Пример #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
Пример #2
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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
Пример #3
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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))
Пример #4
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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))
Пример #5
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#!/usr/bin/python

from sympy import summation, sequence, pprint
from sympy.abc import x

s = sequence(x, (x, 1, 10))
print(s)
pprint(s)
print(list(s))

print(s.length)

print(summation(s.formula, (x, s.start, s.stop)))
# print(sum(list(s)))
Пример #6
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def test_find_linear_recurrence():
    assert sequence((0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55), \
    (n, 0, 10)).find_linear_recurrence(11) == [1, 1]
    assert sequence((1, 2, 4, 7, 28, 128, 582, 2745, 13021, 61699, 292521, \
    1387138), (n, 0, 11)).find_linear_recurrence(12) == [5, -2, 6, -11]
    assert sequence(x*n**3+y*n, (n, 0, oo)).find_linear_recurrence(10) \
    == [4, -6, 4, -1]
    assert sequence(x**n, (n, 0, 20)).find_linear_recurrence(21) == [x]
    assert sequence((1, 2, 3)).find_linear_recurrence(10, 5) == [0, 0, 1]
    assert sequence(((1 + sqrt(5))/2)**n + \
    (-(1 + sqrt(5))/2)**(-n)).find_linear_recurrence(10) == [1, 1]
    assert sequence(x*((1 + sqrt(5))/2)**n + y*(-(1 + sqrt(5))/2)**(-n), \
    (n,0,oo)).find_linear_recurrence(10) == [1, 1]
    assert sequence((1, 2, 3, 4, 6), (n, 0, 4)).find_linear_recurrence(5) == []
    assert sequence((2,3,4,5,6,79),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
    == ([], None)
    assert sequence((2,3,4,5,8,30),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
    == ([Rational(19, 2), -20, Rational(27, 2)], (-31*x**2 + 32*x - 4)/(27*x**3 - 40*x**2 + 19*x -2))
    assert sequence(fibonacci(n)).find_linear_recurrence(30,gfvar=x) \
    == ([1, 1], -x/(x**2 + x - 1))
    assert sequence(tribonacci(n)).find_linear_recurrence(30,gfvar=x) \
    ==  ([1, 1, 1], -x/(x**3 + x**2 + x - 1))
Пример #7
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def test_find_linear_recurrence():
    assert sequence((0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55), \
    (n, 0, 10)).find_linear_recurrence(11) == [1, 1]
    assert sequence((1, 2, 4, 7, 28, 128, 582, 2745, 13021, 61699, 292521, \
    1387138), (n, 0, 11)).find_linear_recurrence(12) == [5, -2, 6, -11]
    assert sequence(x*n**3+y*n, (n, 0, oo)).find_linear_recurrence(10) \
    == [4, -6, 4, -1]
    assert sequence(x**n, (n,0,20)).find_linear_recurrence(21) == [x]
    assert sequence((1,2,3)).find_linear_recurrence(10, 5) == [0, 0, 1]
    assert sequence(((1 + sqrt(5))/2)**n + \
    (-(1 + sqrt(5))/2)**(-n)).find_linear_recurrence(10) == [1, 1]
    assert sequence(x*((1 + sqrt(5))/2)**n + y*(-(1 + sqrt(5))/2)**(-n), \
    (n,0,oo)).find_linear_recurrence(10) == [1, 1]
    assert sequence((1,2,3,4,6),(n, 0, 4)).find_linear_recurrence(5) == []
    assert sequence((2,3,4,5,6,79),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
    == ([], None)
    assert sequence((2,3,4,5,8,30),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
    == ([19/2, -20, 27/2], (-31*x**2 + 32*x - 4)/(27*x**3 - 40*x**2 + 19*x -2))
    assert sequence(fibonacci(n)).find_linear_recurrence(30,gfvar=x) \
    == ([1, 1], -x/(x**2 + x - 1))
Пример #8
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k, i = sp.symbols('k, i', integer=True)
xy = x * y
yx = y * x

# Not including x(yx)^k=0 because it's a Mul, not a Pow.
# I'm not handling those yet.
my_relations = {
    x**2: y * xy**(k - 1) + c * xy**k,
    y**2: d * xy**k,
    yx**k: xy**k
}

basis = [
    S.One,
    sp.sequence(y * xy**i, (i, 0, k - 1)),
    sp.sequence(x * yx**i, (i, 0, k - 1)),
    sp.sequence(xy**i, (i, 1, k - 1)),
    sp.sequence(yx**i, (i, 1, k - 1)), xy**k
]

zeros_mul = {
    '(x*y)**(k - 1)*y',
    'x*(x*y)**(k - 1)',
    'y*(y*x)**(k - 1)',
    'x**2*y',
    'x*(x*y)**k',
    '(x*y)**k*y',
    'y*(x*y)**k',
    '(y*x)**(k - 1)*x',
    # TODO: get rid at least of these
Пример #9
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# from tool import *
import sympy
from sympy import *
# from sympy import sequence,SeqFormula,SeqPer

from sympy import sequence, SeqPer, SeqFormula
from sympy.abc import n

a = sequence(n**2, (n, 0, 5))
print(a)
# SeqFormula(n**2, (n, 0, 5))
b = sequence((1, 2, 3, 4), (n, 0, 4))
# 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))