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| from sympy.calculus.accumulationbounds import AccumBounds | |
| from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo) | |
| from sympy.core.relational import (Eq, Ge, Gt, Le, Lt, Ne) | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import (Symbol, symbols) | |
| from sympy.functions.combinatorial.factorials import factorial | |
| from sympy.functions.elementary.exponential import (exp, log) | |
| from sympy.functions.elementary.integers import (ceiling, floor, frac) | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.functions.elementary.trigonometric import sin, cos, tan | |
| from sympy.polys.rootoftools import RootOf, CRootOf | |
| from sympy import Integers | |
| from sympy.sets.sets import Interval | |
| from sympy.sets.fancysets import ImageSet | |
| from sympy.core.function import Lambda | |
| from sympy.core.expr import unchanged | |
| from sympy.testing.pytest import XFAIL, raises | |
| x = Symbol('x') | |
| i = Symbol('i', imaginary=True) | |
| y = Symbol('y', real=True) | |
| k, n = symbols('k,n', integer=True) | |
| def test_floor(): | |
| assert floor(nan) is nan | |
| assert floor(oo) is oo | |
| assert floor(-oo) is -oo | |
| assert floor(zoo) is zoo | |
| assert floor(0) == 0 | |
| assert floor(1) == 1 | |
| assert floor(-1) == -1 | |
| assert floor(E) == 2 | |
| assert floor(-E) == -3 | |
| assert floor(2*E) == 5 | |
| assert floor(-2*E) == -6 | |
| assert floor(pi) == 3 | |
| assert floor(-pi) == -4 | |
| assert floor(S.Half) == 0 | |
| assert floor(Rational(-1, 2)) == -1 | |
| assert floor(Rational(7, 3)) == 2 | |
| assert floor(Rational(-7, 3)) == -3 | |
| assert floor(-Rational(7, 3)) == -3 | |
| assert floor(Float(17.0)) == 17 | |
| assert floor(-Float(17.0)) == -17 | |
| assert floor(Float(7.69)) == 7 | |
| assert floor(-Float(7.69)) == -8 | |
| assert floor(I) == I | |
| assert floor(-I) == -I | |
| e = floor(i) | |
| assert e.func is floor and e.args[0] == i | |
| assert floor(oo*I) == oo*I | |
| assert floor(-oo*I) == -oo*I | |
| assert floor(exp(I*pi/4)*oo) == exp(I*pi/4)*oo | |
| assert floor(2*I) == 2*I | |
| assert floor(-2*I) == -2*I | |
| assert floor(I/2) == 0 | |
| assert floor(-I/2) == -I | |
| assert floor(E + 17) == 19 | |
| assert floor(pi + 2) == 5 | |
| assert floor(E + pi) == 5 | |
| assert floor(I + pi) == 3 + I | |
| assert floor(floor(pi)) == 3 | |
| assert floor(floor(y)) == floor(y) | |
| assert floor(floor(x)) == floor(x) | |
| assert unchanged(floor, x) | |
| assert unchanged(floor, 2*x) | |
| assert unchanged(floor, k*x) | |
| assert floor(k) == k | |
| assert floor(2*k) == 2*k | |
| assert floor(k*n) == k*n | |
| assert unchanged(floor, k/2) | |
| assert unchanged(floor, x + y) | |
| assert floor(x + 3) == floor(x) + 3 | |
| assert floor(x + k) == floor(x) + k | |
| assert floor(y + 3) == floor(y) + 3 | |
| assert floor(y + k) == floor(y) + k | |
| assert floor(3 + I*y + pi) == 6 + floor(y)*I | |
| assert floor(k + n) == k + n | |
| assert unchanged(floor, x*I) | |
| assert floor(k*I) == k*I | |
| assert floor(Rational(23, 10) - E*I) == 2 - 3*I | |
| assert floor(sin(1)) == 0 | |
| assert floor(sin(-1)) == -1 | |
| assert floor(exp(2)) == 7 | |
| assert floor(log(8)/log(2)) != 2 | |
| assert int(floor(log(8)/log(2)).evalf(chop=True)) == 3 | |
