# Field

# Class: Field

A Field is an element of a prime order finite field. Every other provable type is built using the Field type.

The field is the pasta base field of order 2^254 + 0x224698fc094cf91b992d30ed00000001 (ORDER).

You can create a new Field from everything "field-like" (`bigint`

, integer `number`

, decimal `string`

, `Field`

).

`Example`

`Field(10n); // Field contruction from a big integer`

Field(100); // Field construction from a number

Field("1"); // Field construction from a decimal string

**Beware**: Fields *cannot* be constructed from fractional numbers or alphanumeric strings:

`Field(3.141); // ERROR: Cannot convert a float to a field element`

Field("abc"); // ERROR: Invalid argument "abc"

Creating a Field from a negative number can result in unexpected behavior if you are not familiar with modular arithmetic.

`Example`

`const x = Field(-1); // Valid Field construction from negative number`

const y = Field(Field.ORDER - 1n); // equivalent to `x`

**Important**: All the functions defined on a Field (arithmetic, logic, etc.) take their arguments as "field-like". A Field itself is also defined as a "field-like" element.

`Param`

the value to convert to a Field

## Table of contents

### Constructors

### Properties

### Methods

- #compare
- #toConstant
- add
- assertBool
- assertEquals
- assertGreaterThan
- assertGreaterThanOrEqual
- assertLessThan
- assertLessThanOrEqual
- assertNotEquals
- div
- equals
- greaterThan
- greaterThanOrEqual
- inv
- isConstant
- isEven
- isZero
- lessThan
- lessThanOrEqual
- mul
- neg
- rangeCheckHelper
- seal
- sqrt
- square
- sub
- toAuxiliary
- toBigInt
- toBits
- toConstant
- toFields
- toJSON
- toString
- #checkBitLength
- #isField
- #toConst
- #toVar
- check
- from
- fromBits
- fromBytes
- fromFields
- fromJSON
- random
- readBytes
- sizeInBytes
- sizeInFields
- toAuxiliary
- toBytes
- toFields
- toInput
- toJSON

## Constructors

### constructor

• **new Field**(`x`

)

Coerce anything "field-like" (bigint, number, string, and Field) to a Field.

#### Parameters

Name | Type |
---|---|

`x` | `string` | `number` | `bigint` | `Uint8Array` | `FieldVar` | `Field` |

#### Defined in

## Properties

### value

• **value**: `FieldVar`

#### Defined in

### ORDER

▪ `Static`

**ORDER**: `bigint`

= `Fp.modulus`

The order of the pasta curve that Field type build on as a `bigint`

.
Order of the Field is 28948022309329048855892746252171976963363056481941560715954676764349967630337.

#### Defined in

## Methods

### #compare

▸ `Private`

**#compare**(`y`

): `Object`

#### Parameters

Name | Type |
---|---|

`y` | `FieldVar` |

#### Returns

`Object`

Name | Type |
---|---|

`less` | `Bool` |

`lessOrEqual` | `Bool` |

#### Defined in

### #toConstant

▸ `Private`

**#toConstant**(`name`

): `ConstantField`

#### Parameters

Name | Type |
---|---|

`name` | `string` |

#### Returns

#### Defined in

### add

▸ **add**(`y`

): `Field`

Add a "field-like" value to this Field element.

`Example`

`const x = Field(3);`

const sum = x.add(5);

sum.assertEquals(Field(8));

**Warning**: This is a modular addition in the pasta field.

`Example`

`const x = Field(1);`

const sum = x.add(Field(-7));

// If you try to print sum - `console.log(sum.toBigInt())` - you will realize that it prints a very big integer because this is modular arithmetic, and 1 + (-7) circles around the field to become p - 6.

// You can use the reverse operation of addition (substraction) to prove the sum is calculated correctly.

sum.sub(x).assertEquals(Field(-7));

sum.sub(Field(-7)).assertEquals(x);

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Field element equivalent to the modular addition of the two value.

#### Defined in

### assertBool

▸ **assertBool**(`message?`

): `void`

Assert that this Field is equal to 1 or 0 as a "field-like" value.
Calling this function is equivalent to `Bool.or(Field(...).equals(1), Field(...).equals(0)).assertEquals(Bool(true))`

.

