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)
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)
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))
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
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)
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))
def test_SeqPer():
s = SeqPer((1, n, 3), (x, 0, 5))
assert isinstance(s, SeqPer)
assert s.periodical == Tuple(1, n, 3)
assert s.period == 3
assert s.coeff(3) == 1
assert s.free_symbols == {n}
assert list(s) == [1, n, 3, 1, n, 3]
assert s[:] == [1, n, 3, 1, n, 3]
assert SeqPer((1, n, 3), (x, -oo, 0))[0:6] == [1, n, 3, 1, n, 3]
raises(ValueError, lambda: SeqPer((1, 2, 3), (0, 1, 2)))
raises(ValueError, lambda: SeqPer((1, 2, 3), (x, -oo, oo)))
raises(ValueError, lambda: SeqPer(n**2, (0, oo)))
assert SeqPer((n, n**2, n**3), (m, 0, oo))[:6] == \
[n, n**2, n**3, n, n**2, n**3]
assert SeqPer((n, n**2, n**3), (n, 0, oo))[:6] == [0, 1, 8, 3, 16, 125]
assert SeqPer((n, m), (n, 0, oo))[:6] == [0, m, 2, m, 4, m]
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))
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))
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]
def test_neg():
assert -SeqPer((1, -2), (n, 0, oo)) == SeqPer((-1, 2), (n, 0, oo))
assert -SeqFormula(n**2) == SeqFormula(-n**2)