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docs/API.md
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docs/API.md
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@ -39,7 +39,7 @@ Some common functions for modular arithmetic using native JS implementation of B
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#### Defined in
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[modPow.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/modPow.ts#L8)
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[modPow.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modPow.ts#L8)
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___
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@ -49,7 +49,7 @@ ___
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#### Defined in
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phi.ts:1
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[phi.ts:1](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/phi.ts#L1)
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___
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@ -59,7 +59,7 @@ ___
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#### Defined in
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[modPow.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/modPow.ts#L7)
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[modPow.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modPow.ts#L7)
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## Functions
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@ -83,7 +83,7 @@ The absolute value of a
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#### Defined in
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[abs.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/abs.ts#L8)
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[abs.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/abs.ts#L8)
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___
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@ -107,7 +107,7 @@ The bit length
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#### Defined in
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[bitLength.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/bitLength.ts#L7)
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[bitLength.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/bitLength.ts#L7)
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___
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@ -137,7 +137,7 @@ x
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#### Defined in
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crt.ts:16
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[crt.ts:16](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/crt.ts#L16)
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___
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@ -167,7 +167,7 @@ A triple (g, x, y), such that ax + by = g = gcd(a, b).
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#### Defined in
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[egcd.ts:17](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/egcd.ts#L17)
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[egcd.ts:17](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/egcd.ts#L17)
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___
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@ -192,7 +192,7 @@ The greatest common divisor of a and b
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#### Defined in
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[gcd.ts:11](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/gcd.ts#L11)
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[gcd.ts:11](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/gcd.ts#L11)
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___
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@ -217,7 +217,7 @@ The least common multiple of a and b
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#### Defined in
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[lcm.ts:11](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/lcm.ts#L11)
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[lcm.ts:11](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/lcm.ts#L11)
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___
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@ -242,7 +242,7 @@ Maximum of numbers a and b
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#### Defined in
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[max.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/max.ts#L9)
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[max.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/max.ts#L9)
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___
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@ -267,7 +267,7 @@ Minimum of numbers a and b
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#### Defined in
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[min.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/min.ts#L9)
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[min.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/min.ts#L9)
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___
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@ -292,7 +292,7 @@ The smallest positive integer that is congruent with (a_1 + ... + a_r) mod n
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#### Defined in
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modAdd.ts:9
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[modAdd.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modAdd.ts#L9)
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___
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@ -321,7 +321,7 @@ The inverse modulo n
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#### Defined in
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[modInv.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/modInv.ts#L14)
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[modInv.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modInv.ts#L14)
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___
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@ -347,7 +347,7 @@ The smallest positive integer that is congruent with (a_1 * ... * a_r) mod n
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#### Defined in
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modMultiply.ts:9
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[modMultiply.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modMultiply.ts#L9)
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___
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@ -378,7 +378,7 @@ b**e mod n
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#### Defined in
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[modPow.ts:22](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/modPow.ts#L22)
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[modPow.ts:22](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/modPow.ts#L22)
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___
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@ -392,7 +392,7 @@ A function that computes the Euler's totien function of a number n, whose prime
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| Name | Type | Description |
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| :------ | :------ | :------ |
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| `primeFactorization` | [`PrimeFactorization`](API.md#primefactorization) | an array of arrays containing the prime power factorization, i.e. for n = (p1**k1)*(p2**k2)*...*(pr**kr), one should provide [[p1, k1], [p2, k2], ... , [pr, kr]] |
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| `primeFactorization` | [`PrimeFactorization`](API.md#primefactorization) | an array of arrays containing the prime power factorization of a number n. For example, for n = (p1**k1)*(p2**k2)*...*(pr**kr), one should provide [[p1, k1], [p2, k2], ... , [pr, kr]] |
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#### Returns
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@ -402,7 +402,7 @@ phi((p1**k1)*(p2**k2)*...*(pr**kr))
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#### Defined in
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phi.ts:9
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[phi.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/phi.ts#L9)
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___
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@ -435,4 +435,4 @@ A bigint with the smallest positive representation of a modulo n
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#### Defined in
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[toZn.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/toZn.ts#L14)
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[toZn.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/toZn.ts#L14)
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@ -16,7 +16,7 @@
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#### Defined in
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[egcd.ts:2](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/egcd.ts#L2)
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[egcd.ts:2](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/egcd.ts#L2)
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___
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#### Defined in
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[egcd.ts:3](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/egcd.ts#L3)
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[egcd.ts:3](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/egcd.ts#L3)
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___
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#### Defined in
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[egcd.ts:4](https://github.com/juanelas/bigint-mod-arith/blob/80793b3/src/ts/egcd.ts#L4)
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[egcd.ts:4](https://github.com/juanelas/bigint-mod-arith/blob/fbe007f/src/ts/egcd.ts#L4)
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@ -3,7 +3,7 @@ export type PrimeFactorization = Array<[bigint, bigint]>
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/**
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* A function that computes the Euler's totien function of a number n, whose prime power factorization is known
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*
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* @param primeFactorization an array of arrays containing the prime power factorization, i.e. for n = (p1**k1)*(p2**k2)*...*(pr**kr), one should provide [[p1, k1], [p2, k2], ... , [pr, kr]]
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* @param primeFactorization an array of arrays containing the prime power factorization of a number n. For example, for n = (p1**k1)*(p2**k2)*...*(pr**kr), one should provide [[p1, k1], [p2, k2], ... , [pr, kr]]
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* @returns phi((p1**k1)*(p2**k2)*...*(pr**kr))
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*/
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export function phi (primeFactorization: PrimeFactorization): bigint {
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