functions: add wrt kwarg for rewrite() helpers, use for Abs

diofant/core/basic.py

@@ -1074,7 +1074,7 @@ def _eval_rewrite(self, pattern, rule, **hints):
 
         if pattern is None or isinstance(self, pattern):
             if hasattr(self, rule):
-                rewritten = getattr(self, rule)(*args)
+                rewritten = getattr(self, rule)(*args, **hints)
                 if rewritten is not None:
                     return rewritten
         return self.func(*args)

diofant/functions/combinatorial/factorials.py

@@ -92,7 +92,7 @@ def _eval_rewrite_as_gamma(self, n):
         from .. import gamma
         return gamma(n + 1)
 
-    def _eval_rewrite_as_tractable(self, n):
+    def _eval_rewrite_as_tractable(self, n, **kwargs):
         from .. import exp, loggamma
         return exp(loggamma(n + 1))
 
@@ -350,7 +350,7 @@ def _eval_rewrite_as_gamma(self, x, k):
         from .. import gamma
         return gamma(x + k) / gamma(x)
 
-    def _eval_rewrite_as_tractable(self, x, k):
+    def _eval_rewrite_as_tractable(self, x, k, **kwargs):
         return self._eval_rewrite_as_gamma(x, k).rewrite('tractable')
 
     def _eval_is_integer(self):
@@ -554,14 +554,14 @@ def _eval_expand_func(self, **hints):
 
         return self.func(*self.args)
 
-    def _eval_rewrite_as_factorial(self, n, k):
+    def _eval_rewrite_as_factorial(self, n, k, **kwargs):
         return factorial(n)/(factorial(k)*factorial(n - k))
 
     def _eval_rewrite_as_gamma(self, n, k):
         from .. import gamma
         return gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1))
 
-    def _eval_rewrite_as_tractable(self, n, k):
+    def _eval_rewrite_as_tractable(self, n, k, **kwargs):
         return self._eval_rewrite_as_gamma(n, k).rewrite('tractable')
 
     def _eval_is_integer(self):

diofant/functions/combinatorial/numbers.py

@@ -112,11 +112,10 @@ def eval(cls, n, sym=None):
                                      'only for positive integer indices.')
                 return cls._fibpoly(n).subs({_sym: sym})
 
-    def _eval_rewrite_as_sqrt(self, n, sym=None):
+    def _eval_rewrite_as_sqrt(self, n, sym=None, **kwargs):
         from .. import sqrt
         if sym is None:
             return (GoldenRatio**n - cos(pi*n)/GoldenRatio**n)/sqrt(5)
-
     _eval_rewrite_as_tractable = _eval_rewrite_as_sqrt
 
 
@@ -672,7 +671,7 @@ def _eval_expand_func(self, **hints):
 
         return self
 
-    def _eval_rewrite_as_tractable(self, n, m=1):
+    def _eval_rewrite_as_tractable(self, n, m=1, **kwargs):
         from .. import polygamma
         return self.rewrite(polygamma).rewrite('tractable', deep=True)
 

diofant/functions/elementary/complexes.py

@@ -526,6 +526,10 @@ def _eval_rewrite_as_Piecewise(self, arg):
     def _eval_rewrite_as_sign(self, arg):
         return arg/sign(arg)
 
+    def _eval_rewrite_as_tractable(self, arg, wrt=None, **kwargs):
+        if (s := sign(arg.limit(wrt, oo))) in (1, -1):
+            return s*arg
+
 
 class arg(Function):
     """Returns the argument (in radians) of a complex number.

diofant/functions/elementary/hyperbolic.py

@@ -148,7 +148,7 @@ def _eval_expand_trig(self, **hints):
             return (sinh(x)*cosh(y) + sinh(y)*cosh(x)).expand(trig=True)
         return sinh(arg)
 
-    def _eval_rewrite_as_exp(self, arg):
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
         return (exp(arg) - exp(-arg)) / 2
     _eval_rewrite_as_tractable = _eval_rewrite_as_exp
 
@@ -288,7 +288,7 @@ def _eval_expand_trig(self, deep=True, **hints):
             return (cosh(x)*cosh(y) + sinh(x)*sinh(y)).expand(trig=True)
         return cosh(arg)
 
-    def _eval_rewrite_as_exp(self, arg):
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
         return (exp(arg) + exp(-arg)) / 2
     _eval_rewrite_as_tractable = _eval_rewrite_as_exp
 
@@ -421,7 +421,7 @@ def as_real_imag(self, deep=True, **hints):
         denom = sinh(re)**2 + cos(im)**2
         return sinh(re)*cosh(re)/denom, sin(im)*cos(im)/denom
 
