Class: Field

Table of contents

Constructors

• constructor

Properties

• ORDER
• minusOne
• one
• zero

Methods

• add
• assertBool
• assertBoolean
• assertEquals
• assertGreaterThan
• assertGreaterThanOrEqual
• assertGt
• assertGte
• assertLessThan
• assertLessThanOrEqual
• assertLt
• assertLte
• div
• equals
• fromFields
• greaterThan
• greaterThanOrEqual
• gt
• gte
• inv
• isConstant
• isZero
• lessThan
• lessThanOrEqual
• lt
• lte
• mul
• neg
• rangeCheckHelper
• seal
• sizeInFields
• sqrt
• square
• sub
• toBigInt
• toBits
• toConstant
• toFields
• toJSON
• toString
• check
• fromBits
• fromBytes
• fromFields
• fromJSON
• random
• readBytes
• sizeInBytes
• sizeInFields
• toAuxiliary
• toBytes
• 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:61

Properties

ORDER

▪ Static ORDER: bigint

The field order as a bigint.

Defined in

snarky.d.ts:432

---

minusOne

▪ Static minusOne: Field

Deprecated

Static constant values on Field are deprecated in favor of using the constructor Field(-1).

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

Defined in

snarky.d.ts:428

---

one

▪ Static one: Field

Deprecated

Static constant values on Field are deprecated in favor of using the constructor Field(1).

The number 1 as a [[Field]].

Defined in

snarky.d.ts:416

---

zero

▪ Static zero: Field

Deprecated

Static constant values on Field are deprecated in favor of using the constructor Field(0).

The number 0 as a [[Field]].

Defined in

snarky.d.ts:422

Methods

add

▸ add(y): Field

Adds this Field element to another to a Field element.

let a = Field(3);
let sum = a.add(5)

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Field

Defined in

snarky.d.ts:94

---

assertBool

▸ assertBool(message?): void

Assert that this Field is either 0 or 1.

Field(0).assertBool();

Parameters

Name	Type
message?	string

Returns

void

Defined in

snarky.d.ts:356

---

assertBoolean

▸ assertBoolean(message?): void

Deprecated

Deprecated - use assertBool instead

Assert that this Field is either 0 or 1.

Field(0).assertBoolean();

Parameters

Name	Type
message?	string

Returns

void

Defined in

snarky.d.ts:368

---

assertEquals

▸ assertEquals(y, message?): void

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

Field(1).assertEquals(1);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:346

---

assertGreaterThan

▸ assertGreaterThan(y, message?): void

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

Field(1).assertGt(0);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:230

---

assertGreaterThanOrEqual

▸ assertGreaterThanOrEqual(y, message?): void

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

Field(1).assertGte(0);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:243

---

assertGt

▸ assertGt(y, message?): void

Deprecated

Deprecated - use assertGreaterThan instead

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

Field(1).assertGt(0);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:325

---

assertGte

▸ assertGte(y, message?): void

Deprecated

Deprecated - use assertGreaterThanOrEqual instead

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

Field(1).assertGte(0);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:336

---

assertLessThan

▸ assertLessThan(y, message?): void

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

Field(1).assertLessThan(2);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:207

---

assertLessThanOrEqual

▸ assertLessThanOrEqual(y, message?): void

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

Field(1).assertLessThanOrEqual(2);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:217

---

assertLt

▸ assertLt(y, message?): void

Deprecated

Deprecated - use assertLessThan instead

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

Field(1).assertLessThan(2);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:304

---

assertLte

▸ assertLte(y, message?): void

Deprecated

Deprecated - use assertLessThanOrEqualinstead

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

Field(1).assertLte(2);

Parameters

Name	Type
y	string | number | boolean | Field
message?	string

Returns

void

Defined in

snarky.d.ts:314

---

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:109

---

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:391

---

fromFields

▸ fromFields(fields): Field

Creates a data structure from an array of serialized Field elements.

Parameters

Name	Type
fields	Field[]

Returns

Field

Defined in

snarky.d.ts:469

---

greaterThan

▸ greaterThan(y): Bool

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

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

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:185

---

greaterThanOrEqual

▸ greaterThanOrEqual(y): Bool

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

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

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:195

---

gt

▸ gt(y): Bool

Deprecated

Deprecated - use {@link greaterThan} instead

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:280

---

gte

▸ gte(y): Bool

Deprecated

Deprecated - use greaterThanOrEqual instead

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:291

---

inv

▸ inv(): Field

Inverts this Field element.

const invX = x.inv();
invX.assertEquals(Field(1).div(x));

Returns

Field

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

Defined in

snarky.d.ts:84

---

isConstant

▸ isConstant(): boolean

Checks whether this is a hard-coded constant in the Circuit.

