Class: Field

Table of contents

Constructors

• constructor

Properties

• ORDER
• minusOne
• one
• zero

Methods

• add
• assertBoolean
• assertEquals
• assertGt
• assertGte
• assertLt
• assertLte
• div
• equals
• gt
• gte
• inv
• isConstant
• isZero
• lt
• lte
• mul
• neg
• ofFields
• rangeCheckHelper
• seal
• sizeInFields
• sqrt
• square
• sub
• toBigInt
• toBits
• toConstant
• toFields
• toJSON
• toString
• check
• fromBigInt
• fromJSON
• fromNumber
• fromString
• ofBits
• ofFields
• random
• sizeInFields
• toFields
• toInput
• toJSON

Constructors

constructor

• new Field(x)

Coerces anything field-like to a [[Field]].

Parameters

Name	Type
x	string | number | bigint | boolean | Field

Defined in

snarky.d.ts:28

Properties

ORDER

▪ Static ORDER: bigint

The field order as a bigint.

Defined in

snarky.d.ts:266

---

minusOne

▪ Static minusOne: Field

The number -1 as a [[Field]].

Defined in

snarky.d.ts:262

---

one

▪ Static one: Field

The number 1 as a [[Field]].

Defined in

snarky.d.ts:254

---

zero

▪ Static zero: Field

The number 0 as a [[Field]].

Defined in

snarky.d.ts:258

Methods

add

▸ add(y): Field

Adds this [[Field]] element to another coercible to a field.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Field

Defined in

snarky.d.ts:56

---

assertBoolean

▸ assertBoolean(): void

Assert that this [[Field]] is either 0 or 1.

Field.zero.assertBoolean();

This function can only be called inside a checked computation, like a SmartContract method, and throws an error if the assertion fails.

Returns

void

Defined in

snarky.d.ts:216

---

assertEquals

▸ assertEquals(y): void

Assert that this [[Field]] equals another Field-like value. Throws an error if the assertion fails.

Field.one.assertEquals(1);

Parameters

Name	Type
y	string | number | boolean | Field

Returns

void

Defined in

snarky.d.ts:205

---

assertGt

▸ assertGt(y): void

Assert that this [[Field]] is greater than another Field-like value.

Field.one.assertGt(0);

This function can only be called inside a checked computation, like a SmartContract method, and causes it to fail if the assertion fails.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

void

Defined in

snarky.d.ts:184

---

assertGte

▸ assertGte(y): void

Assert that this [[Field]] is greater than or equal to another Field-like value.

Field.one.assertGte(0);

This function can only be called inside a checked computation, like a SmartContract method, and causes it to fail if the assertion fails.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

void

Defined in

snarky.d.ts:195

---

assertLt

▸ assertLt(y): void

Assert that this [[Field]] is lower than another Field-like value.

Field.one.assertLt(2);

This function can only be called inside a checked computation, like a SmartContract method, and causes it to fail if the assertion fails.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

void

Defined in

snarky.d.ts:162

---

assertLte

▸ assertLte(y): void

Assert that this [[Field]] is lower than or equal to another Field-like value.

Field.one.assertLte(2);

This function can only be called inside a checked computation, like a SmartContract method, and causes it to fail if the assertion fails.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

void

Defined in

snarky.d.ts:173

---

div

▸ div(y): Field

Divides this [[Field]] element through another coercible to a field.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Field

Defined in

snarky.d.ts:71

---

equals

▸ equals(y): Bool

Check if this [[Field]] equals another [[Field]]-like value. Returns a [[Bool]].

Field(2).equals(2); // Bool(true)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:238

---

gt

▸ gt(y): Bool

Check if this [[Field]] is greater than another Field-like value. Returns a [[Bool]].

Field(2).gt(1); // Bool(true)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:140

---

gte

▸ gte(y): Bool

Check if this [[Field]] is greater than or equal to another Field-like value. Returns a [[Bool]].

Field(2).gte(1); // Bool(true)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:149

---

inv

▸ inv(): Field

Inverts this [[Field]] element.

const invX = x.inv();
invX.assertEquals(Field.one.div(x));

Returns

Field

A field element that is equivalent to one divided by this element.

Defined in

snarky.d.ts:51

---

isConstant

▸ isConstant(): boolean

Returns

boolean

Defined in

snarky.d.ts:245

---

isZero

▸ isZero(): Bool

Returns

Bool

Defined in

snarky.d.ts:217

---

lt

▸ lt(y): Bool

Check if this [[Field]] is lower than another Field-like value. Returns a [[Bool]].

Field(2).lt(3); // Bool(true)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:122

---

lte

▸ lte(y): Bool

Check if this [[Field]] is lower than or equal to another Field-like value. Returns a [[Bool]].

