functions: set default value for Piecewise to nan if not provided

diofant/functions/elementary/piecewise.py

@@ -1,5 +1,5 @@
 from ...core import (Basic, Dummy, Equality, Expr, Function, Integer, Tuple,
-                     diff, oo)
+                     diff, nan, oo)
 from ...core.relational import Relational
 from ...logic import And, Not, Or, false, to_cnf, true
 from ...logic.boolalg import Boolean
@@ -81,6 +81,9 @@ def __new__(cls, *args, **options):
             if cond == true:
                 break
 
+        if cond != true:
+            newargs.append(ExprCondPair(nan, true))
+
         if options.pop('evaluate', True):
             r = cls.eval(*newargs)
         else:
@@ -517,9 +520,9 @@ def piecewise_fold(expr):
     Examples
     ========
 
-    >>> p = Piecewise((x, x < 1), (1, x >= 1))
+    >>> p = Piecewise((x, x < 1), (1, True))
     >>> piecewise_fold(x*p)
-    Piecewise((x**2, x < 1), (x, x >= 1))
+    Piecewise((x**2, x < 1), (x, true))
 
     See Also
     ========

diofant/tests/functions/test_piecewise.py

@@ -3,8 +3,8 @@
 from diofant import (And, Basic, Eq, Function, Gt, I, Integral, Interval, Max,
                      Min, Not, O, Or, Piecewise, Rational, Symbol, adjoint,
                      conjugate, cos, diff, exp, expand, integrate, lambdify,
-                     log, oo, pi, piecewise_fold, sin, solve, symbols, sympify,
-                     transpose)
+                     log, nan, oo, pi, piecewise_fold, sin, solve, symbols,
+                     sympify, transpose)
 from diofant.abc import a, t, x, y
 
 
@@ -14,7 +14,6 @@
 
 
 def test_piecewise():
-
     # Test canonization
     assert Piecewise((x, x < 1), (0, True)) == Piecewise((x, x < 1), (0, True))
     assert Piecewise((x, x < 1), (0, True), (1, True)) == \
@@ -34,8 +33,8 @@ def test_piecewise():
     assert Piecewise((0, Eq(z, 0, evaluate=False)), (1, True)) == 1
 
     # Test subs
-    p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >= 0))
-    p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >= 0))
+    p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), True))
+    p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), True))
     assert p.subs({x: x**2}) == p_x2
     assert p.subs({x: -5}) == -1
     assert p.subs({x: -1}) == 1
@@ -81,7 +80,7 @@ def test_piecewise():
     # Test differentiation
     f = x
     fp = x*p
-    dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, x >= 0))
+    dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, True))
     fp_dx = x*dp + p
     assert diff(p, x) == dp
     assert diff(f*p, x) == fp_dx
@@ -94,7 +93,7 @@ def test_piecewise():
     assert p - dp == -(dp - p)
 
     # Test power
-    dp2 = Piecewise((0, x < -1), (4*x**2, x < 0), (1/x**2, x >= 0))
+    dp2 = Piecewise((0, x < -1), (4*x**2, x < 0), (1/x**2, True))
     assert dp**2 == dp2
 
     # Test _eval_interval
@@ -119,15 +118,15 @@ def test_piecewise():
     assert peval4._eval_interval(x, -1, 1) == 2
 
     # Test integration
-    p_int = Piecewise((-x, x < -1), (x**3/3.0, x < 0), (-x + x*log(x), x >= 0))
+    p_int = Piecewise((-x, x < -1), (x**3/3.0, x < 0), (-x + x*log(x), True))
     assert integrate(p, x) == p_int
     p = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
     assert integrate(p, (x, -2, 2)) == 5.0/6.0
     assert integrate(p, (x, 2, -2)) == -5.0/6.0
     p = Piecewise((0, x < 0), (1, x < 1), (0, x < 2), (1, x < 3), (0, True))
     assert integrate(p, (x, -oo, oo)) == 2
     p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
-    pytest.raises(ValueError, lambda: integrate(p, (x, -2, 2)))
+    assert integrate(p, (x, -2, 2)) is nan
 
     # Test commutativity
     assert p.is_commutative is True
@@ -446,8 +445,8 @@ def test_piecewise_as_leading_term():
 
 
 def test_piecewise_complex():
-    p1 = Piecewise((2, x < 0), (1, 0 <= x))
-    p2 = Piecewise((2*I, x < 0), (I, 0 <= x))
+    p1 = Piecewise((2, x < 0), (1, True))
+    p2 = Piecewise((2*I, x < 0), (I, True))
     p3 = Piecewise((I*x, x > 1), (1 + I, True))
     p4 = Piecewise((-I*conjugate(x), x > 1), (1 - I, True))
 