| assert floor(factorial(50)/exp(1)) == \ | |
| 11188719610782480504630258070757734324011354208865721592720336800 | |
| assert (floor(y) < y) == False | |
| assert (floor(y) <= y) == True | |
| assert (floor(y) > y) == False | |
| assert (floor(y) >= y) == False | |
| assert (floor(x) <= x).is_Relational # x could be non-real | |
| assert (floor(x) > x).is_Relational | |
| assert (floor(x) <= y).is_Relational # arg is not same as rhs | |
| assert (floor(x) > y).is_Relational | |
| assert (floor(y) <= oo) == True | |
| assert (floor(y) < oo) == True | |
| assert (floor(y) >= -oo) == True | |
| assert (floor(y) > -oo) == True | |
| assert floor(y).rewrite(frac) == y - frac(y) | |
| assert floor(y).rewrite(ceiling) == -ceiling(-y) | |
| assert floor(y).rewrite(frac).subs(y, -pi) == floor(-pi) | |
| assert floor(y).rewrite(frac).subs(y, E) == floor(E) | |
| assert floor(y).rewrite(ceiling).subs(y, E) == -ceiling(-E) | |
| assert floor(y).rewrite(ceiling).subs(y, -pi) == -ceiling(pi) | |
| assert Eq(floor(y), y - frac(y)) | |
| assert Eq(floor(y), -ceiling(-y)) | |
| neg = Symbol('neg', negative=True) | |
| nn = Symbol('nn', nonnegative=True) | |
| pos = Symbol('pos', positive=True) | |
| np = Symbol('np', nonpositive=True) | |
| assert (floor(neg) < 0) == True | |
| assert (floor(neg) <= 0) == True | |
| assert (floor(neg) > 0) == False | |
| assert (floor(neg) >= 0) == False | |
| assert (floor(neg) <= -1) == True | |
| assert (floor(neg) >= -3) == (neg >= -3) | |
| assert (floor(neg) < 5) == (neg < 5) | |
| assert (floor(nn) < 0) == False | |
| assert (floor(nn) >= 0) == True | |
| assert (floor(pos) < 0) == False | |
| assert (floor(pos) <= 0) == (pos < 1) | |
| assert (floor(pos) > 0) == (pos >= 1) | |
| assert (floor(pos) >= 0) == True | |
| assert (floor(pos) >= 3) == (pos >= 3) | |
| assert (floor(np) <= 0) == True | |
| assert (floor(np) > 0) == False | |
| assert floor(neg).is_negative == True | |
| assert floor(neg).is_nonnegative == False | |
| assert floor(nn).is_negative == False | |
| assert floor(nn).is_nonnegative == True | |
| assert floor(pos).is_negative == False | |
| assert floor(pos).is_nonnegative == True | |
| assert floor(np).is_negative is None | |
| assert floor(np).is_nonnegative is None | |
| assert (floor(7, evaluate=False) >= 7) == True | |
| assert (floor(7, evaluate=False) > 7) == False | |
| assert (floor(7, evaluate=False) <= 7) == True | |
| assert (floor(7, evaluate=False) < 7) == False | |
| assert (floor(7, evaluate=False) >= 6) == True | |
| assert (floor(7, evaluate=False) > 6) == True | |
| assert (floor(7, evaluate=False) <= 6) == False | |
| assert (floor(7, evaluate=False) < 6) == False | |
| assert (floor(7, evaluate=False) >= 8) == False | |
| assert (floor(7, evaluate=False) > 8) == False | |
| assert (floor(7, evaluate=False) <= 8) == True | |
| assert (floor(7, evaluate=False) < 8) == True | |
| assert (floor(x) <= 5.5) == Le(floor(x), 5.5, evaluate=False) | |
| assert (floor(x) >= -3.2) == Ge(floor(x), -3.2, evaluate=False) | |
| assert (floor(x) < 2.9) == Lt(floor(x), 2.9, evaluate=False) | |
| assert (floor(x) > -1.7) == Gt(floor(x), -1.7, evaluate=False) | |
| assert (floor(y) <= 5.5) == (y < 6) | |
| assert (floor(y) >= -3.2) == (y >= -3) | |
| assert (floor(y) < 2.9) == (y < 3) | |
| assert (floor(y) > -1.7) == (y >= -1) | |