**Important**: If an assertion fails, the code throws an error.

#### Parameters

Name | Type |
---|---|

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertEquals

▸ **assertEquals**(`y`

, `message?`

): `void`

Assert that this Field is equal another "field-like" value.
Calling this function is equivalent to `Field(...).equals(...).assertEquals(Bool(true))`

.
See equals for more details.

**Important**: If an assertion fails, the code throws an error.

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertGreaterThan

▸ **assertGreaterThan**(`y`

, `message?`

): `void`

Assert that this Field is greater than another "field-like" value.
Calling this function is equivalent to `Field(...).greaterThan(...).assertEquals(Bool(true))`

.
See greaterThan for more details.

**Important**: If an assertion fails, the code throws an error.

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertGreaterThanOrEqual

▸ **assertGreaterThanOrEqual**(`y`

, `message?`

): `void`

Assert that this Field is greater than or equal to another "field-like" value.
Calling this function is equivalent to `Field(...).greaterThanOrEqual(...).assertEquals(Bool(true))`

.
See greaterThanOrEqual for more details.

**Important**: If an assertion fails, the code throws an error.

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertLessThan

▸ **assertLessThan**(`y`

, `message?`

): `void`

Assert that this Field is less than another "field-like" value.
Calling this function is equivalent to `Field(...).lessThan(...).assertEquals(Bool(true))`

.
See lessThan for more details.

**Important**: If an assertion fails, the code throws an error.

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertLessThanOrEqual

▸ **assertLessThanOrEqual**(`y`

, `message?`

): `void`

Assert that this Field is less than or equal to another "field-like" value.
Calling this function is equivalent to `Field(...).lessThanOrEqual(...).assertEquals(Bool(true))`

.
See lessThanOrEqual for more details.

**Important**: If an assertion fails, the code throws an error.

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### assertNotEquals

▸ **assertNotEquals**(`y`

, `message?`

): `void`

Assert that this Field does not equal another field-like value.

Note: This uses fewer constraints than `x.equals(y).assertFalse()`

.

`Example`

`x.assertNotEquals(0, "expect x to be non-zero");`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

`message?` | `string` |

#### Returns

`void`

#### Defined in

### div

▸ **div**(`y`

): `Field`

Divide another "field-like" value through this Field.

Proves that the denominator is non-zero, or throws a "Division by zero" error.

`Example`

`const x = Field(6);`

const quotient = x.div(Field(3));

quotient.assertEquals(Field(2));

**Warning**: This is a modular division in the pasta field. You can think this as the reverse operation of modular multiplication.

`Example`

`const x = Field(2);`

const y = Field(5);

const quotient = x.div(y);

// If you try to print quotient - `console.log(quotient.toBigInt())` - you will realize that it prints a very big integer because this is a modular inverse.

// You can use the reverse operation of division (multiplication) to prove the quotient is calculated correctly.

quotient.mul(y).assertEquals(x);

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Field element equivalent to the modular division of the two value.

#### Defined in

### equals

▸ **equals**(`y`

): `Bool`

Check if this Field is equal another "field-like" value. Returns a Bool, which is a provable type and can be used to prove the validity of this statement.

`Example`

`Field(5).equals(5).assertEquals(Bool(true));`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Bool representing if this Field is equal another "field-like" value.

#### Defined in

### greaterThan

▸ **greaterThan**(`y`

): `Bool`

Check if this Field is greater than another "field-like" value. Returns a Bool, which is a provable type and can be used to prove the validity of this statement.

`Example`

`Field(5).greaterThan(3).assertEquals(Bool(true));`

**Warning**: Comparison methods currently only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

**Warning**: As this method compares the bigint value of a Field, it can result in unexpected behaviour when used with negative inputs or modular division.

`Example`

`Field(1).div(Field(2)).greaterThan(Field(1).div(Field(3))).assertEquals(Bool(true)); // This code will throw an error`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Bool representing if this Field is greater than another "field-like" value.

#### Defined in

### greaterThanOrEqual

▸ **greaterThanOrEqual**(`y`

): `Bool`

Check if this Field is greater than or equal another "field-like" value. Returns a Bool, which is a provable type and can be used to prove the validity of this statement.

`Example`

`Field(3).greaterThanOrEqual(3).assertEquals(Bool(true));`

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

**Warning**: As this method compares the bigint value of a Field, it can result in unexpected behaviour when used with negative inputs or modular division.

`Example`

`Field(1).div(Field(2)).greaterThanOrEqual(Field(1).div(Field(3))).assertEquals(Bool(true)); // This code will throw an error`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Bool representing if this Field is greater than or equal another "field-like" value.

#### Defined in

### inv

▸ **inv**(): `Field`

Modular inverse of this Field element. Equivalent to 1 divided by this Field, in the sense of modular arithmetic.

Proves that this Field is non-zero, or throws a "Division by zero" error.

`Example`

`const someField = Field(42);`

const inverse = someField.inv();

inverse.assertEquals(Field(1).div(example)); // This statement is always true regardless of the value of `someField`

**Warning**: This is a modular inverse. See div method for more details.

#### Returns

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

#### Defined in

### isConstant

▸ **isConstant**(): this is Object

Check whether this Field element is a hard-coded constant in the constraint system. If a Field is constructed outside a zkApp method, it is a constant.

`Example`

`console.log(Field(42).isConstant()); // true`

`Example`

`\@method myMethod(x: Field) {`

console.log(x.isConstant()); // false

}

#### Returns

this is Object

A `boolean`

showing if this Field is a constant or not.

#### Defined in

### isEven

▸ **isEven**(): `Bool`

Checks if this Field is even. Returns `true`

for even elements and `false`

for odd elements.

`Example`

`let a = Field(5);`

a.isEven(); // false

a.isEven().assertTrue(); // throws, as expected!

let b = Field(4);

b.isEven(); // true

b.isEven().assertTrue(); // does not throw, as expected!

#### Returns

#### Defined in

### isZero

▸ **isZero**(): `Bool`

`Deprecated`

use `x.equals(0)`

which is equivalent

#### Returns

#### Defined in

### lessThan

▸ **lessThan**(`y`

): `Bool`

Check if this Field is less than another "field-like" value. Returns a Bool, which is a provable type and can be used prove to the validity of this statement.

`Example`

`Field(2).lessThan(3).assertEquals(Bool(true));`

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

**Warning**: As this method compares the bigint value of a Field, it can result in unexpected behavior when used with negative inputs or modular division.

`Example`

`Field(1).div(Field(3)).lessThan(Field(1).div(Field(2))).assertEquals(Bool(true)); // This code will throw an error`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Bool representing if this Field is less than another "field-like" value.

#### Defined in

### lessThanOrEqual

▸ **lessThanOrEqual**(`y`

): `Bool`

Check if this Field is less than or equal to another "field-like" value. Returns a Bool, which is a provable type and can be used to prove the validity of this statement.

`Example`

`Field(3).lessThanOrEqual(3).assertEquals(Bool(true));`

**Warning**: Comparison methods only support Field elements of size <= 253 bits in provable code.
The method will throw if one of the inputs exceeds 253 bits.

**Warning**: As this method compares the bigint value of a Field, it can result in unexpected behaviour when used with negative inputs or modular division.

`Example`

`Field(1).div(Field(3)).lessThanOrEqual(Field(1).div(Field(2))).assertEquals(Bool(true)); // This code will throw an error`

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Bool representing if this Field is less than or equal another "field-like" value.

#### Defined in

### mul

▸ **mul**(`y`

): `Field`

Multiply another "field-like" value with this Field element.

`Example`

`const x = Field(3);`

const product = x.mul(Field(5));

product.assertEquals(Field(15));

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Field element equivalent to the modular difference of the two value.

#### Defined in

### neg

▸ **neg**(): `Field`

Negate a Field. This is equivalent to multiplying the Field by -1.

`Example`

`const negOne = Field(1).neg();`

negOne.assertEquals(-1);

`Example`

`const someField = Field(42);`

someField.neg().assertEquals(someField.mul(Field(-1))); // This statement is always true regardless of the value of `someField`

**Warning**: This is a modular negation. For details, see the sub method.

#### Returns

A Field element that is equivalent to the element multiplied by -1.

#### Defined in

### rangeCheckHelper

▸ **rangeCheckHelper**(`length`

): `Field`

Create a new Field element from the first `length`

bits of this Field element.

The `length`

has to be a multiple of 16, and has to be between 0 and 255, otherwise the method throws.

As Field elements are represented using little endian binary representation,
the resulting Field element will equal the original one if it fits in `length`

bits.

#### Parameters

Name | Type | Description |
---|---|---|

`length` | `number` | The number of bits to take from this Field element. |

#### Returns

A Field element that is equal to the `length`

of this Field element.

#### Defined in

### seal

▸ **seal**(): `Field`

**Warning**: This function is mainly for internal use. Normally it is not intended to be used by a zkApp developer.

In o1js, addition and scaling (multiplication of variables by a constant) of variables is represented as an AST - abstract syntax tree. For example, the expression `x.add(y).mul(2)`

is represented as `Scale(2, Add(x, y))`

.

A new internal variable is created only when the variable is needed in a multiplicative or any higher level constraint (for example multiplication of two Field elements) to represent the operation.

The `seal()`

function tells o1js to stop building an AST and create a new variable right away.

#### Returns

A Field element that is equal to the result of AST that was previously on this Field element.

#### Defined in

### sqrt

▸ **sqrt**(): `Field`

Take the square root of this Field element.

Proves that the Field element has a square root in the finite field, or throws if it doesn't.

`Example`

`let z = x.sqrt();`

z.mul(z).assertEquals(x); // true for every `x`

**Warning**: This is a modular square root, which is any number z that satisfies z*z = x (mod p).
Note that, if a square root z exists, there also exists a second one, -z (which is different if z != 0).
Therefore, this method leaves an adversarial prover the choice between two different values to return.

#### Returns

A Field element equivalent to the square root of the Field element.

#### Defined in

### square

▸ **square**(): `Field`

Square this Field element.

`Example`

`const someField = Field(7);`

const square = someField.square();

square.assertEquals(someField.mul(someField)); // This statement is always true regardless of the value of `someField`

** Warning: This is a modular multiplication. See `mul()`

method for more details.

#### Returns

A Field element equivalent to the multiplication of the Field element with itself.

#### Defined in

### sub

▸ **sub**(`y`

): `Field`

Substract another "field-like" value from this Field element.

`Example`

`const x = Field(3);`

const difference = x.sub(5);

difference.assertEquals(Field(-2));

**Warning**: This is a modular substraction in the pasta field.

`Example`

`const x = Field(1);`

const difference = x.sub(Field(2));

// If you try to print difference - `console.log(difference.toBigInt())` - you will realize that it prints a very big integer because this is modular arithmetic, and 1 - 2 circles around the field to become p - 1.

// You can use the reverse operation of substraction (addition) to prove the difference is calculated correctly.

difference.add(Field(2)).assertEquals(x);

#### Parameters

Name | Type |
---|---|

`y` | `string` | `number` | `bigint` | `Field` |

#### Returns

A Field element equivalent to the modular difference of the two value.

#### Defined in

### toAuxiliary

▸ **toAuxiliary**(): []

This function is the implementation of toAuxiliary for the Field type.

As the primitive Field type has no auxiliary data associated with it, this function will always return an empty array.

#### Returns

[]

#### Defined in

### toBigInt

▸ **toBigInt**(): `bigint`

Serialize the Field to a bigint, e.g. for printing. Trying to print a Field without this function will directly stringify the Field object, resulting in unreadable output.

**Warning**: This operation does *not* affect the circuit and can't be used to prove anything about the bigint representation of the Field. Use the operation only during debugging.

`Example`

`const someField = Field(42);`

console.log(someField.toBigInt());

#### Returns

`bigint`

A bigint equivalent to the bigint representation of the Field.

#### Defined in

### toBits

▸ **toBits**(`length?`

): `Bool`

[]

Returns an array of Bool elements representing little endian binary representation of this Field element.

If you use the optional `length`

argument, proves that the field element fits in `length`

bits.
The `length`

has to be between 0 and 255 and the method throws if it isn't.

**Warning**: The cost of this operation in a zk proof depends on the `length`

you specify,
which by default is 255 bits. Prefer to pass a smaller `length`

if possible.

#### Parameters

Name | Type | Description |
---|---|---|

`length?` | `number` | the number of bits to fit the element. If the element does not fit in `length` bits, the functions throws an error. |

#### Returns

`Bool`

[]

An array of Bool element representing little endian binary representation of this Field.

#### Defined in

### toConstant

▸ **toConstant**(): `ConstantField`

Create a Field element equivalent to this Field element's value, but is a constant. See isConstant for more information about what is a constant Field.

`Example`

`const someField = Field(42);`

someField.toConstant().assertEquals(someField); // Always true

#### Returns

A constant Field element equivalent to this Field element.

#### Defined in

### toFields

▸ **toFields**(): `Field`

[]

This function is the implementation of toFields for the Field type.

The result will be always an array of length 1, where the first and only element equals the Field itself.

#### Returns

`Field`

[]

A Field array of length 1 created from this Field.

#### Defined in

### toJSON

▸ **toJSON**(): `string`

Serialize the Field to a JSON string, e.g. for printing. Trying to print a Field without this function will directly stringify the Field object, resulting in unreadable output.

**Warning**: This operation does *not* affect the circuit and can't be used to prove anything about the JSON string representation of the Field. Use the operation only during debugging.

`Example`

`const someField = Field(42);`

console.log(someField.toJSON());

#### Returns

`string`

A string equivalent to the JSON representation of the Field.

#### Defined in

### toString

▸ **toString**(): `string`

Serialize the Field to a string, e.g. for printing. Trying to print a Field without this function will directly stringify the Field object, resulting in unreadable output.

**Warning**: This operation does *not* affect the circuit and can't be used to prove anything about the string representation of the Field. Use the operation only during debugging.

`Example`

`const someField = Field(42);`

console.log(someField.toString());

#### Returns

`string`

A string equivalent to the string representation of the Field.

#### Defined in

### #checkBitLength

▸ `Static`

`Private`

**#checkBitLength**(`name`

, `length`

): `void`

#### Parameters

Name | Type |
---|---|

`name` | `string` |

`length` | `number` |

#### Returns

`void`

#### Defined in

### #isField

▸ `Static`

`Private`

**#isField**(`x`

): x is Field

#### Parameters

Name | Type |
---|---|

`x` | `string` | `number` | `bigint` | `Uint8Array` | `FieldVar` | `Field` |

#### Returns

x is Field

#### Defined in

### #toConst

▸ `Static`

`Private`

**#toConst**(`x`

): `Uint8Array`

#### Parameters

Name | Type |
---|---|

`x` | `string` | `number` | `bigint` | `ConstantField` |

#### Returns

`Uint8Array`

#### Defined in

### #toVar

▸ `Static`

`Private`

**#toVar**(`x`

): `FieldVar`

#### Parameters

Name | Type |
---|---|

`x` | `string` | `number` | `bigint` | `Field` |

#### Returns

#### Defined in

### check

▸ `Static`

**check**(): `void`

This function is the implementation of check in Field type.

As any field element can be a Field, this function does not create any assertions, so it does nothing.

#### Returns

`void`

#### Defined in

### from

▸ `Static`

**from**(`x`

): `Field`

#### Parameters

Name | Type |
---|---|

`x` | `string` | `number` | `bigint` | `Field` |

#### Returns

#### Defined in

### fromBits

▸ `Static`

**fromBits**(`bits`

): `Field`

Convert a bit array into a Field element using little endian binary representation

The method throws if the given bits do not fit in a single Field element. A Field element can be at most 255 bits.

**Important**: If the given `bytes`

array is an array of `booleans`

or Bool elements that all are `constant`

, the resulting Field element will be a constant as well. Or else, if the given array is a mixture of constants and variables of Bool type, the resulting Field will be a variable as well.

#### Parameters

Name | Type |
---|---|

`bits` | (`boolean` | `Bool` )[] |

#### Returns

A Field element matching the little endian binary representation of the given `bytes`

array.

#### Defined in

### fromBytes

▸ `Static`

**fromBytes**(`bytes`

): `Field`

Coerce a new Field element using the little-endian representation of the given `bytes`

array.
Note that the given `bytes`

array may have at most 32 elements as the Field is a `finite-field`

in the order of ORDER.

**Warning**: This operation does *not* affect the circuit and can't be used to prove anything about the byte representation of the Field.

#### Parameters

Name | Type | Description |
---|---|---|

`bytes` | `number` [] | The bytes array to coerce the Field from. |

#### Returns

A new Field element created using the little-endian representation of the given `bytes`

array.

#### Defined in

### fromFields

▸ `Static`

**fromFields**(`fields`

): `Field`

Implementation of fromFields for the Field type.

