_Equation

it.grypho.scala.leonardo.equation._Equation
case class _Equation(lhs: _Expression, rhs: _Expression) extends _ElementWise

A relation between two expressions: lhs = rhs.

eval reduces both sides and compares them when both are concrete. Numeric equality is tolerance-based, tied to env.precision -- exact Double comparison would make sin(pi) = 0 false on floating-point noise; instead two numbers are equal when |a - b| <= 0.5 * 10^(-p). Concrete matrices compare element-wise under the same tolerance. Anything else stays symbolic with the sides reduced.

Marked _ElementWise: an equation is a container of its two sides, so derive/simplify/expand/integrate apply the algorithm to both sides (e.g. d/dx (lhs = rhs) is d(lhs)/dx = d(rhs)/dx).

toString is "lhs = rhs" (no outer parentheses): equations exist only at the top level of the grammar, and the round-trip invariant parse(toString(e)) == e holds.

Value parameters

lhs

left-hand side expression

rhs

right-hand side expression

Attributes

Graph
Supertypes
trait Serializable
trait Product
trait Equals
trait _ElementWise
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