| assert (floor(y) <= n) == (y < n + 1) | |
| assert (floor(y) >= n) == (y >= n) | |
| assert (floor(y) < n) == (y < n) | |
| assert (floor(y) > n) == (y >= n + 1) | |
| assert floor(RootOf(x**3 - 27*x, 2)) == 5 | |
| def test_ceiling(): | |
| assert ceiling(nan) is nan | |
| assert ceiling(oo) is oo | |
| assert ceiling(-oo) is -oo | |
| assert ceiling(zoo) is zoo | |
| assert ceiling(0) == 0 | |
| assert ceiling(1) == 1 | |
| assert ceiling(-1) == -1 | |
| assert ceiling(E) == 3 | |
| assert ceiling(-E) == -2 | |
| assert ceiling(2*E) == 6 | |
| assert ceiling(-2*E) == -5 | |
| assert ceiling(pi) == 4 | |
| assert ceiling(-pi) == -3 | |
| assert ceiling(S.Half) == 1 | |
| assert ceiling(Rational(-1, 2)) == 0 | |
| assert ceiling(Rational(7, 3)) == 3 | |
| assert ceiling(-Rational(7, 3)) == -2 | |
| assert ceiling(Float(17.0)) == 17 | |
| assert ceiling(-Float(17.0)) == -17 | |
| assert ceiling(Float(7.69)) == 8 | |
| assert ceiling(-Float(7.69)) == -7 | |
| assert ceiling(I) == I | |
| assert ceiling(-I) == -I | |
| e = ceiling(i) | |
| assert e.func is ceiling and e.args[0] == i | |
| assert ceiling(oo*I) == oo*I | |
| assert ceiling(-oo*I) == -oo*I | |
| assert ceiling(exp(I*pi/4)*oo) == exp(I*pi/4)*oo | |
| assert ceiling(2*I) == 2*I | |
| assert ceiling(-2*I) == -2*I | |
| assert ceiling(I/2) == I | |
| assert ceiling(-I/2) == 0 | |
| assert ceiling(E + 17) == 20 | |
| assert ceiling(pi + 2) == 6 | |
| assert ceiling(E + pi) == 6 | |
| assert ceiling(I + pi) == I + 4 | |
| assert ceiling(ceiling(pi)) == 4 | |
| assert ceiling(ceiling(y)) == ceiling(y) | |
| assert ceiling(ceiling(x)) == ceiling(x) | |
| assert unchanged(ceiling, x) | |
| assert unchanged(ceiling, 2*x) | |
| assert unchanged(ceiling, k*x) | |
| assert ceiling(k) == k | |
| assert ceiling(2*k) == 2*k | |
| assert ceiling(k*n) == k*n | |
| assert unchanged(ceiling, k/2) | |
| assert unchanged(ceiling, x + y) | |
| assert ceiling(x + 3) == ceiling(x) + 3 | |
| assert ceiling(x + 3.0) == ceiling(x) + 3 | |
| assert ceiling(x + 3.0*I) == ceiling(x) + 3*I | |
| assert ceiling(x + k) == ceiling(x) + k | |
| assert ceiling(y + 3) == ceiling(y) + 3 | |
| assert ceiling(y + k) == ceiling(y) + k | |
| assert ceiling(3 + pi + y*I) == 7 + ceiling(y)*I | |
| assert ceiling(k + n) == k + n | |
| assert unchanged(ceiling, x*I) | |
| assert ceiling(k*I) == k*I | |
| assert ceiling(Rational(23, 10) - E*I) == 3 - 2*I | |
| assert ceiling(sin(1)) == 1 | |
| assert ceiling(sin(-1)) == 0 | |
| assert ceiling(exp(2)) == 8 | |
| assert ceiling(-log(8)/log(2)) != -2 | |
| assert int(ceiling(-log(8)/log(2)).evalf(chop=True)) == -3 | |
| assert ceiling(factorial(50)/exp(1)) == \ | |
| 11188719610782480504630258070757734324011354208865721592720336801 | |
| assert (ceiling(y) >= y) == True | |
| assert (ceiling(y) > y) == False | |
| assert (ceiling(y) < y) == False | |
| assert (ceiling(y) <= y) == False | |
| assert (ceiling(x) >= x).is_Relational # x could be non-real | |
| assert (ceiling(x) < x).is_Relational | |
| assert (ceiling(x) >= y).is_Relational # arg is not same as rhs | |
| assert (ceiling(x) < y).is_Relational | |
| assert (ceiling(y) >= -oo) == True | |
| assert (ceiling(y) > -oo) == True | |
| assert (ceiling(y) <= oo) == True | |
| assert (ceiling(y) < oo) == True | |
