rational

package
v0.0.2-0...-db6250e Latest Latest
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 Go to latest Published: Dec 17, 2020 License: CC0-1.0, CC0-1.0 Imports: 16 Imported by: 4

Documentation

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func AreEqual 

func AreEqual(x *Element, y *Element) bool

AreEqual returns true iff x equals y.

func Cmp 

func Cmp(x *Element, y *Element) int

Cmp returns -1 if x < y, 0 if x == y, and +1 if x > y.

func SetBigRat 

func SetBigRat(q *big.Rat, r *Element) *big.Rat

SetBigRat sets the given *big.Rat q to the value of the given rational r. Returns the *big.Rat q.

Types

type Element 

type Element struct {
	// contains filtered or unexported fields
}

Element is an element of the field of rational numbers.

func Add 

func Add(x *Element, y *Element) *Element

Add returns x + y.

func AddInt64 

func AddInt64(x int64, y *Element) *Element

AddInt64 returns x + y.

func AddInteger 

func AddInteger(x *integer.Element, y *Element) *Element

AddInteger returns x + y.

func CopySlice 

func CopySlice(S []*Element) []*Element

CopySlice returns a copy of the slice S. The capacity will be preserved.

func Divide 

func Divide(x *Element, y *Element) (*Element, error)

Divide returns the quotient x / y. It will return an error if y is zero.

func DotProduct 

func DotProduct(S1 []*Element, S2 []*Element) *Element

DotProduct returns the dot-product of the slices S1 and S2. That is, it returns S1[0] * S2[0] + ... + S1[k] * S2[k], where k+1 is the minimum of len(S1) and len(S2). The dot-product of two empty slices is the zero element.

func FromBigInt 

func FromBigInt(n *big.Int) *Element

FromBigInt returns n as a rational.

func FromBigIntPair 

func FromBigIntPair(a *big.Int, b *big.Int) (*Element, error)

FromBigIntPair returns a/b as a rational. It will return an error if b is zero.

func FromBigRat 

func FromBigRat(q *big.Rat) *Element

FromBigRat returns a *Element with value q.

func FromInt 

func FromInt(n int) *Element

FromInt returns n as a rational.

func FromInt32 

func FromInt32(n int32) *Element

FromInt32 returns n as a rational.

func FromInt32Pair 

func FromInt32Pair(a int32, b int32) (*Element, error)

FromInt32Pair returns a/b as a rational. It will return an error if b is zero.

func FromInt64 

func FromInt64(n int64) *Element

FromInt64 returns a *Element with value n.

func FromInt64Pair 

func FromInt64Pair(a int64, b int64) (*Element, error)

FromInt64Pair returns a/b as a rational. It will return an error if b is zero.

func FromIntPair 

func FromIntPair(a int, b int) (*Element, error)

FromIntPair returns a/b as a rational. It will return an error if b is zero.

func FromInteger 

func FromInteger(n *integer.Element) *Element

FromInteger returns n as a rational.

func FromIntegerPair 

func FromIntegerPair(a *integer.Element, b *integer.Element) (*Element, error)

FromIntegerPair returns a/b as a rational. It will return an error if b is zero.

func FromString 

func FromString(s string) (*Element, error)

FromString returns the rational represented by the string s.

func FromUint64 

func FromUint64(n uint64) *Element

FromUint64 returns a *Element with value n.

func FromUint64Pair 

func FromUint64Pair(a uint64, b uint64) (*Element, error)

FromUint64Pair returns a/b as a rational. It will return an error if b is zero.

func GobDecode 

func GobDecode(dec *gob.Decoder) (*Element, error)

GobDecode reads the next value from the given gob.Decoder and decodes it as a rational.

func GobDecodeSlice 

func GobDecodeSlice(dec *gob.Decoder) ([]*Element, error)

GobDecodeSlice reads the next value from the given gob.Decoder and decodes it as a slice of rationals.

func Inverse 

func Inverse(q *Element) (*Element, error)

Inverse returns 1/q. It will return an error if q is zero.

func Max 

func Max(S ...*Element) (*Element, error)

Max returns the maximum element in the slice S. If S is empty then an error is returned.

func MaxAndIndex 

func MaxAndIndex(S []*Element) (*Element, int, error)

MaxAndIndex returns the maximum element in the slice S, along with the index of the first occurrence of that element in S. If S is empty then an error is returned.

func MaxOfPair 

func MaxOfPair(x *Element, y *Element) *Element

MaxOfPair returns the maximum element of x and y.

func Min 

func Min(S ...*Element) (*Element, error)

Min returns the minimum element in the slice S. If S is empty then an error is returned.

func MinAndIndex 

func MinAndIndex(S []*Element) (*Element, int, error)

