arb#

Arblib wrapper using ctypes.

Functions#

`arb_sub()`	Returns `x - y`.
`arb_add()`	Returns sum of `x` and `y`.
`arb_mul()`	Returns product of `x` and `y`.
`arb_div()`	Returns quotient of `x` divided by `y`.
`arb_log()`	Returns `log(x)`.
`arb_max()`	Returns max of `x` and `y`.
`arb_exp()`	Returns `exp(x)`.
`arb_pow()`	Returns `x^y`.
`arb_min()`	Returns min of `x` and `y`.
`arb_abs()`	Returns absolute value of x.
`arb_neg()`	Returns -x.
`arb_sgn()`	Sign function.
`arb_erf()`	Error function.
`arb_erfc()`	Complementary error function.
`arb_erfinv()`	Inverse error function.
`arb_sqrt()`	Returns square root of `x`.
`arb_const_pi()`	Returns pi.
`arb_union()`	Returns union of `x` and `y`.
`arb_sum()`	Sum of elements in xs.
`arb_product()`	Product of elements in xs.
`arb_lambertw()`	Lambert W function.

arb_sub(x, y, prec)#

Returns x - y.

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_add(x, y, prec)#

Returns sum of x and y.

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_mul(x, y, prec)#

Returns product of x and y.

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_div(x, y, prec)#

Returns quotient of x divided by y.

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_log(x, prec)#

Returns log(x).

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_max(x, y, prec)#

Returns max of x and y.

If x and y represent intervals [x_l, x_u] and [y_l, y_u], this returns an interval containing [max(x_l, y_l), max(x_u, y_u)].

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_exp(x, prec)#

Returns exp(x).

If x represents an interval [x_l, x_u], this returns an interval containing [exp(x_l), exp(x_u)].

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_pow(x, y, prec)#

Returns x^y.

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_min(x, y, prec)#

Returns min of x and y.

If x and y represent intervals [x_l, x_u] and [y_l, y_u], this returns an interval containing [min(x_l, y_l), min(x_u, y_u)].

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_abs(x)#

Returns absolute value of x.

Parameters:: x (Arb)
Return type:: Arb

arb_neg(x)#

Returns -x.

Parameters:: x (Arb)
Return type:: Arb

arb_sgn(x)#

Sign function.

If x contains both zero and nonzero numbers, this returns an Arb with mid=0 and rad=1.

Parameters:: x (Arb)
Return type:: Arb

arb_erf(x, prec)#

Error function.

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_erfc(x, prec)#

Complementary error function.

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_erfinv(x, prec)#

Inverse error function.

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_sqrt(x, prec)#

Returns square root of x.

Parameters:

x (Arb)
prec (int)

Return type:

Arb

arb_const_pi(prec)#

Returns pi.

Parameters:: prec (int)
Return type:: Arb

arb_union(x, y, prec)#

Returns union of x and y.

If x and y represent intervals [x_l, x_u] and [y_l, y_u], this returns an interval containing [min(x_l, y_l), max(x_u, y_u)].

Parameters:

x (Arb)
y (Arb)
prec (int)

Return type:

Arb

arb_sum(xs, prec)#

Sum of elements in xs.

Parameters:

xs (List[Arb])
prec (int)

Return type:

Arb

arb_product(xs, prec)#

Product of elements in xs.

Parameters:

xs (List[Arb])
prec (int)

Return type:

Arb

arb_lambertw(x, branch, prec)#

Lambert W function.

Parameters:

x (Arb)
branch (int)
prec (int)

Return type:

Arb

Classes#

Arb

An interval on the real line represented by a midpoint and a radius.

class Arb(ptr)#

An interval on the real line represented by a midpoint and a radius.

Note: Arbs with radius=0 are referred to as exact arbs.

Methods#
`from_midpoint_radius()`	Constructs an Arb by specifying its midpoint and radius.
`from_int()`	Constructs an exact Arb with midpoint `val`.
`from_float()`	Construct an exact Arb with midpoint `val`.
`from_man_exp()`	Constructs an exact arb with midpoint specified as mantissa and exponent.
`one()`	Returns an exact Arb with midpoint 1 and radius 0.
`positive_infinity()`	Returns an Arb representing positive infinity.
`negative_infinity()`	Returns an Arb representing negative infinity.
`__lt__()`	Returns True if self is less than other.
`__le__()`	Returns True if self is less than or equal to other.
`__ne__()`	Returns True if self is not equal to other.
`__gt__()`	Returns True if self is greater than other.
`__ge__()`	Returns True if self is greater than or equal to other.
`__eq__()`	Returns True if self is equal to other.
`__neg__()`	Returns -1 * `self`.
`is_exact()`	Returns True if radius is 0.
`is_finite()`	Returns True if self is finite.
`is_nan()`	Returns True if midpoint is NaN.
`__float__()`	Returns a float approximating the midpoint of `self`.
`to_float()`	Returns the only floating point number contained in `self`.
`man_exp()`	Returns a pair (Mantissa, Exponent) if exact.
`lower()`	Returns an exact Arb representing the smallest value in `self`.
`upper()`	Returns an exact Arb representing the largest value in `self`.
`midpoint()`	Returns the midpoint of `self`.
`radius()`	Returns the radius of `self`.
`__contains__()`	Returns True if value is contained in the interval represented by `self`.
`__del__()`	Cleanup.

__init__(ptr)#

Construct a ball represented exactly.

NOTE: Do not use directly. Use a from_ constructor instead.

static from_midpoint_radius(mid, rad)#

Constructs an Arb by specifying its midpoint and radius.

Parameters:

mid (Union[Arb, int, float, Tuple[int, int]])
rad (Union[Arb, int, float, Tuple[int, int]])

Return type:

Arb

static from_int(val)#

Constructs an exact Arb with midpoint val.

Parameters:: val (int)
Return type:: Arb

static from_float(val)#

Construct an exact Arb with midpoint val.

Parameters:: val (float)
Return type:: Arb

static from_man_exp(man, exp)#

Constructs an exact arb with midpoint specified as mantissa and exponent.

Parameters:

man (int)
exp (int)

Return type:

Arb

static one()#

Returns an exact Arb with midpoint 1 and radius 0.

Return type:: Arb

static positive_infinity()#

Returns an Arb representing positive infinity.

Return type:: Arb

static negative_infinity()#

Returns an Arb representing negative infinity.

Return type:: Arb

__lt__(other)#

Returns True if self is less than other.

This returns True if each value in the interval represented by self is less than every value in other.