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############################################
# Copyright (c) 2013 Microsoft Corporation
#
# Z3 Python interface for Z3 Real Closed Fields
# that may contain
# - computable transcendentals
# - infinitesimals
# - algebraic extensions
#
# Author: Leonardo de Moura (leonardo)
############################################
from .z3 import *
from .z3core import *
from .z3printer import *
from fractions import Fraction
def _to_rcfnum(num, ctx=None):
if isinstance(num, RCFNum):
return num
else:
return RCFNum(num, ctx)
def Pi(ctx=None):
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_pi(ctx.ref()), ctx)
def E(ctx=None):
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_e(ctx.ref()), ctx)
def MkInfinitesimal(name="eps", ctx=None):
# Todo: remove parameter name.
# For now, we keep it for backward compatibility.
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_infinitesimal(ctx.ref()), ctx)
def MkRoots(p, ctx=None):
ctx = z3._get_ctx(ctx)
num = len(p)
_tmp = []
_as = (RCFNumObj * num)()
_rs = (RCFNumObj * num)()
for i in range(num):
_a = _to_rcfnum(p[i], ctx)
_tmp.append(_a) # prevent GC
_as[i] = _a.num
nr = Z3_rcf_mk_roots(ctx.ref(), num, _as, _rs)
r = []
for i in range(nr):
r.append(RCFNum(_rs[i], ctx))
return r
class RCFNum:
def __init__(self, num, ctx=None):
# TODO: add support for converting AST numeral values into RCFNum
if isinstance(num, RCFNumObj):
self.num = num
self.ctx = z3._get_ctx(ctx)
else:
self.ctx = z3._get_ctx(ctx)
self.num = Z3_rcf_mk_rational(self.ctx_ref(), str(num))
def __del__(self):
Z3_rcf_del(self.ctx_ref(), self.num)
def ctx_ref(self):
return self.ctx.ref()
def __repr__(self):
return Z3_rcf_num_to_string(self.ctx_ref(), self.num, False, in_html_mode())
def compact_str(self):
return Z3_rcf_num_to_string(self.ctx_ref(), self.num, True, in_html_mode())
def __add__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_add(self.ctx_ref(), self.num, v.num), self.ctx)
def __radd__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_add(self.ctx_ref(), v.num, self.num), self.ctx)
def __mul__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_mul(self.ctx_ref(), self.num, v.num), self.ctx)
def __rmul__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_mul(self.ctx_ref(), v.num, self.num), self.ctx)
def __sub__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_sub(self.ctx_ref(), self.num, v.num), self.ctx)
def __rsub__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_sub(self.ctx_ref(), v.num, self.num), self.ctx)
def __div__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_div(self.ctx_ref(), self.num, v.num), self.ctx)
def __rdiv__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_div(self.ctx_ref(), v.num, self.num), self.ctx)
def __neg__(self):
return self.__rsub__(0)
def power(self, k):
return RCFNum(Z3_rcf_power(self.ctx_ref(), self.num, k), self.ctx)
def __pow__(self, k):
return self.power(k)
def decimal(self, prec=5):
return Z3_rcf_num_to_decimal_string(self.ctx_ref(), self.num, prec)
def __lt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_lt(self.ctx_ref(), self.num, v.num)
def __rlt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_lt(self.ctx_ref(), v.num, self.num)
def __gt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_gt(self.ctx_ref(), self.num, v.num)
def __rgt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_gt(self.ctx_ref(), v.num, self.num)
def __le__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_le(self.ctx_ref(), self.num, v.num)
def __rle__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_le(self.ctx_ref(), v.num, self.num)
def __ge__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_ge(self.ctx_ref(), self.num, v.num)
def __rge__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_ge(self.ctx_ref(), v.num, self.num)
def __eq__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_eq(self.ctx_ref(), self.num, v.num)
def __ne__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_neq(self.ctx_ref(), self.num, v.num)
def split(self):
n = (RCFNumObj * 1)()
d = (RCFNumObj * 1)()
Z3_rcf_get_numerator_denominator(self.ctx_ref(), self.num, n, d)
return (RCFNum(n[0], self.ctx), RCFNum(d[0], self.ctx))
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