| assert ceiling(y).rewrite(floor) == -floor(-y) | |
| assert ceiling(y).rewrite(frac) == y + frac(-y) | |
| assert ceiling(y).rewrite(floor).subs(y, -pi) == -floor(pi) | |
| assert ceiling(y).rewrite(floor).subs(y, E) == -floor(-E) | |
| assert ceiling(y).rewrite(frac).subs(y, pi) == ceiling(pi) | |
| assert ceiling(y).rewrite(frac).subs(y, -E) == ceiling(-E) | |
| assert Eq(ceiling(y), y + frac(-y)) | |
| assert Eq(ceiling(y), -floor(-y)) | |
| neg = Symbol('neg', negative=True) | |
| nn = Symbol('nn', nonnegative=True) | |
| pos = Symbol('pos', positive=True) | |
| np = Symbol('np', nonpositive=True) | |
| assert (ceiling(neg) <= 0) == True | |
| assert (ceiling(neg) < 0) == (neg <= -1) | |
| assert (ceiling(neg) > 0) == False | |
| assert (ceiling(neg) >= 0) == (neg > -1) | |
| assert (ceiling(neg) > -3) == (neg > -3) | |
| assert (ceiling(neg) <= 10) == (neg <= 10) | |
| assert (ceiling(nn) < 0) == False | |
| assert (ceiling(nn) >= 0) == True | |
| assert (ceiling(pos) < 0) == False | |
| assert (ceiling(pos) <= 0) == False | |
| assert (ceiling(pos) > 0) == True | |
| assert (ceiling(pos) >= 0) == True | |
| assert (ceiling(pos) >= 1) == True | |
| assert (ceiling(pos) > 5) == (pos > 5) | |
| assert (ceiling(np) <= 0) == True | |
| assert (ceiling(np) > 0) == False | |
| assert ceiling(neg).is_positive == False | |
| assert ceiling(neg).is_nonpositive == True | |
| assert ceiling(nn).is_positive is None | |
| assert ceiling(nn).is_nonpositive is None | |
| assert ceiling(pos).is_positive == True | |
| assert ceiling(pos).is_nonpositive == False | |
| assert ceiling(np).is_positive == False | |
| assert ceiling(np).is_nonpositive == True | |
| assert (ceiling(7, evaluate=False) >= 7) == True | |
| assert (ceiling(7, evaluate=False) > 7) == False | |
| assert (ceiling(7, evaluate=False) <= 7) == True | |
| assert (ceiling(7, evaluate=False) < 7) == False | |
| assert (ceiling(7, evaluate=False) >= 6) == True | |
| assert (ceiling(7, evaluate=False) > 6) == True | |
| assert (ceiling(7, evaluate=False) <= 6) == False | |
| assert (ceiling(7, evaluate=False) < 6) == False | |
| assert (ceiling(7, evaluate=False) >= 8) == False | |
| assert (ceiling(7, evaluate=False) > 8) == False | |
| assert (ceiling(7, evaluate=False) <= 8) == True | |
| assert (ceiling(7, evaluate=False) < 8) == True | |
| assert (ceiling(x) <= 5.5) == Le(ceiling(x), 5.5, evaluate=False) | |
| assert (ceiling(x) >= -3.2) == Ge(ceiling(x), -3.2, evaluate=False) | |
| assert (ceiling(x) < 2.9) == Lt(ceiling(x), 2.9, evaluate=False) | |
| assert (ceiling(x) > -1.7) == Gt(ceiling(x), -1.7, evaluate=False) | |
| assert (ceiling(y) <= 5.5) == (y <= 5) | |
| assert (ceiling(y) >= -3.2) == (y > -4) | |
| assert (ceiling(y) < 2.9) == (y <= 2) | |
| assert (ceiling(y) > -1.7) == (y > -2) | |
| assert (ceiling(y) <= n) == (y <= n) | |
| assert (ceiling(y) >= n) == (y > n - 1) | |
| assert (ceiling(y) < n) == (y <= n - 1) | |
| assert (ceiling(y) > n) == (y > n) | |
| assert ceiling(RootOf(x**3 - 27*x, 2)) == 6 | |
| s = ImageSet(Lambda(n, n + (CRootOf(x**5 - x**2 + 1, 0))), Integers) | |
| f = CRootOf(x**5 - x**2 + 1, 0) | |
| s = ImageSet(Lambda(n, n + f), Integers) | |
| assert s.intersect(Interval(-10, 10)) == {i + f for i in range(-9, 11)} | |
| def test_frac(): | |
| assert isinstance(frac(x), frac) | |
