Class

Assumption

src/core/classes/assumption/Assumption.ts:159

Describes the admissible real values of a symbolic variable as one numeric interval.

remarks

`Assumption`

is an interval constraint, not a symbolic theorem. It can prove relations when the interval bounds force an answer, disprove them when the bounds force the opposite answer, and otherwise reports an unknown result as

`undefined`

. Two variables having the same admissible interval therefore does not prove that the variables are equal. Instances are immutable. Repeated assumptions for a variable are intersected by the global assumption registry rather than modifying an existing interval. Finite bounds preserve an exact rational value internally. Decimal inputs therefore retain the exact value represented by their decimal text, while Rational inputs such as

`1/3`

are not rounded through Decimal precision before comparisons are made. The 2.0 assumption vocabulary is intentionally conservative: a single real interval with numeric bounds. Integer, parity, complex-domain, relational (

`x > y`

), union, and general predicate assumptions are not represented by this class.

Members

atLeast(x: AssumptionValue, inclusive: boolean): AssumptionMethod

Creates an interval extending upward from

`x`

Parameters

Name	Type	Description
`x`	`AssumptionValue`	Lower endpoint.
`inclusive`	`boolean`	Whether a finite lower endpoint belongs to the interval.

Returns

Assumption — The interval `[x, +∞)` when inclusive, otherwise `(x, +∞)`.

atMost(x: AssumptionValue, inclusive: boolean): AssumptionMethod

Creates an interval extending downward from

`x`

Parameters

Name	Type	Description
`x`	`AssumptionValue`	Upper endpoint.
`inclusive`	`boolean`	Whether a finite upper endpoint belongs to the interval.

Returns

Assumption — The interval `(-∞, x]` when inclusive, otherwise `(-∞, x)`.

Assumption(start: AssumptionValue, end: AssumptionValue, startInclusive: boolean, endInclusive: boolean): AssumptionConstructor

Creates a non-empty real interval.

remarks

Infinite endpoints are normalized to open bounds. A zero-width interval is valid only when both endpoints are inclusive, in which case it represents one exact value. Rational inputs retain their exact value even when their Decimal projection is necessarily finite precision.

throws

Error Thrown when a bound is

`NaN`

, the bounds are reversed, or the interval is empty.

Parameters

Name	Type	Description
`start`	`AssumptionValue`	Lower numeric endpoint.
`end`	`AssumptionValue`	Upper numeric endpoint.
`startInclusive`	`boolean`	Include the lower endpoint when it is finite.
`endInclusive`	`boolean`	Include the upper endpoint when it is finite.

Returns

Assumption

contains(x: AssumptionValue): booleanMethod

Tests whether a numeric value belongs to this interval.

Parameters

Name	Type	Description
`x`	`AssumptionValue`	Numeric value to test.

Returns

boolean — `true` when `x` satisfies both interval bounds.

dataType: "ASSUMPTION"Property

Runtime tag used by Nerdamer's assumption type guard.

end: BoundProperty

Upper endpoint of the admissible interval.

eq(x: Expression | Assumption): AssumptionComparisonMethod

Determines whether values constrained by this interval are equal to

`x`

remarks

Equality is proved only when both sides identify the same single value. It is disproved when the admissible values are disjoint. Overlapping ranges, including identical non-singleton ranges, return

`undefined`

because equality depends on the actual values chosen from those ranges.

Parameters

Name	Type	Description
`x`	`Expression \| Assumption`	Another interval-constrained value or a numeric expression.

Returns

AssumptionComparison — `true` when equality is forced, `false` when inequality is forced, or `undefined` when the available information permits either outcome.

exactly(x: AssumptionValue): AssumptionMethod

Creates the singleton interval containing exactly

`x`

Parameters

Name	Type	Description
`x`	`AssumptionValue`	The one admissible value.

Returns

Assumption — The closed singleton interval `[x, x]`.

getSingletonValue(): Expression | undefinedMethod

Returns the exact value represented by a singleton interval.

