Z3
Public Member Functions
AlgebraicNumRef Class Reference
+ Inheritance diagram for AlgebraicNumRef:

Public Member Functions

def approx (self, precision=10)
 
def as_decimal (self, prec)
 
def poly (self)
 
def index (self)
 
- Public Member Functions inherited from ArithRef
def sort (self)
 
def is_int (self)
 
def is_real (self)
 
def __add__ (self, other)
 
def __radd__ (self, other)
 
def __mul__ (self, other)
 
def __rmul__ (self, other)
 
def __sub__ (self, other)
 
def __rsub__ (self, other)
 
def __pow__ (self, other)
 
def __rpow__ (self, other)
 
def __div__ (self, other)
 
def __truediv__ (self, other)
 
def __rdiv__ (self, other)
 
def __rtruediv__ (self, other)
 
def __mod__ (self, other)
 
def __rmod__ (self, other)
 
def __neg__ (self)
 
def __pos__ (self)
 
def __le__ (self, other)
 
def __lt__ (self, other)
 
def __gt__ (self, other)
 
def __ge__ (self, other)
 
- Public Member Functions inherited from ExprRef
def as_ast (self)
 
def get_id (self)
 
def sort_kind (self)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def params (self)
 
def decl (self)
 
def num_args (self)
 
def arg (self, idx)
 
def children (self)
 
- Public Member Functions inherited from AstRef
def __init__ (self, ast, ctx=None)
 
def __del__ (self)
 
def __deepcopy__ (self, memo={})
 
def __str__ (self)
 
def __repr__ (self)
 
def __nonzero__ (self)
 
def __bool__ (self)
 
def sexpr (self)
 
def ctx_ref (self)
 
def eq (self, other)
 
def translate (self, target)
 
def __copy__ (self)
 
def hash (self)
 
- Public Member Functions inherited from Z3PPObject
def use_pp (self)
 

Additional Inherited Members

- Data Fields inherited from AstRef
 ast
 
 ctx
 

Detailed Description

Algebraic irrational values.

Definition at line 3051 of file z3py.py.

Member Function Documentation

◆ approx()

def approx (   self,
  precision = 10 
)
Return a Z3 rational number that approximates the algebraic number `self`.
The result `r` is such that |r - self| <= 1/10^precision

>>> x = simplify(Sqrt(2))
>>> x.approx(20)
6838717160008073720548335/4835703278458516698824704
>>> x.approx(5)
2965821/2097152

Definition at line 3054 of file z3py.py.

3054  def approx(self, precision=10):
3055  """Return a Z3 rational number that approximates the algebraic number `self`.
3056  The result `r` is such that |r - self| <= 1/10^precision
3057 
3058  >>> x = simplify(Sqrt(2))
3059  >>> x.approx(20)
3060  6838717160008073720548335/4835703278458516698824704
3061  >>> x.approx(5)
3062  2965821/2097152
3063  """
3064  return RatNumRef(Z3_get_algebraic_number_upper(self.ctx_ref(), self.as_ast(), precision), self.ctx)
3065 
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...

◆ as_decimal()

def as_decimal (   self,
  prec 
)
Return a string representation of the algebraic number `self` in decimal notation
using `prec` decimal places.

>>> x = simplify(Sqrt(2))
>>> x.as_decimal(10)
'1.4142135623?'
>>> x.as_decimal(20)
'1.41421356237309504880?'

Definition at line 3066 of file z3py.py.

3066  def as_decimal(self, prec):
3067  """Return a string representation of the algebraic number `self` in decimal notation
3068  using `prec` decimal places.
3069 
3070  >>> x = simplify(Sqrt(2))
3071  >>> x.as_decimal(10)
3072  '1.4142135623?'
3073  >>> x.as_decimal(20)
3074  '1.41421356237309504880?'
3075  """
3076  return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3077 
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.

◆ index()

def index (   self)

Definition at line 3081 of file z3py.py.

3081  def index(self):
3082  return Z3_algebraic_get_i(self.ctx_ref(), self.as_ast())
3083 
3084 
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.

◆ poly()

def poly (   self)

Definition at line 3078 of file z3py.py.

3078  def poly(self):
3079  return AstVector(Z3_algebraic_get_poly(self.ctx_ref(), self.as_ast()), self.ctx)
3080 
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.