| assert frac(oo) == AccumBounds(0, 1) | |
| assert frac(-oo) == AccumBounds(0, 1) | |
| assert frac(zoo) is nan | |
| assert frac(n) == 0 | |
| assert frac(nan) is nan | |
| assert frac(Rational(4, 3)) == Rational(1, 3) | |
| assert frac(-Rational(4, 3)) == Rational(2, 3) | |
| assert frac(Rational(-4, 3)) == Rational(2, 3) | |
| r = Symbol('r', real=True) | |
| assert frac(I*r) == I*frac(r) | |
| assert frac(1 + I*r) == I*frac(r) | |
| assert frac(0.5 + I*r) == 0.5 + I*frac(r) | |
| assert frac(n + I*r) == I*frac(r) | |
| assert frac(n + I*k) == 0 | |
| assert unchanged(frac, x + I*x) | |
| assert frac(x + I*n) == frac(x) | |
| assert frac(x).rewrite(floor) == x - floor(x) | |
| assert frac(x).rewrite(ceiling) == x + ceiling(-x) | |
| assert frac(y).rewrite(floor).subs(y, pi) == frac(pi) | |
| assert frac(y).rewrite(floor).subs(y, -E) == frac(-E) | |
| assert frac(y).rewrite(ceiling).subs(y, -pi) == frac(-pi) | |
| assert frac(y).rewrite(ceiling).subs(y, E) == frac(E) | |
| assert Eq(frac(y), y - floor(y)) | |
| assert Eq(frac(y), y + ceiling(-y)) | |
| r = Symbol('r', real=True) | |
| p_i = Symbol('p_i', integer=True, positive=True) | |
| n_i = Symbol('p_i', integer=True, negative=True) | |
| np_i = Symbol('np_i', integer=True, nonpositive=True) | |
| nn_i = Symbol('nn_i', integer=True, nonnegative=True) | |
| p_r = Symbol('p_r', positive=True) | |
| n_r = Symbol('n_r', negative=True) | |
| np_r = Symbol('np_r', real=True, nonpositive=True) | |
| nn_r = Symbol('nn_r', real=True, nonnegative=True) | |
| # Real frac argument, integer rhs | |
| assert frac(r) <= p_i | |
| assert not frac(r) <= n_i | |
| assert (frac(r) <= np_i).has(Le) | |
| assert (frac(r) <= nn_i).has(Le) | |
| assert frac(r) < p_i | |
| assert not frac(r) < n_i | |
| assert not frac(r) < np_i | |
| assert (frac(r) < nn_i).has(Lt) | |
| assert not frac(r) >= p_i | |
| assert frac(r) >= n_i | |
| assert frac(r) >= np_i | |
| assert (frac(r) >= nn_i).has(Ge) | |
| assert not frac(r) > p_i | |
| assert frac(r) > n_i | |
| assert (frac(r) > np_i).has(Gt) | |
| assert (frac(r) > nn_i).has(Gt) | |
| assert not Eq(frac(r), p_i) | |
| assert not Eq(frac(r), n_i) | |
| assert Eq(frac(r), np_i).has(Eq) | |
| assert Eq(frac(r), nn_i).has(Eq) | |
| assert Ne(frac(r), p_i) | |
| assert Ne(frac(r), n_i) | |
| assert Ne(frac(r), np_i).has(Ne) | |
| assert Ne(frac(r), nn_i).has(Ne) | |
| # Real frac argument, real rhs | |
| assert (frac(r) <= p_r).has(Le) | |
| assert not frac(r) <= n_r | |
| assert (frac(r) <= np_r).has(Le) | |
| assert (frac(r) <= nn_r).has(Le) | |
| assert (frac(r) < p_r).has(Lt) | |
| assert not frac(r) < n_r | |
| assert not frac(r) < np_r | |
| assert (frac(r) < nn_r).has(Lt) | |
| assert (frac(r) >= p_r).has(Ge) | |
| assert frac(r) >= n_r | |
| assert frac(r) >= np_r | |
| assert (frac(r) >= nn_r).has(Ge) | |
| assert (frac(r) > p_r).has(Gt) | |
| assert frac(r) > n_r | |
| assert (frac(r) > np_r).has(Gt) | |
| assert (frac(r) > nn_r).has(Gt) | |
| assert not Eq(frac(r), n_r) | |
| assert Eq(frac(r), p_r).has(Eq) | |
| assert Eq(frac(r), np_r).has(Eq) | |
| assert Eq(frac(r), nn_r).has(Eq) | |
| assert Ne(frac(r), p_r).has(Ne) | |
| assert Ne(frac(r), n_r) | |
| assert Ne(frac(r), np_r).has(Ne) | |
| assert Ne(frac(r), nn_r).has(Ne) | |
| # Real frac argument, +/- oo rhs | |