-    def _eval_rewrite_as_exp(self, arg):
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
         neg_exp, pos_exp = exp(-arg), exp(arg)
         return (pos_exp - neg_exp)/(pos_exp + neg_exp)
     _eval_rewrite_as_tractable = _eval_rewrite_as_exp
@@ -546,7 +546,7 @@ def as_real_imag(self, deep=True, **hints):
         denom = sinh(re)**2 + sin(im)**2
         return sinh(re)*cosh(re)/denom, -sin(im)*cos(im)/denom
 
-    def _eval_rewrite_as_exp(self, arg):
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
         neg_exp, pos_exp = exp(-arg), exp(arg)
         return (pos_exp + neg_exp)/(pos_exp - neg_exp)
     _eval_rewrite_as_tractable = _eval_rewrite_as_exp
@@ -904,7 +904,7 @@ def inverse(self, argindex=1):
         """Returns the inverse of this function."""
         return cosh
 
-    def _eval_rewrite_as_log(self, x):
+    def _eval_rewrite_as_log(self, x, **hints):
         return log(x + sqrt(x - 1)*sqrt(x + 1))
     _eval_rewrite_as_tractable = _eval_rewrite_as_log
 
@@ -1054,7 +1054,7 @@ def _eval_as_leading_term(self, x):
         else:
             return self.func(arg)
 
-    def _eval_rewrite_as_log(self, x):
+    def _eval_rewrite_as_log(self, x, **kwargs):
         return (log((x + 1)/x) - log((x - 1)/x))/2
     _eval_rewrite_as_tractable = _eval_rewrite_as_log
 

diofant/functions/special/bessel.py

@@ -878,7 +878,7 @@ def _eval_rewrite_as_hyper(self, z):
         pf2 = z / (root(3, 3)*gamma(Rational(1, 3)))
         return pf1 * hyper([], [Rational(2, 3)], z**3/9) - pf2 * hyper([], [Rational(4, 3)], z**3/9)
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return exp(-Rational(2, 3)*z**Rational(3, 2))*sqrt(pi*sqrt(z))/2*_airyais(z)
 
     def _eval_expand_func(self, **hints):
@@ -1036,7 +1036,7 @@ def _eval_rewrite_as_hyper(self, z):
         pf2 = z*root(3, 6) / gamma(Rational(1, 3))
         return pf1 * hyper([], [Rational(2, 3)], z**3/9) + pf2 * hyper([], [Rational(4, 3)], z**3/9)
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return exp(Rational(2, 3)*z**Rational(3, 2))*sqrt(pi*sqrt(z))*_airybis(z)
 
     def _eval_expand_func(self, **hints):
@@ -1065,7 +1065,7 @@ def _eval_expand_func(self, **hints):
 
 
 class _airyais(Function):
-    def _eval_rewrite_as_intractable(self, x):
+    def _eval_rewrite_as_intractable(self, x, **kwargs):
         return 2*airyai(x)*exp(Rational(2, 3)*x**Rational(3, 2))/sqrt(pi*sqrt(x))
 
     def _eval_aseries(self, n, args0, x, logx):
@@ -1094,7 +1094,7 @@ def _eval_nseries(self, x, n, logx):
 
 
 class _airybis(Function):
-    def _eval_rewrite_as_intractable(self, x):
+    def _eval_rewrite_as_intractable(self, x, **kwargs):
         return airybi(x)*exp(-Rational(2, 3)*x**Rational(3, 2))/sqrt(pi*sqrt(x))
 
     def _eval_aseries(self, n, args0, x, logx):

diofant/functions/special/error_functions.py

@@ -172,7 +172,7 @@ def _eval_rewrite_as_hyper(self, z):
     def _eval_rewrite_as_expint(self, z):
         return sqrt(z**2)/z - z*expint(Rational(1, 2), z**2)/sqrt(pi)
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return 1 - _erfs(z)*exp(-z**2)
 
     def _eval_rewrite_as_erfc(self, z):
@@ -339,7 +339,7 @@ def _eval_is_extended_real(self):
         elif arg.is_imaginary and arg.is_nonzero:
             return False
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return self.rewrite(erf).rewrite('tractable', deep=True)
 
     def _eval_rewrite_as_erf(self, z):
@@ -517,7 +517,7 @@ def _eval_is_extended_real(self):
         elif arg.is_imaginary and arg.is_nonzero:
             return False
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return self.rewrite(erf).rewrite('tractable', deep=True)
 
     def _eval_rewrite_as_erf(self, z):
@@ -1054,7 +1054,7 @@ def _eval_rewrite_as_uppergamma(self, z):
         #     immediately turns into expint
         return -uppergamma(0, polar_lift(-1)*z) - I*pi
 