Field(2).lte(3); // Bool(true)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:131

---

mul

▸ mul(y): Field

Multiplies this [[Field]] element with another coercible to a field.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Field

Defined in

snarky.d.ts:66

---

neg

▸ neg(): Field

Negates this [[Field]]. This is equivalent to multiplying the [[Field]] by -1.

const negOne = Field.one.neg();
negOne.assertEquals(-1);

Returns

Field

Defined in

snarky.d.ts:39

---

ofFields

▸ ofFields(fields): Field

Parameters

Name	Type
fields	Field[]

Returns

Field

Defined in

snarky.d.ts:301

---

rangeCheckHelper

▸ rangeCheckHelper(numBits): Field

Parameters

Name	Type
numBits	number

Returns

Field

Defined in

snarky.d.ts:243

---

seal

▸ seal(): Field

Returns

Field

Defined in

snarky.d.ts:241

---

sizeInFields

▸ sizeInFields(): number

Returns

number

Defined in

snarky.d.ts:109

---

sqrt

▸ sqrt(): Field

Square roots this [[Field]] element.

x.square().sqrt().assertEquals(x);

Returns

Field

Defined in

snarky.d.ts:90

---

square

▸ square(): Field

Squares this [[Field]] element.

const x2 = x.square();
x2.assertEquals(x.mul(x));

Returns

Field

Defined in

snarky.d.ts:81

---

sub

▸ sub(y): Field

Subtracts another [[Field]]-like element from this one.

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Field

Defined in

snarky.d.ts:61

---

toBigInt

▸ toBigInt(): bigint

Serialize the [[Field]] to a bigint. This operation does NOT affect the circuit and can't be used to prove anything about the bigint representation of the Field.

Returns

bigint

Defined in

snarky.d.ts:101

---

toBits

▸ toBits(): Bool[]

Little endian binary representation of the field element.

Returns

Bool[]

Defined in

snarky.d.ts:222

▸ toBits(length): Bool[]

Little endian binary representation of the field element. Fails if the field element cannot fit in length bits.

Parameters

Name	Type
length	number

Returns

Bool[]

Defined in

snarky.d.ts:228

---

toConstant

▸ toConstant(): Field

Returns

Field

Defined in

snarky.d.ts:246

---

toFields

▸ toFields(): Field[]

Returns

Field[]

Defined in

snarky.d.ts:111

---

toJSON

▸ toJSON(): JSONValue

Serialize the [[Field]] to a JSON string. This operation does NOT affect the circuit and can't be used to prove anything about the string representation of the Field.

Returns

JSONValue

Defined in

snarky.d.ts:106

---

toString

▸ toString(): string

Serialize the [[Field]] to a string, e.g. for printing. This operation does NOT affect the circuit and can't be used to prove anything about the string representation of the Field.

Returns

string

Defined in

snarky.d.ts:96

---

check

▸ Static check(x): void

Parameters

Name	Type
x	Field

Returns

void

Defined in

snarky.d.ts:344

---

fromBigInt

▸ Static fromBigInt(x): Field

Parameters

Name	Type
x	bigint

Returns

Field

Defined in

snarky.d.ts:342

---

fromJSON

▸ Static fromJSON(x): null | Field

Parameters

Name	Type
x	JSONValue

Returns

null | Field

Defined in

snarky.d.ts:338

---

fromNumber

▸ Static fromNumber(x): Field

Parameters

Name	Type
x	number

Returns

Field

Defined in

snarky.d.ts:341

---

fromString

▸ Static fromString(x): Field

Parameters

Name	Type
x	string

Returns

Field

Defined in

snarky.d.ts:340

---

ofBits

▸ Static ofBits(x): Field

Converts a bit array into a field element (little endian) Fails if the field element cannot fit given too many bits.

TODO: Rename to fromBits

Parameters

Name	Type
x	(boolean | Bool)[]

Returns

Field

Defined in

snarky.d.ts:325

---

ofFields

▸ Static ofFields(fields): Field

Parameters

Name	Type
fields	Field[]

Returns

Field

Defined in

snarky.d.ts:304

---

random

▸ Static random(): Field

A random field element.

Returns

Field

Defined in

snarky.d.ts:271

---

sizeInFields

▸ Static sizeInFields(): number

Returns

number

Defined in

snarky.d.ts:306

---

toFields

▸ Static toFields(x): Field[]

Parameters

Name	Type
x	Field

Returns

Field[]

Defined in

snarky.d.ts:308

---

toInput

▸ Static toInput(x): Object

Parameters

Name	Type
x	Field

Returns

Object

Name	Type
fields	Field[]

Defined in

snarky.d.ts:347

---

toJSON

▸ Static toJSON(x): JSONValue

Parameters

Name	Type
x	Field

Returns

JSONValue

Defined in

snarky.d.ts:337