@@ -487,7 +486,7 @@ def test_piecewise_evaluate():
 
 
 def test_as_expr_set_pairs():
-    assert Piecewise((x, x > 0), (-x, x <= 0)).as_expr_set_pairs() == \
+    assert Piecewise((x, x > 0), (-x, True)).as_expr_set_pairs() == \
         [(x, Interval(0, oo, True)), (-x, Interval(-oo, 0))]
 
     assert Piecewise(((x - 2)**2, x >= 0), (0, True)).as_expr_set_pairs() == \

diofant/tests/printing/test_ccode.py

@@ -181,9 +181,6 @@ def test_ccode_Piecewise():
         'else {\n'
         '   c = pow(x, 2);\n'
         '}')
-    # Check that Piecewise without a True (default) condition error
-    expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
-    pytest.raises(ValueError, lambda: ccode(expr))
 
 
 def test_ccode_Piecewise_deep():

diofant/tests/printing/test_fcode.py

@@ -379,9 +379,6 @@ def test_fcode_Piecewise():
     code = fcode(Piecewise((x, x < 1), (x**2, x > 1), (sin(x), True)), standard=95)
     expected = '      merge(x, merge(x**2, sin(x), x > 1), x < 1)'
     assert code == expected
-    # Check that Piecewise without a True (default) condition error
-    expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
-    pytest.raises(ValueError, lambda: fcode(expr))
 
     assert (fcode(Piecewise((0, x < -1), (1, And(x >= -1, x < 0)),
                             (-1, True)), assign_to='var') ==

diofant/tests/printing/test_lambdarepr.py

@@ -45,7 +45,7 @@ def test_piecewise():
     p = Piecewise((x, x < 0))
     l = lambdarepr(p)
     eval(h + l)  # pylint: disable=eval-used
-    assert l == '((x) if (x < 0) else None)'
+    assert l == '((x) if (x < 0) else (((nan) if (True) else None)))'
 
     p = Piecewise(
         (1, x < 1),
@@ -63,7 +63,7 @@ def test_piecewise():
     )
     l = lambdarepr(p)
     eval(h + l)  # pylint: disable=eval-used
-    assert l == '((1) if (x < 1) else (((2) if (x < 2) else None)))'
+    assert l == '((1) if (x < 1) else (((2) if (x < 2) else (((nan) if (True) else None)))))'
 
     p = Piecewise(
         (x, x < 1),
@@ -93,8 +93,8 @@ def test_piecewise():
     )
     l = lambdarepr(p)
     eval(h + l)  # pylint: disable=eval-used
-    assert l == '((x**2) if (x < 0) else (((x) if (((x >= 0) and ' \
-        '(x < 1))) else (((-x + 2) if (x >= 1) else None)))))'
+    assert l == ('((x**2) if (x < 0) else (((x) if (((x >= 0) and (x < 1))) '
+                 'else (((-x + 2) if (x >= 1) else (((nan) if (True) else None)))))))')
 
     p = Piecewise(
         (1, x >= 1),

diofant/tests/printing/test_latex.py

@@ -813,8 +813,8 @@ def test_latex_Piecewise():
     assert latex(p, itex=True) == r'\begin{cases} x & \text{for}\: x \lt 1 \\x^{2} &' \
                                   r' \text{otherwise} \end{cases}'
     p = Piecewise((x, x < 0), (0, x >= 0))
-    assert latex(p) == r'\begin{cases} x & \text{for}\: x < 0 \\0 &' \
-                       r' \text{for}\: x \geq 0 \end{cases}'
+    assert latex(p) == r'\begin{cases} x & \text{for}\: x < 0 \\0 & '\
+                       r'\text{for}\: x \geq 0 \\\mathrm{NaN} & \text{otherwise} \end{cases}'
     A, B = symbols('A B', commutative=False)
     p = Piecewise((A**2, Eq(A, B)), (A*B, True))
     s = r'\begin{cases} A^{2} & \text{for}\: A = B \\A B & \text{otherwise} \end{cases}'

diofant/tests/printing/test_octave.py

@@ -232,9 +232,6 @@ def test_octave_piecewise():
         'else\n'
         '  r = x.^5;\n'
         'end')
-    # Check that Piecewise without a True (default) condition error
-    expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
-    pytest.raises(ValueError, lambda: octave_code(expr))
 
 
 def test_octave_piecewise_times_const():

diofant/tests/solvers/test_inequalities.py

@@ -253,7 +253,7 @@ def test_reduce_piecewise_inequalities():
     # sympy/sympy#10255
     assert reduce_inequalities(Piecewise((1, x < 1), (3, True)) > 1) == \
         Le(1, x)
-    assert reduce_inequalities(Piecewise((x**2, x < 0), (2*x, x >= 0)) < 1) == \
+    assert reduce_inequalities(Piecewise((x**2, x < 0), (2*x, True)) < 1) == \
         And(Lt(-1, x), x < Rational(1, 2))
 
 

diofant/tests/test_wester.py

@@ -1716,8 +1716,8 @@ def test_U1():
 
 
 def test_U2():
-    f = Lambda(x, Piecewise((-x, x < 0), (x, x >= 0)))
-    assert diff(f(x), x) == Piecewise((-1, x < 0), (1, x >= 0))
+    f = Lambda(x, Piecewise((-x, x < 0), (x, True)))
+    assert diff(f(x), x) == Piecewise((-1, x < 0), (1, True))
 
 
 def test_U3():