-    def _eval_rewrite_as_expint(self, z):
+    def _eval_rewrite_as_expint(self, z, **kwargs):
         return -expint(1, polar_lift(-1)*z) - I*pi
 
     def _eval_rewrite_as_li(self, z):
@@ -1072,7 +1072,7 @@ def _eval_rewrite_as_Si(self, z):
     _eval_rewrite_as_Chi = _eval_rewrite_as_Si
     _eval_rewrite_as_Shi = _eval_rewrite_as_Si
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return exp(z) * _eis(z)
 
     def _eval_nseries(self, x, n, logx):
@@ -1404,7 +1404,7 @@ def _eval_rewrite_as_meijerg(self, z):
         return (-log(-log(z)) - (log(1/log(z)) - log(log(z)))/2
                 - meijerg(((), (1,)), ((0, 0), ()), -log(z)))
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return z * _eis(log(z))
 
 
@@ -1484,7 +1484,7 @@ def _eval_evalf(self, prec):
     def _eval_rewrite_as_li(self, z):
         return li(z) - li(2)
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return self.rewrite(li).rewrite('tractable', deep=True)
 
 ###############################################################################

diofant/functions/special/gamma_functions.py

@@ -162,7 +162,7 @@ def _eval_is_positive(self):
         elif x.is_noninteger:
             return floor(x).is_even
 
-    def _eval_rewrite_as_tractable(self, z):
+    def _eval_rewrite_as_tractable(self, z, **kwargs):
         return exp(loggamma(z))
 
     def _eval_rewrite_as_factorial(self, z):
@@ -316,7 +316,7 @@ def _eval_conjugate(self):
     def _eval_rewrite_as_uppergamma(self, s, x):
         return gamma(s) - uppergamma(s, x)
 
-    def _eval_rewrite_as_tractable(self, s, x):
+    def _eval_rewrite_as_tractable(self, s, x, **kwargs):
         return self.rewrite(uppergamma)
 
     def _eval_rewrite_as_expint(self, s, x):
@@ -878,7 +878,7 @@ def _eval_aseries(self, n, args0, x, logx):
         # It is very inefficient to first add the order and then do the nseries
         return (r + Add(*l))._eval_nseries(x, n, logx) + o
 
-    def _eval_rewrite_as_intractable(self, z):
+    def _eval_rewrite_as_intractable(self, z, **kwargs):
         return log(gamma(z))
 
     def _eval_is_extended_real(self):

diofant/functions/special/zeta_functions.py

@@ -461,13 +461,13 @@ def fdiff(self, argindex=1):
         else:
             raise ArgumentIndexError
 
-    def _eval_rewrite_as_tractable(self, s, a=1):
+    def _eval_rewrite_as_tractable(self, s, a=1, **kwargs):
         if len(self.args) == 1:
             return _zetas(exp(s))
 
 
 class _zetas(Function):
-    def _eval_rewrite_as_intractable(self, s):
+    def _eval_rewrite_as_intractable(self, s, **kwargs):
         return zeta(log(s))
 
     def _eval_aseries(self, n, args0, x, logx):

diofant/series/gruntz.py

@@ -202,7 +202,7 @@ def limitinf(e, x):
     assert not e.has(Float)
 
     # Rewrite e in terms of tractable functions only:
-    e = e.rewrite('tractable', deep=True)
+    e = e.rewrite('tractable', deep=True, wrt=x)
 
     if not e.has(x):
         # This is a bit of a heuristic for nice results.  We always rewrite

diofant/series/limits.py

@@ -1,6 +1,6 @@
 from ..core import Dummy, Expr, Float, PoleError, Rational, nan, oo, sympify
 from ..core.function import UndefinedFunction
-from ..functions import Abs, cos, sign, sin
+from ..functions import cos, sign, sin
 from ..sets import Reals
 from .gruntz import limitinf
 from .order import Order
@@ -173,10 +173,6 @@ def doit(self, **hints):
                 return has_oo
             raise NotImplementedError
 
-        def tr_abs(f):
-            s = sign(limit(f.args[0], z, oo))
-            return s*f.args[0] if s in (1, -1) else f
-
         def tr_Piecewise(f):
             for a, c in f.args:
                 if not c.is_Atom:
@@ -188,7 +184,6 @@ def tr_Piecewise(f):
                         break
             return a
 
-        e = e.replace(lambda f: isinstance(f, Abs) and f.has(z), tr_abs)
         e = e.replace(lambda f: f.is_Piecewise and f.has(z), tr_Piecewise)
 
         try: