AngouriMath
DomainCondition
Property
Summary
Returns the complete condition under which this expression is defined (has a valid value).
This represents the mathematical "domain of definition" as a logical predicate.
For example:
- For x/y: returns "y ≠ 0"
- For sqrt(x) (over reals): returns "x ≥ 0"
- For tan(x): returns "cos(x) ≠ 0" (or equivalently "x ≠ π/2 + πn")
- For x + y: returns "true" (always defined)
- For x/y + log(z): returns "y ≠ 0 and z > 0"
This combines the node's own definition condition (IntrinsicCondition) with all
its children's conditions using logical AND, propagating domain restrictions throughout the expression tree.
This is used by simplification patterns to preserve mathematical correctness by adding
"provided" clauses when simplifications might hide singularities or undefined regions.
For instance: (x-1)/(x-1) simplifies to "1 provided x ≠ 1", not just "1".
This represents the mathematical "domain of definition" as a logical predicate.
For example:
- For x/y: returns "y ≠ 0"
- For sqrt(x) (over reals): returns "x ≥ 0"
- For tan(x): returns "cos(x) ≠ 0" (or equivalently "x ≠ π/2 + πn")
- For x + y: returns "true" (always defined)
- For x/y + log(z): returns "y ≠ 0 and z > 0"
This combines the node's own definition condition (IntrinsicCondition) with all
its children's conditions using logical AND, propagating domain restrictions throughout the expression tree.
This is used by simplification patterns to preserve mathematical correctness by adding
"provided" clauses when simplifications might hide singularities or undefined regions.
For instance: (x-1)/(x-1) simplifies to "1 provided x ≠ 1", not just "1".
Remarks
Mathematical concepts:
- Domain of definition (the set where a function is defined)
- Singularities and poles (points where a function is undefined)
- Piecewise continuity (tracking where discontinuities occur)
- Domain of definition (the set where a function is defined)
- Singularities and poles (points where a function is undefined)
- Piecewise continuity (tracking where discontinuities occur)
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