Returns

boolean

Defined in

snarky.d.ts:401

---

isZero

▸ isZero(): Bool

Returns

Bool

Defined in

snarky.d.ts:370

---

lessThan

▸ lessThan(y): Bool

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

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

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:165

---

lessThanOrEqual

▸ lessThanOrEqual(y): Bool

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

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

Parameters

Name	Type
y	string | number | boolean | Field

Returns

Bool

Defined in

snarky.d.ts:175

---

lt

▸ lt(y): Bool

Deprecated

Deprecated - use lessThan instead

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:258

---

lte

▸ lte(y): Bool

Deprecated

Deprecated - use lessThanOrEqual instead

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:269

---

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:104

---

neg

▸ neg(): Field

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

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

Returns

Field

Defined in

snarky.d.ts:72

---

rangeCheckHelper

▸ rangeCheckHelper(numBits): Field

Parameters

Name	Type
numBits	number

Returns

Field

Defined in

snarky.d.ts:396

---

seal

▸ seal(): Field

Returns

Field

Defined in

snarky.d.ts:394

---

sizeInFields

▸ sizeInFields(): number

Returns the size of this type.

Returns

number

Defined in

snarky.d.ts:149

---

sqrt

▸ sqrt(): Field

Square roots this Field element.

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

Returns

Field

Defined in

snarky.d.ts:128

---

square

▸ square(): Field

Squares this Field element.

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

Returns

Field

Defined in

snarky.d.ts:119

---

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:99

---

toBigInt

▸ toBigInt(): bigint

Serialize this instance of a 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:139

---

toBits

▸ toBits(): Bool[]

Little endian binary representation of the field element.

Returns

Bool[]

Defined in

snarky.d.ts:375

▸ 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:381

---

toConstant

▸ toConstant(): Field

Returns a constant.

Returns

Field

Defined in

snarky.d.ts:406

---

toFields

▸ toFields(): Field[]

Serializes this data structure into Field elements.

Returns

Field[]

Defined in

snarky.d.ts:154

---

toJSON

▸ toJSON(): string

Serialize this instance of a 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

string

Defined in

snarky.d.ts:144

---

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:134

---

check

▸ Static check(x): void

Parameters

Name	Type
x	Field

Returns

void

Defined in

snarky.d.ts:527

---

fromBits

▸ Static fromBits(x): Field

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

Parameters

Name	Type
x	(boolean | Bool)[]

Returns

Field

Defined in

snarky.d.ts:503

---

fromBytes

▸ Static fromBytes(bytes): Field

Parameters

Name	Type
bytes	number[]

Returns

Field

Defined in

snarky.d.ts:532

---

fromFields

▸ Static fromFields(fields): Field

Creates a data structure from an array of serialized Field elements.

Parameters

Name	Type
fields	Field[]

Returns

Field

Defined in

snarky.d.ts:474

---

fromJSON

▸ Static fromJSON(x): Field

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

Parameters

Name	Type
x	string

Returns

Field

Defined in

snarky.d.ts:525

---

random

▸ Static random(): Field

A random field element.

Returns

Field

Defined in

snarky.d.ts:437

---

readBytes

▸ Static readBytes(bytes, offset): [value: Field, offset: number]

Parameters

Name	Type
bytes	number[]
offset	number

Returns

[value: Field, offset: number]

Defined in

snarky.d.ts:533

---

sizeInBytes

▸ Static sizeInBytes(): number

Returns

number

Defined in

snarky.d.ts:537

---

sizeInFields

▸ Static sizeInFields(): number

Returns the size of this type.

Returns

number

Defined in

snarky.d.ts:479

---

toAuxiliary

▸ Static toAuxiliary(x?): []

Static method to serialize a Field into its auxiliary data.

Parameters

Name	Type
x?	Field

Returns

[]

Defined in

snarky.d.ts:488

---

toBytes

▸ Static toBytes(x): number[]

Parameters

Name	Type
x	Field

Returns

number[]

Defined in

snarky.d.ts:531

---

toFields

▸ Static toFields(x): Field[]

Static method to serialize a Field into an array of Field elements.

Parameters

Name	Type
x	Field

Returns

Field[]

Defined in

snarky.d.ts:484

---

toInput

▸ Static toInput(x): Object

Parameters

Name	Type
x	Field

Returns

Object

Name	Type
fields	Field[]

Defined in

snarky.d.ts:530

---

toJSON

▸ Static toJSON(x): string

Serialize a 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.

Parameters

Name	Type
x	Field

Returns

string

Defined in

snarky.d.ts:519