º 3
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def test_add():
    per = SeqPer((1, 2), (n, 0, oo))
    form = SeqFormula(n**2)

    assert per + (SeqPer((2, 3))) == SeqPer((3, 5), (n, 0, oo))
    assert form + SeqFormula(n**3) == SeqFormula(n**2 + n**3)

    assert per + form == SeqAdd(per, form)

    raises(TypeError, lambda: per + n)
    raises(TypeError, lambda: n + per)
Exemplo n.º 4
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def test_SeqFormula():
    s = SeqFormula(n**2, (n, 0, 5))

    assert isinstance(s, SeqFormula)
    assert s.formula == n**2
    assert s.coeff(3) == 9

    assert list(s) == [i**2 for i in range(6)]
    assert s[:] == [i**2 for i in range(6)]
    assert SeqFormula(n**2, (n, -oo, 0))[0:6] == [i**2 for i in range(6)]

    assert SeqFormula(n**2, (0, oo)) == SeqFormula(n**2, (n, 0, oo))

    assert SeqFormula(n**2, (0, m)).subs(m, x) == SeqFormula(n**2, (0, x))
    assert SeqFormula(m*n**2, (n, 0, oo)).subs(m, x) == \
        SeqFormula(x*n**2, (n, 0, oo))

    raises(ValueError, lambda: SeqFormula(n**2, (0, 1, 2)))
    raises(ValueError, lambda: SeqFormula(n**2, (n, -oo, oo)))
    raises(ValueError, lambda: SeqFormula(m*n**2, (0, oo)))
Exemplo n.º 5
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def test_SeqExprOp():
    form = SeqFormula(n**2, (n, 0, 10))
    per = SeqPer((1, 2, 3), (m, 5, 10))

    s = SeqExprOp(form, per)
    assert s.gen == (n**2, (1, 2, 3))
    assert s.interval == Interval(5, 10)
    assert s.start == 5
    assert s.stop == 10
    assert s.length == 6
    assert s.variables == (n, m)
Exemplo n.º 6
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def test_operations():
    per = SeqPer((1, 2), (n, 0, oo))
    per2 = SeqPer((2, 4), (n, 0, oo))
    form = SeqFormula(n**2)
    form2 = SeqFormula(n**3)

    assert per + form + form2 == SeqAdd(per, form, form2)
    assert per + form - form2 == SeqAdd(per, form, -form2)
    assert per + form - S.EmptySequence == SeqAdd(per, form)
    assert per + per2 + form == SeqAdd(SeqPer((3, 6), (n, 0, oo)), form)
    assert S.EmptySequence - per == -per
    assert form + form == SeqFormula(2*n**2)

    assert per * form * form2 == SeqMul(per, form, form2)
    assert form * form == SeqFormula(n**4)
    assert form * -form == SeqFormula(-n**4)

    assert form * (per + form2) == SeqMul(form, SeqAdd(per, form2))
    assert form * (per + per) == SeqMul(form, per2)

    assert form.coeff_mul(m) == SeqFormula(m*n**2, (n, 0, oo))
    assert per.coeff_mul(m) == SeqPer((m, 2*m), (n, 0, oo))
Exemplo n.º 7
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def test_mul__coeff_mul():
    assert SeqPer((1, 2), (n, 0, oo)).coeff_mul(2) == SeqPer((2, 4), (n, 0, oo))
    assert SeqFormula(n**2).coeff_mul(2) == SeqFormula(2*n**2)
    assert S.EmptySequence.coeff_mul(100) == S.EmptySequence

    assert SeqPer((1, 2), (n, 0, oo)) * (SeqPer((2, 3))) == \
        SeqPer((2, 6), (n, 0, oo))
    assert SeqFormula(n**2) * SeqFormula(n**3) == SeqFormula(n**5)

    assert S.EmptySequence * SeqFormula(n**2) == S.EmptySequence
    assert SeqFormula(n**2) * S.EmptySequence == S.EmptySequence

    raises(TypeError, lambda: sequence(n**2) * n)
    raises(TypeError, lambda: n * sequence(n**2))
Exemplo n.º 8
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def test_operations():
    per = SeqPer((1, 2), (n, 0, oo))
    per2 = SeqPer((2, 4), (n, 0, oo))
    form = SeqFormula(n**2)
    form2 = SeqFormula(n**3)