**Warning**: This function is designed for internal use. It is not intended to be used by a zkApp developer.

Creates a Field from an array of Fields of length 1.

#### Parameters

Name | Type | Description |
---|---|---|

`fields` | `Field` [] | an array of length 1 serialized from Field elements. |

#### Returns

The first Field element of the given array.

#### Defined in

### fromJSON

▸ `Static`

**fromJSON**(`json`

): `Field`

Deserialize a JSON string containing a "field-like" value into a Field element.

**Warning**: 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 |
---|---|

`json` | `string` |

#### Returns

A Field coerced from the given JSON string.

#### Defined in

### random

▸ `Static`

**random**(): `Field`

A random Field element.

`Example`

`console.log(Field.random().toBigInt()); // Run this code twice!`

#### Returns

A random Field element.

#### Defined in

### readBytes

▸ `Static`

**readBytes**<`N`

>(`bytes`

, `offset`

): [value: Field, offset: number]

Part of the `Binable`

interface.

**Warning**: This function is for internal use. It is not intended to be used by a zkApp developer.

#### Type parameters

Name | Type |
---|---|

`N` | extends `number` |

#### Parameters

Name | Type |
---|---|

`bytes` | `number` [] |

`offset` | `NonNegativeInteger` <`N` > |

#### Returns

[value: Field, offset: number]

#### Defined in

### sizeInBytes

▸ `Static`

**sizeInBytes**(): `number`

**Warning**: This function is mainly for internal use. Normally it is not intended to be used by a zkApp developer.

As all Field elements have 31 bits, this function returns 31.

#### Returns

`number`

The size of a Field element - 31.

#### Defined in

### sizeInFields

▸ `Static`

**sizeInFields**(): `number`

This function is the implementation of sizeInFields for the Field type.

Size of the Field type is 1, as it is the primitive type. This function returns a regular number, so you cannot use it to prove something on chain. You can use it during debugging or to understand the memory complexity of some type.

`Example`

`console.log(Field.sizeInFields()); // Prints 1`

#### Returns

`number`

A number representing the size of the Field type in terms of Field type itself.

#### Defined in

### toAuxiliary

▸ `Static`

**toAuxiliary**(): []

This function is the implementation of toAuxiliary for the Field type.

As the primitive Field type has no auxiliary data associated with it, this function will always return an empty array.

#### Returns

[]

#### Defined in

### toBytes

▸ `Static`

**toBytes**(`x`

): `number`

[]

Create an array of digits equal to the little-endian byte order of the given Field element.
Note that the array has always 32 elements as the Field is a `finite-field`

in the order of ORDER.

#### Parameters

Name | Type |
---|---|

`x` | `Field` |

#### Returns

`number`

[]

An array of digits equal to the little-endian byte order of the given Field element.

#### Defined in

### toFields

▸ `Static`

**toFields**(`x`

): `Field`

[]

This function is the implementation of toFields for the Field type.

Static function to serializes a Field into an array of Field elements. This will be always an array of length 1, where the first and only element equals the given parameter itself.

#### Parameters

Name | Type |
---|---|

`x` | `Field` |

#### Returns

`Field`

[]

A Field array of length 1 created from this Field.

#### Defined in

### toInput

▸ `Static`

**toInput**(`x`

): `Object`

**Warning**: This function is mainly for internal use. Normally it is not intended to be used by a zkApp developer.

This function is the implementation of `ProvableExtended.toInput()`

for the Field type.

#### Parameters

Name | Type |
---|---|

`x` | `Field` |

#### Returns

`Object`

An object where the `fields`

key is a Field array of length 1 created from this Field.

Name | Type |
---|---|

`fields` | `Field` [] |

#### Defined in

### toJSON

▸ `Static`

**toJSON**(`x`

): `string`

Serialize the given Field element to a JSON string, e.g. for printing. Trying to print a Field without this function will directly stringify the Field object, resulting in unreadable output.

**Warning**: This operation does *not* affect the circuit and can't be used to prove anything about the JSON string representation of the Field. Use the operation only during debugging.

`Example`

`const someField = Field(42);`

console.log(Field.toJSON(someField));

#### Parameters

Name | Type |
---|---|

`x` | `Field` |

#### Returns

`string`

A string equivalent to the JSON representation of the given Field.