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AlgebraicNumRef Class Reference
+ Inheritance diagram for AlgebraicNumRef:

Public Member Functions

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

Additional Inherited Members

- Data Fields inherited from AstRef
 ast = ast
 
 ctx = _get_ctx(ctx)
 
- Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)
 

Detailed Description

Algebraic irrational values.

Definition at line 3167 of file z3py.py.

Member Function Documentation

◆ approx()

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 3170 of file z3py.py.

3170 def approx(self, precision=10):
3171 """Return a Z3 rational number that approximates the algebraic number `self`.
3172 The result `r` is such that |r - self| <= 1/10^precision
3173
3174 >>> x = simplify(Sqrt(2))
3175 >>> x.approx(20)
3176 6838717160008073720548335/4835703278458516698824704
3177 >>> x.approx(5)
3178 2965821/2097152
3179 """
3180 return RatNumRef(Z3_get_algebraic_number_upper(self.ctx_ref(), self.as_ast(), precision), self.ctx)
3181
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()

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 3182 of file z3py.py.

3182 def as_decimal(self, prec):
3183 """Return a string representation of the algebraic number `self` in decimal notation
3184 using `prec` decimal places.
3185
3186 >>> x = simplify(Sqrt(2))
3187 >>> x.as_decimal(10)
3188 '1.4142135623?'
3189 >>> x.as_decimal(20)
3190 '1.41421356237309504880?'
3191 """
3192 return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3193
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()

index ( self)

Definition at line 3197 of file z3py.py.

3197 def index(self):
3198 return Z3_algebraic_get_i(self.ctx_ref(), self.as_ast())
3199
3200
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.

◆ poly()

poly ( self)

Definition at line 3194 of file z3py.py.

3194 def poly(self):
3195 return AstVector(Z3_algebraic_get_poly(self.ctx_ref(), self.as_ast()), self.ctx)
3196
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.