    assert per + form + form2 == SeqAdd(per, form, form2)
    assert per + form - form2 == SeqAdd(per, form, -form2)
    assert per + form - S.EmptySequence == SeqAdd(per, form)
    assert per + per2 + form == SeqAdd(SeqPer((3, 6), (n, 0, oo)), form)
    assert S.EmptySequence - per == -per
    assert form + form == SeqFormula(2 * n**2)

    assert per * form * form2 == SeqMul(per, form, form2)
    assert form * form == SeqFormula(n**4)
    assert form * -form == SeqFormula(-n**4)

    assert form * (per + form2) == SeqMul(form, SeqAdd(per, form2))
    assert form * (per + per) == SeqMul(form, per2)

    assert form.coeff_mul(m) == SeqFormula(m * n**2, (n, 0, oo))
    assert per.coeff_mul(m) == SeqPer((m, 2 * m), (n, 0, oo))
Exemplo n.º 9
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def test_SeqAdd():
    per = SeqPer((1, 2, 3), (n, 0, oo))
    form = SeqFormula(n**2)

    per_bou = SeqPer((1, 2), (n, 1, 5))
    form_bou = SeqFormula(n**2, (6, 10))
    form_bou2 = SeqFormula(n**2, (1, 5))

    assert SeqAdd() == S.EmptySequence
    assert SeqAdd(S.EmptySequence) == S.EmptySequence
    assert SeqAdd(per) == per
    assert SeqAdd(per, S.EmptySequence) == per
    assert SeqAdd(per_bou, form_bou) == S.EmptySequence

    s = SeqAdd(per_bou, form_bou2, evaluate=False)
    assert s.args == (form_bou2, per_bou)
    assert s[:] == [2, 6, 10, 18, 26]
    assert list(s) == [2, 6, 10, 18, 26]

    assert isinstance(SeqAdd(per, per_bou, evaluate=False), SeqAdd)

    s1 = SeqAdd(per, per_bou)
    assert isinstance(s1, SeqPer)
    assert s1 == SeqPer((2, 4, 4, 3, 3, 5), (n, 1, 5))
    s2 = SeqAdd(form, form_bou)
    assert isinstance(s2, SeqFormula)
    assert s2 == SeqFormula(2 * n**2, (6, 10))

    assert SeqAdd(form, form_bou, per) == SeqAdd(per,
                                                 SeqFormula(2 * n**2, (6, 10)))
    assert SeqAdd(form, SeqAdd(form_bou,
                               per)) == SeqAdd(per,
                                               SeqFormula(2 * n**2, (6, 10)))
    assert SeqAdd(per, SeqAdd(form, form_bou),
                  evaluate=False) == SeqAdd(per, SeqFormula(2 * n**2, (6, 10)))

    assert SeqAdd(SeqPer((1, 2), (n, 0, oo)), SeqPer(
        (1, 2), (m, 0, oo))) == SeqPer((2, 4), (n, 0, oo))
Exemplo n.º 10
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def test_SeqMul():
    per = SeqPer((1, 2, 3), (n, 0, oo))
    form = SeqFormula(n**2)

    per_bou = SeqPer((1, 2), (n, 1, 5))
    form_bou = SeqFormula(n**2, (n, 6, 10))
    form_bou2 = SeqFormula(n**2, (1, 5))

    assert SeqMul() == S.EmptySequence
    assert SeqMul(S.EmptySequence) == S.EmptySequence
    assert SeqMul(per) == per
    assert SeqMul(per, S.EmptySequence) == S.EmptySequence
    assert SeqMul(per_bou, form_bou) == S.EmptySequence

    s = SeqMul(per_bou, form_bou2, evaluate=False)
    assert s.args == (form_bou2, per_bou)
    assert s[:] == [1, 8, 9, 32, 25]
    assert list(s) == [1, 8, 9, 32, 25]

    assert isinstance(SeqMul(per, per_bou, evaluate=False), SeqMul)

    s1 = SeqMul(per, per_bou)
    assert isinstance(s1, SeqPer)
    assert s1 == SeqPer((1, 4, 3, 2, 2, 6), (n, 1, 5))
    s2 = SeqMul(form, form_bou)
    assert isinstance(s2, SeqFormula)
    assert s2 == SeqFormula(n**4, (6, 10))