Returns

Expression | undefined — A numeric Expression when this interval is a singleton, otherwise `undefined`.

gt(x: Expression | Assumption): AssumptionComparisonMethod

Determines whether every value in this interval is strictly greater than

`x`

Parameters

Name	Type	Description
`x`	`Expression \| Assumption`	Another interval-constrained value or a numeric expression.

Returns

AssumptionComparison — `true` when `>` is forced, `false` when `<=` is forced, or `undefined` when the interval information permits both outcomes.

gte(x: Expression | Assumption): AssumptionComparisonMethod

Determines whether every value in this interval is greater than or equal to

`x`

Parameters

Name	Type	Description
`x`	`Expression \| Assumption`	Another interval-constrained value or a numeric expression.

Returns

AssumptionComparison — `true` when `>=` is forced, `false` when `<` is forced, or `undefined` when the interval information permits both outcomes.

intersect(x: Assumption): Assumption | undefinedMethod

Intersects this interval with another interval. Endpoint selection uses the exact finite representation retained by each interval, so repeated constraints do not lose rational precision while narrowing the range.

Parameters

Name	Type	Description
`x`	`Assumption`	Interval to intersect with this one.

Returns

Assumption | undefined — The non-empty intersection, or `undefined` when the intervals are disjoint.

isAssumption(obj: unknown): objMethod

No description is available yet.

Parameters

Name	Type	Description
`obj`	`unknown`	—

Returns

obj

isSingleton: booleanProperty

Whether the interval contains exactly one finite value.

lt(x: Expression | Assumption): AssumptionComparisonMethod

Determines whether every value in this interval is strictly less than

`x`

Parameters

Name	Type	Description
`x`	`Expression \| Assumption`	Another interval-constrained value or a numeric expression.

Returns

AssumptionComparison — `true` when `<` is forced, `false` when `>=` is forced, or `undefined` when the interval information permits both outcomes.

lte(x: Expression | Assumption): AssumptionComparisonMethod

Determines whether every value in this interval is less than or equal to

`x`

Parameters

Name	Type	Description
`x`	`Expression \| Assumption`	Another interval-constrained value or a numeric expression.

Returns

AssumptionComparison — `true` when `<=` is forced, `false` when `>` is forced, or `undefined` when the interval information permits both outcomes.

overlaps(x: Assumption): booleanMethod

Tests whether this interval and

`x`

share at least one admissible value.

Parameters

Name	Type	Description
`x`	`Assumption`	Interval to test for overlap.

Returns

boolean — `true` when the intersection is non-empty.

parse(expr: string): ParsedAssumptionMethod

Parses one numeric interval constraint such as

`x >= 0`

`n < 10`

remarks

Whitespace is ignored. Variable names use the ASCII identifier form

`[A-Za-z_][A-Za-z0-9_]*`

. Supported operators are

`=`

`==`

`>`

`>=`

`<`

, and

`<=`

. Bounds are Decimal-compatible numeric literals;

`inf`

`infinity`

`+inf`

`+infinity`

`-inf`

, and

`-infinity`

are also accepted. Expressions such as

`x > y`

`x = 1/2`

, and property predicates such as

`integer(x)`

are outside the string assumption grammar. Parser assertive calls may still provide already-evaluated Rational bounds directly.

throws

Error Thrown when the constraint has an invalid identifier, operator, or numeric bound.

Parameters

Name	Type	Description
`expr`	`string`	Constraint to parse.

Returns

ParsedAssumption — The parsed symbol and its interval assumption.

sameInterval(x: Assumption): booleanMethod

Tests whether two objects describe the same interval constraint.

remarks

This is structural interval equality. It is deliberately separate from eq: two different variables may have identical intervals without being known to have the same value.

Parameters

Name	Type	Description
`x`	`Assumption`	Interval constraint to compare with this one.

Returns

boolean — `true` when both endpoints and their inclusivity are identical.

start: BoundProperty

Lower endpoint of the admissible interval.

toString(): stringMethod

Formats the interval using mathematical bracket notation.

Returns

string — A representation such as `[0, 10)` or `(-Infinity, Infinity)`.