Leonardo
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Leonardo/it.grypho.scala.leonardo/it.grypho.scala.leonardo.domain/_Singularities

_Singularities

it.grypho.scala.leonardo.domain._Singularities
case class _Singularities(e: _Expression, v: _Variable) extends _Expression

singularities(e, v) — the isolated singularities of a rational e.

Three outcomes, deliberately distinguishable:

  • some — a 2×n matrix, locations in the first row and pole order in the second, with 0 marking a removable singularity. Two rows rather than one because the order is the part the Laurent series actually needs — it is the length of the principal part — and a bare list of locations would lose it.
  • provably none — _Bool(false), the empty set. This follows the inequality solver, which renders an empty solution set the same way, and _Matrix cannot be 2×0 in any case.
  • cannot enumerate — stays symbolic, which is everything that is not a numeric rational function. Collapsing this into "none" would turn "I do not know" into a confident and wrong answer.

Varying the result type by cardinality is the convention equation._Solve already uses: one solution is an equation, several are a matrix, none stays symbolic.

Attributes

Graph
Supertypes
trait Serializable
trait Product
trait Equals
trait _Expression
class Object
trait Matchable
class Any
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Members list

Value members

Concrete methods

override def children: List[_Expression]

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Attributes

Definition Classes
override def eval(env: Environment): Either[_Expression, _Value]

Reduces this expression in the given environment.

Reduces this expression in the given environment.

Value parameters

env

variable bindings and display precision

Attributes

Returns

Right(v) when all free variables resolved to concrete values; Left(e) when reduction is partial or impossible

Definition Classes
override def rebuild(c: List[_Expression]): _Expression

Reconstructs the same node shape with replacement sub-expressions.

Reconstructs the same node shape with replacement sub-expressions.

Value parameters

newChildren

replacements in the same order and count as children

Attributes

Definition Classes
override def toString: String

Returns a string representation of the object.

Returns a string representation of the object.

The default representation is platform dependent.

Attributes

Returns

a string representation of the object.

Definition Classes
Any

Inherited methods

def productElementNames: Iterator[String]

Attributes

Inherited from:
Product
def productIterator: Iterator[Any]

Attributes

Inherited from:
Product

Inherited fields

lazy val freeVars: Set[String]

Cached set of free variable names; O(1) after the first access.

Cached set of free variable names; O(1) after the first access.

Attributes

Inherited from:
_Expression
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