    assert SeqMul(form, form_bou, per) == SeqMul(per,
                                                 SeqFormula(n**4, (6, 10)))
    assert SeqMul(form, SeqMul(form_bou,
                               per)) == SeqMul(per, SeqFormula(n**4, (6, 10)))
    assert SeqMul(per, SeqMul(form, form_bou2, evaluate=False),
                  evaluate=False) == SeqMul(form,
                                            per,
                                            form_bou2,
                                            evaluate=False)

    assert SeqMul(SeqPer((1, 2), (n, 0, oo)), SeqPer(
        (1, 2), (n, 0, oo))) == SeqPer((1, 4), (n, 0, oo))
Exemplo n.º 11
0
# SeqPer((1, 2, 3), (n, 0, 5))
print(b)

print(a.coeff(3))  # 在自变量取特定值时的值
print(a[:])
print(b[:])
print(b.periodical)  # 周期序列
print(b.period)  # 周期序列长度

k = sympy.symbols('k')
c = SeqPer((k, k**2, k**3), (k, 0, oo))
print(c.periodical)
print(c[0:10])
print(c.coeff(4))

d = SeqFormula(n**3, (n, -oo, 0))  # 不能写0,-oo
print(d[0:6])

print(SeqAdd(SeqPer((1, 2), (n, 0, oo)), S.EmptySequence))
# SeqPer((1, 2), (n, 0, oo))
print(SeqAdd(SeqPer((1, 2), (n, 0, 5)), SeqPer((1, 2), (n, 6, 10))))
# EmptySequence()
print(SeqAdd(SeqPer((1, 2), (n, 0, oo)), SeqFormula(n**2, (n, 0, oo))))
# SeqAdd(SeqFormula(n**2, (n, 0, oo)), SeqPer((1, 2), (n, 0, oo)))
print(SeqAdd(SeqFormula(n**3), SeqFormula(n**2)))
# SeqFormula(n**3 + n**2, (n, 0, oo))

e = SeqAdd(SeqPer((1, 2), (n, 0, oo)), SeqFormula(n**2, (n, 0, oo)))
print(e[0:6])

print(SeqMul(SeqPer((1, 2), (n, 0, oo)), S.EmptySequence))
Exemplo n.º 12
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def test_SeqFormula():
    s = SeqFormula(n**2, (n, 0, 5))

    assert isinstance(s, SeqFormula)
    assert s.formula == n**2
    assert s.coeff(3) == 9

    assert list(s) == [i**2 for i in range(6)]
    assert s[:] == [i**2 for i in range(6)]
    assert SeqFormula(n**2, (n, -oo, 0))[0:6] == [i**2 for i in range(6)]

    assert SeqFormula(n**2, (0, oo)) == SeqFormula(n**2, (n, 0, oo))

    assert SeqFormula(n**2, (0, m)).subs(m, x) == SeqFormula(n**2, (0, x))
    assert SeqFormula(m*n**2, (n, 0, oo)).subs(m, x) == \
        SeqFormula(x*n**2, (n, 0, oo))

    raises(ValueError, lambda: SeqFormula(n**2, (0, 1, 2)))
    raises(ValueError, lambda: SeqFormula(n**2, (n, -oo, oo)))
    raises(ValueError, lambda: SeqFormula(m*n**2, (0, oo)))

    seq = SeqFormula(x*(y**2 + z), (z, 1, 100))
    assert seq.expand() == SeqFormula(x*y**2 + x*z, (z, 1, 100))
    seq = SeqFormula(sin(x*(y**2 + z)),(z, 1, 100))
    assert seq.expand(trig=True) == SeqFormula(sin(x*y**2)*cos(x*z) + sin(x*z)*cos(x*y**2), (z, 1, 100))
    assert seq.expand() == SeqFormula(sin(x*y**2 + x*z), (z, 1, 100))
    assert seq.expand(trig=False) == SeqFormula(sin(x*y**2 + x*z), (z, 1, 100))
    seq = SeqFormula(exp(x*(y**2 + z)), (z, 1, 100))
    assert seq.expand() == SeqFormula(exp(x*y**2)*exp(x*z), (z, 1, 100))
    assert seq.expand(power_exp=False) == SeqFormula(exp(x*y**2 + x*z), (z, 1, 100))
    assert seq.expand(mul=False, power_exp=False) == SeqFormula(exp(x*(y**2 + z)), (z, 1, 100))
Exemplo n.º 13
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def test_SeqFormula():
    s = SeqFormula(n**2, (n, 0, 5))

