Miscellany

Bits and bobs not belonging to the main features of the package, but needed by the package and useful nonetheless.

Contents

• Profiling
• Default associative arrays
• Warnings
• Promotion
• Lower bounds

Profiling

To help isolate the slow parts of code, we provide some profiling tools.

ExactpAdics_SetProfile (doProfile :: BoolElt)

Turn profiling on or off.

Parameters

• Reset := false: When true, also resets the profile.

ExactpAdics_GetProfile ()

-> BoolElt

True if profiling is enabled.

ExactpAdics_ResetProfile ()

Resets the profile.

ExactpAdics_GetProfileUpdates ()

-> []

Returns the profile, a sequence of records for each update with the following fields:

• x: the element being updated.
• initial_apr: the initial absolute precision of the element.
• target_apr: the absolute precision being updated to.
• initial_time: the Cputime() when the update was made.
• time_elapsed: the time taken to perform the update.

Default associative arrays

The new type AssocDflt is an associative array with a default value. Hence it may be used to describe a function which is constant save for finitely many exceptions.

IsCoercible_DefaultAssociativeArray (x)

-> BoolElt, AssocDflt

True if we can create a default associative array with default x.

IsCoercible_DefaultAssociativeArray (x, keys, values)

-> BoolElt, AssocDflt

True if we can create a default associative array with default x and given keys and values.

IsCoercible_DefaultAssociativeArray (x, y)

IsCoercible_DefaultAssociativeArray (x, y :: Assoc)

IsCoercible_DefaultAssociativeArray (x, y :: [Tup])

-> BoolElt, AssocDflt

True if we can create a default associative array with default x and values y.

DefaultAssociativeArray (x)

-> AssocDflt

The default associative array with default value x.

DefaultAssociativeArray (x, ys)

-> AssocDflt

The default associative array with default value x and keys and values specified by ys (an associative array or sequence of <key,value> pairs).

DefaultAssociativeArray (x, keys, values)

-> AssocDflt

The default associative array with default value x, and given keys and values.

Print (x :: AssocDflt, lvl :: MonStgElt)

Print.

'@' (i, x :: AssocDflt)

-> Any

The value at index i of x.

ApplyPointwise (f, x :: AssocDflt, y :: AssocDflt)

-> AssocDflt

Applies the function f pointwise to values of x and y.

ApplyPointwise (f, x :: AssocDflt)

-> AssocDflt

Applies the function f pointwise to values of x.

Image (x :: AssocDflt)

-> {}

The set of possible output values.

DefaultValue (x :: AssocDflt)

-> Any

The default value of x.

SpecialAssociativeArray (x :: AssocDflt)

-> Assoc

The associative array of the special values of x.

SpecialKeys (x :: AssocDflt)

-> Assoc

The keys of special values of x.

Zip (xs :: [AssocDflt])

-> AssocDflt

The array [i] -> [x(i) : x in xs]. The inputs must have compatible indices.

ZipApplyPointwise (f, xs :: [AssocDflt])

-> AssocDflt

The array [i] -> f([x(i) : x in xs]). Equivalent to ApplyPointwise(f,Zip(xs)).

ForAll (x :: AssocDflt, f)

-> BoolElt

True if f(x(i)) is true for all i.

ForAll (x :: AssocDflt, y :: AssocDflt, f)

-> BoolElt

True if f(x(i),y(i)) is true for all i.

Warnings

For controlling the extent to which errors and warnings occur in the ExactpAdics package.

ExactpAdics_SetWarningAction (name :: MonStgElt, action :: MonStgElt)

Sets how the warning name is displayed. action is one of:

• "Ignore": ignores the warning and does nothing
• "Warn": prints the warning to the screen
• "WarnOnce": prints the warning to the screen the first time it occurs
• "Error": raises an error

ExactpAdics_WarningActionIsDefined (name :: MonStgElt)

-> BoolElt, MonStgElt

True if there is a warning action defined for warning name. If so, also returns the action.

ExactpAdics_GetWarningAction (name :: MonStgElt, dflt :: MonStgElt)

-> MonStgElt

The warning action set for warning name, if set, or else dflt.

ExactpAdics_Warn (name :: MonStgElt, msg)

Raises the warning name with message msg.

Parameters

• DefaultAction
• Action

Promotion

A basic scheme for promoting values in different structures to a common strucure.

IsPromotable (x, y)

-> BoolElt, Any, Any

True if x and y are promotable to the same parent.

Promote (x, y)

-> Any, Any

Promotes x and y to a common type.

Lower bounds

A ExactpAdics_BndLow is a lower bound on a possibly unknown value.

ExactpAdics_LowerBound (v)

-> ExactpAdics_BndLow

The lower bound v.

Parameters

• IsSharp

IsSharp (b :: ExactpAdics_BndLow)

-> BoolElt

True if b is a sharp bound.

BoundValue (b :: ExactpAdics_BndLow)

-> Any

The lower bound.

Value (b :: ExactpAdics_BndLow)

-> Any

The value of b, assuming it is sharp.

Print (b :: ExactpAdics_BndLow, lvl :: MonStgElt)

Print.

'&+' (bs :: [ExactpAdics_BndLow])

-> ExactpAdics_BndLow

Lower bound on the sum of the values being bounded.

Max (bs :: [ExactpAdics_BndLow])

-> ExactpAdics_BndLow

Lower bound on the maximum of the values being bounded.

Min (bs :: [ExactpAdics_BndLow])

-> ExactpAdics_BndLow

Lower bound on the minimum of the values being bounded.