| assert frac(r) < oo | |
| assert frac(r) <= oo | |
| assert not frac(r) > oo | |
| assert not frac(r) >= oo | |
| assert not frac(r) < -oo | |
| assert not frac(r) <= -oo | |
| assert frac(r) > -oo | |
| assert frac(r) >= -oo | |
| assert frac(r) < 1 | |
| assert frac(r) <= 1 | |
| assert not frac(r) > 1 | |
| assert not frac(r) >= 1 | |
| assert not frac(r) < 0 | |
| assert (frac(r) <= 0).has(Le) | |
| assert (frac(r) > 0).has(Gt) | |
| assert frac(r) >= 0 | |
| # Some test for numbers | |
| assert frac(r) <= sqrt(2) | |
| assert (frac(r) <= sqrt(3) - sqrt(2)).has(Le) | |
| assert not frac(r) <= sqrt(2) - sqrt(3) | |
| assert not frac(r) >= sqrt(2) | |
| assert (frac(r) >= sqrt(3) - sqrt(2)).has(Ge) | |
| assert frac(r) >= sqrt(2) - sqrt(3) | |
| assert not Eq(frac(r), sqrt(2)) | |
| assert Eq(frac(r), sqrt(3) - sqrt(2)).has(Eq) | |
| assert not Eq(frac(r), sqrt(2) - sqrt(3)) | |
| assert Ne(frac(r), sqrt(2)) | |
| assert Ne(frac(r), sqrt(3) - sqrt(2)).has(Ne) | |
| assert Ne(frac(r), sqrt(2) - sqrt(3)) | |
| assert frac(p_i, evaluate=False).is_zero | |
| assert frac(p_i, evaluate=False).is_finite | |
| assert frac(p_i, evaluate=False).is_integer | |
| assert frac(p_i, evaluate=False).is_real | |
| assert frac(r).is_finite | |
| assert frac(r).is_real | |
| assert frac(r).is_zero is None | |
| assert frac(r).is_integer is None | |
| assert frac(oo).is_finite | |
| assert frac(oo).is_real | |
| def test_series(): | |
| x, y = symbols('x,y') | |
| assert floor(x).nseries(x, y, 100) == floor(y) | |
| assert ceiling(x).nseries(x, y, 100) == ceiling(y) | |
| assert floor(x).nseries(x, pi, 100) == 3 | |
| assert ceiling(x).nseries(x, pi, 100) == 4 | |
| assert floor(x).nseries(x, 0, 100) == 0 | |
| assert ceiling(x).nseries(x, 0, 100) == 1 | |
| assert floor(-x).nseries(x, 0, 100) == -1 | |
| assert ceiling(-x).nseries(x, 0, 100) == 0 | |
| def test_issue_14355(): | |
| # This test checks the leading term and series for the floor and ceil | |
| # function when arg0 evaluates to S.NaN. | |
| assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -2 | |
| assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == -1 | |
| assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == -1 | |
| assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 0 | |
| assert floor(sin(x)/x).as_leading_term(x, cdir = 1) == 0 | |
| assert floor(sin(x)/x).as_leading_term(x, cdir = -1) == 0 | |
| assert floor(-tan(x)/x).as_leading_term(x, cdir = 1) == -2 | |
| assert floor(-tan(x)/x).as_leading_term(x, cdir = -1) == -2 | |
| assert floor(sin(x)/x/3).as_leading_term(x, cdir = 1) == 0 | |
| assert floor(sin(x)/x/3).as_leading_term(x, cdir = -1) == 0 | |
| assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -1 | |
| assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == 0 | |
| assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == 0 | |
| assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 1 | |
| assert ceiling(sin(x)/x).as_leading_term(x, cdir = 1) == 1 | |
| assert ceiling(sin(x)/x).as_leading_term(x, cdir = -1) == 1 | |
| assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1 | |
| assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1 | |
| assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = 1) == 1 | |
| assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = -1) == 1 | |