    assert isinstance(s, SeqFormula)
    assert s.formula == n**2
    assert s.coeff(3) == 9

    assert list(s) == [i**2 for i in range(6)]
    assert s[:] == [i**2 for i in range(6)]
    assert SeqFormula(n**2, (n, -oo, 0))[0:6] == [i**2 for i in range(6)]

    assert SeqFormula(n**2, (0, oo)) == SeqFormula(n**2, (n, 0, oo))

    assert SeqFormula(n**2, (0, m)).subs(m, x) == SeqFormula(n**2, (0, x))
    assert SeqFormula(m*n**2, (n, 0, oo)).subs(m, x) == \
        SeqFormula(x*n**2, (n, 0, oo))

    raises(ValueError, lambda: SeqFormula(n**2, (0, 1, 2)))
    raises(ValueError, lambda: SeqFormula(n**2, (n, -oo, oo)))
    raises(ValueError, lambda: SeqFormula(m * n**2, (0, oo)))

    seq = SeqFormula(x * (y**2 + z), (z, 1, 100))
    assert seq.expand() == SeqFormula(x * y**2 + x * z, (z, 1, 100))
    seq = SeqFormula(sin(x * (y**2 + z)), (z, 1, 100))
    assert seq.expand(trig=True) == SeqFormula(
        sin(x * y**2) * cos(x * z) + sin(x * z) * cos(x * y**2), (z, 1, 100))
    assert seq.expand() == SeqFormula(sin(x * y**2 + x * z), (z, 1, 100))
    assert seq.expand(trig=False) == SeqFormula(sin(x * y**2 + x * z),
                                                (z, 1, 100))
    seq = SeqFormula(exp(x * (y**2 + z)), (z, 1, 100))
    assert seq.expand() == SeqFormula(exp(x * y**2) * exp(x * z), (z, 1, 100))
    assert seq.expand(power_exp=False) == SeqFormula(exp(x * y**2 + x * z),
                                                     (z, 1, 100))
    assert seq.expand(mul=False,
                      power_exp=False) == SeqFormula(exp(x * (y**2 + z)),
                                                     (z, 1, 100))
Exemplo n.º 14
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def test_Idx_limits():
    i = symbols('i', cls=Idx)
    r = Indexed('r', i)

    assert SeqFormula(r, (i, 0, 5))[:] == [r.subs(i, j) for j in range(6)]
    assert SeqPer((1, 2), (i, 0, 5))[:] == [1, 2, 1, 2, 1, 2]
Exemplo n.º 15
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def test_neg():
    assert -SeqPer((1, -2), (n, 0, oo)) == SeqPer((-1, 2), (n, 0, oo))
    assert -SeqFormula(n**2) == SeqFormula(-n**2)
Exemplo n.º 16
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from sympy import SeqFormula, oo, Symbol
n = Symbol('n')
print SeqFormula(n**2, (-oo, 0))[0:6]
Exemplo n.º 17
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def test_SeqFormula():
    s = SeqFormula(n**2, (n, 0, 5))

    assert isinstance(s, SeqFormula)
    assert s.formula == n**2
    assert s.coeff(3) == 9

    assert list(s) == [i**2 for i in range(6)]
    assert s[:] == [i**2 for i in range(6)]
    assert SeqFormula(n**2, (n, -oo, 0))[0:6] == [i**2 for i in range(6)]

    assert SeqFormula(n**2, (0, oo)) == SeqFormula(n**2, (n, 0, oo))

    assert SeqFormula(n**2, (0, m)).subs(m, x) == SeqFormula(n**2, (0, x))
    assert SeqFormula(m*n**2, (n, 0, oo)).subs(m, x) == \
        SeqFormula(x*n**2, (n, 0, oo))

    raises(ValueError, lambda: SeqFormula(n**2, (0, 1, 2)))
    raises(ValueError, lambda: SeqFormula(n**2, (n, -oo, oo)))
    raises(ValueError, lambda: SeqFormula(m * n**2, (0, oo)))