Interface RCFNum<Name>

A Real Closed Field (RCF) numeral.

RCF numerals can represent:

Rational numbers
Algebraic numbers (roots of polynomials)
Transcendental extensions (e.g., pi, e)
Infinitesimal extensions

const { RCFNum } = Context('main');

// Create pi
const pi = RCFNum.pi();
console.log(pi.toDecimal(10)); // "3.1415926536"

// Create a rational
const half = new RCFNum('1/2');

// Arithmetic
const sum = pi.add(half);

// Check properties
console.log(pi.isTranscendental()); // true
console.log(half.isRational()); // true

interface RCFNum<Name extends string = "main"> {
    add(other: RCFNum<Name>): RCFNum<Name>;
    div(other: RCFNum<Name>): RCFNum<Name>;
    eq(other: RCFNum<Name>): boolean;
    ge(other: RCFNum<Name>): boolean;
    gt(other: RCFNum<Name>): boolean;
    inv(): RCFNum<Name>;
    isAlgebraic(): boolean;
    isInfinitesimal(): boolean;
    isRational(): boolean;
    isTranscendental(): boolean;
    le(other: RCFNum<Name>): boolean;
    lt(other: RCFNum<Name>): boolean;
    mul(other: RCFNum<Name>): RCFNum<Name>;
    neg(): RCFNum<Name>;
    neq(other: RCFNum<Name>): boolean;
    power(k: number): RCFNum<Name>;
    sub(other: RCFNum<Name>): RCFNum<Name>;
    toDecimal(precision: number): string;
    toString(compact?: boolean): string;
}

Type Parameters

Name extends string = "main"

Index

Methods

add div eq ge gt inv isAlgebraic isInfinitesimal isRational isTranscendental le lt mul neg neq power sub toDecimal toString

Methods

add

add(other: RCFNum<Name>): RCFNum<Name>
Add two RCF numerals.
Parameters
- other: RCFNum<Name>
  The RCF numeral to add
Returns RCFNum<Name>
this + other
- Defined in src/high-level/types.ts:2121

div

div(other: RCFNum<Name>): RCFNum<Name>
Divide two RCF numerals.
Parameters
- other: RCFNum<Name>
  The RCF numeral to divide by
Returns RCFNum<Name>
this / other
- Defined in src/high-level/types.ts:2142

eq

eq(other: RCFNum<Name>): boolean
Check if this RCF numeral is equal to another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this == other
- Defined in src/high-level/types.ts:2196

ge

ge(other: RCFNum<Name>): boolean
Check if this RCF numeral is greater than or equal to another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this >= other
- Defined in src/high-level/types.ts:2189

gt

gt(other: RCFNum<Name>): boolean
Check if this RCF numeral is greater than another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this > other
- Defined in src/high-level/types.ts:2175

inv

inv(): RCFNum<Name>
Compute the multiplicative inverse.

Returns RCFNum<Name>
1/this
- Defined in src/high-level/types.ts:2154

isAlgebraic

isAlgebraic(): boolean
Check if this RCF numeral is an algebraic number.

Returns boolean
true if this is algebraic
- Defined in src/high-level/types.ts:2215

isInfinitesimal

isInfinitesimal(): boolean
Check if this RCF numeral is an infinitesimal.

Returns boolean
true if this is infinitesimal
- Defined in src/high-level/types.ts:2221

isRational

isRational(): boolean
Check if this RCF numeral is a rational number.

Returns boolean
true if this is rational
- Defined in src/high-level/types.ts:2209

isTranscendental

isTranscendental(): boolean
Check if this RCF numeral is a transcendental number.

Returns boolean
true if this is transcendental
- Defined in src/high-level/types.ts:2227

le

le(other: RCFNum<Name>): boolean
Check if this RCF numeral is less than or equal to another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this <= other
- Defined in src/high-level/types.ts:2182

lt

lt(other: RCFNum<Name>): boolean
Check if this RCF numeral is less than another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this < other
- Defined in src/high-level/types.ts:2168

mul

mul(other: RCFNum<Name>): RCFNum<Name>
Multiply two RCF numerals.
Parameters
- other: RCFNum<Name>
  The RCF numeral to multiply
Returns RCFNum<Name>
this * other
- Defined in src/high-level/types.ts:2135

neg

neg(): RCFNum<Name>
Negate this RCF numeral.

Returns RCFNum<Name>
-this
- Defined in src/high-level/types.ts:2148

neq

neq(other: RCFNum<Name>): boolean
Check if this RCF numeral is not equal to another.
Parameters
- other: RCFNum<Name>
  The RCF numeral to compare with
Returns boolean
true if this != other
- Defined in src/high-level/types.ts:2203

power

power(k: number): RCFNum<Name>
Raise this RCF numeral to a power.
Parameters
- k: number
  The exponent
Returns RCFNum<Name>
this^k
- Defined in src/high-level/types.ts:2161

sub

sub(other: RCFNum<Name>): RCFNum<Name>
Subtract two RCF numerals.
Parameters
- other: RCFNum<Name>
  The RCF numeral to subtract
Returns RCFNum<Name>
this - other
- Defined in src/high-level/types.ts:2128

toDecimal

toDecimal(precision: number): string
Convert this RCF numeral to a decimal string.
Parameters
- precision: number
  Number of decimal places
Returns string
Decimal string representation
- Defined in src/high-level/types.ts:2241

toString

toString(compact?: boolean): string
Convert this RCF numeral to a string.
Parameters
- Optionalcompact: boolean
  If true, use compact representation
Returns string
String representation
- Defined in src/high-level/types.ts:2234

Interface RCFNum<Name>

Type Parameters

Index

Methods

Methods

add

Parameters

Returns RCFNum<Name>

div

Parameters

Returns RCFNum<Name>

eq

Parameters

Returns boolean

ge

Parameters

Returns boolean

gt

Parameters

Returns boolean

inv

Returns RCFNum<Name>

isAlgebraic

Returns boolean

isInfinitesimal

Returns boolean

isRational

Returns boolean

isTranscendental

Returns boolean

le

Parameters

Returns boolean

lt

Parameters

Returns boolean

mul

Parameters

Returns RCFNum<Name>

neg

Returns RCFNum<Name>

neq

Parameters

Returns boolean

power

Parameters

Returns RCFNum<Name>

sub

Parameters

Returns RCFNum<Name>

toDecimal

Parameters

Returns string

toString

Parameters

Returns string

Settings

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