| # test for series | |
| assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0 | |
| assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0 | |
| assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -2 | |
| assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == -1 | |
| assert ceiling(sin(x)/x).series(x, 0, 100, cdir = 1) == 1 | |
| assert ceiling(sin(x)/x).series(x, 0, 100, cdir = -1) == 1 | |
| assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -1 | |
| assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == 0 | |
| def test_frac_leading_term(): | |
| assert frac(x).as_leading_term(x) == x | |
| assert frac(x).as_leading_term(x, cdir = 1) == x | |
| assert frac(x).as_leading_term(x, cdir = -1) == 1 | |
| assert frac(x + S.Half).as_leading_term(x, cdir = 1) == S.Half | |
| assert frac(x + S.Half).as_leading_term(x, cdir = -1) == S.Half | |
| assert frac(-2*x + 1).as_leading_term(x, cdir = 1) == S.One | |
| assert frac(-2*x + 1).as_leading_term(x, cdir = -1) == -2*x | |
| assert frac(sin(x) + 5).as_leading_term(x, cdir = 1) == x | |
| assert frac(sin(x) + 5).as_leading_term(x, cdir = -1) == S.One | |
| assert frac(sin(x**2) + 5).as_leading_term(x, cdir = 1) == x**2 | |
| assert frac(sin(x**2) + 5).as_leading_term(x, cdir = -1) == x**2 | |
| def test_issue_4149(): | |
| assert floor(3 + pi*I + y*I) == 3 + floor(pi + y)*I | |
| assert floor(3*I + pi*I + y*I) == floor(3 + pi + y)*I | |
| assert floor(3 + E + pi*I + y*I) == 5 + floor(pi + y)*I | |
| def test_issue_21651(): | |
| k = Symbol('k', positive=True, integer=True) | |
| exp = 2*2**(-k) | |
| assert isinstance(floor(exp), floor) | |
| def test_issue_11207(): | |
| assert floor(floor(x)) == floor(x) | |
| assert floor(ceiling(x)) == ceiling(x) | |
| assert ceiling(floor(x)) == floor(x) | |
| assert ceiling(ceiling(x)) == ceiling(x) | |
| def test_nested_floor_ceiling(): | |
| assert floor(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y) | |
| assert ceiling(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y) | |
| assert floor(ceiling(-floor(x**Rational(7, 2)/y))) == -floor(x**Rational(7, 2)/y) | |
| assert -ceiling(-ceiling(floor(x)/y)) == ceiling(floor(x)/y) | |
| def test_issue_18689(): | |
| assert floor(floor(floor(x)) + 3) == floor(x) + 3 | |
| assert ceiling(ceiling(ceiling(x)) + 1) == ceiling(x) + 1 | |
| assert ceiling(ceiling(floor(x)) + 3) == floor(x) + 3 | |
| def test_issue_18421(): | |
| assert floor(float(0)) is S.Zero | |
| assert ceiling(float(0)) is S.Zero | |
| def test_issue_25230(): | |
| a = Symbol('a', real = True) | |
| b = Symbol('b', positive = True) | |
| c = Symbol('c', negative = True) | |
| raises(NotImplementedError, lambda: floor(x/a).as_leading_term(x, cdir = 1)) | |
| raises(NotImplementedError, lambda: ceiling(x/a).as_leading_term(x, cdir = 1)) | |
| assert floor(x/b).as_leading_term(x, cdir = 1) == 0 | |
| assert floor(x/b).as_leading_term(x, cdir = -1) == -1 | |
| assert floor(x/c).as_leading_term(x, cdir = 1) == -1 | |
| assert floor(x/c).as_leading_term(x, cdir = -1) == 0 | |
| assert ceiling(x/b).as_leading_term(x, cdir = 1) == 1 | |
| assert ceiling(x/b).as_leading_term(x, cdir = -1) == 0 | |
| assert ceiling(x/c).as_leading_term(x, cdir = 1) == 0 | |
| assert ceiling(x/c).as_leading_term(x, cdir = -1) == 1 | |