MinAndIndex returns the minimum element in the slice S, along with the index of the first occurrence of that element in S. If S is empty then an error is returned.

func MinOfPair 

func MinOfPair(x *Element, y *Element) *Element

MinOfPair returns the minimum element of x and y.

func Multiply 

func Multiply(x *Element, y *Element) *Element

Multiply returns the product x * y.

func MultiplyByInt64ThenAdd 

func MultiplyByInt64ThenAdd(a int64, b *Element, c *Element) *Element

MultiplyByInt64ThenAdd returns the value a * b + c.

func MultiplyByIntegerThenAdd 

func MultiplyByIntegerThenAdd(a *integer.Element, b *Element, c *Element) *Element

MultiplyByIntegerThenAdd returns the value a * b + c.

func MultiplyMultiplyThenAdd 

func MultiplyMultiplyThenAdd(a *Element, b *Element, c *Element, d *Element) *Element

MultiplyMultiplyThenAdd returns the value a * b + c * d.

func MultiplyMultiplyThenSubtract 

func MultiplyMultiplyThenSubtract(a *Element, b *Element, c *Element, d *Element) *Element

MultiplyMultiplyThenSubtract returns the value a * b - c * d.

func MultiplyThenAdd 

func MultiplyThenAdd(a *Element, b *Element, c *Element) *Element

MultiplyThenAdd returns the value a * b + c.

func MultiplyThenSubtract 

func MultiplyThenSubtract(a *Element, b *Element, c *Element) *Element

MultiplyThenSubtract returns the value a * b - c.

func Negate 

func Negate(q *Element) *Element

Negate returns -q.

func One 

func One() *Element

One returns 1.

func Power 

func Power(q *Element, k *integer.Element) (*Element, error)

Power returns q^k.

func PowerInt64 

func PowerInt64(q *Element, k int64) (*Element, error)

PowerInt64 returns q^k.

func Product 

func Product(S ...*Element) *Element

Product returns the product of the elements in the slice S. The product of the empty slice is one.

func SliceFromIntPairs 

func SliceFromIntPairs(S []int) ([]*Element, error)

SliceFromIntPairs returns a slice T generated by S, where 2 * len(T) = len(S) and T[i] = S[2 * i] / S[2 * i + 1].

func SliceFromIntSlice 

func SliceFromIntSlice(S []int) []*Element

SliceFromIntSlice returns a slice of rationals corresponding to the integers in S.

func Sort 

func Sort(S []*Element) []*Element

Sort non-destructively sorts the given slice of integers. The sorted slice is returned.

func Subtract 

func Subtract(x *Element, y *Element) *Element

Subtract returns x - y.

func Sum 

func Sum(S ...*Element) *Element

Sum returns the sum of the elements in the slice S. The sum of the empty slice is the zero element.

func ToElement 

func ToElement(x object.Element) (*Element, error)

ToElement attempts to convert the given object.Element to a rational number. If necessary this will be done by first attempting to convert x to an integer, and then from an integer to a rational.

func Zero 

func Zero() *Element

Zero returns 0.

func (*Element) Abs 

func (q *Element) Abs() *Element

Abs returns the absolute value of q.

func (*Element) BigInt 

func (q *Element) BigInt() (*big.Int, error)

BigInt returns the rational as a *big.Int, or an error if this is not possible.

func (*Element) BigRat 

func (q *Element) BigRat() *big.Rat

BigRat returns the rational as a *big.Rat.

func (*Element) Ceiling 

func (q *Element) Ceiling() *integer.Element

Ceiling returns the smallest integer greater than or equal to q

func (*Element) Decrement 

func (q *Element) Decrement() *Element

Decrement returns q - 1.

func (*Element) Denominator 

func (q *Element) Denominator() *integer.Element

Denominator returns the denominator of q as an integer.

func (*Element) Floor 

func (q *Element) Floor() *integer.Element

Floor returns the biggest integer less than or equal to q

func (*Element) GobDecode 

func (q *Element) GobDecode(buf []byte) error

GobDecode implements the gob.GobDecoder interface. Important: Take great care that you are decoding into a new *Element; the safe way to do this is to use the GobDecode(dec *gob.Decode) function.

func (*Element) GobEncode 

func (q *Element) GobEncode() ([]byte, error)

GobEncode implements the gob.GobEncoder interface.

func (*Element) Hash 

func (q *Element) Hash() hash.Value

Hash returns a hash value for the given rational number.

func (*Element) Increment 

func (q *Element) Increment() *Element

Increment returns q + 1.

func (*Element) Int64 

func (q *Element) Int64() (int64, error)

Int64 returns the rational as an int64, or an error if this is not possible.

func (*Element) Inverse 

func (q *Element) Inverse() (*Element, error)

Inverse returns 1/q. It will return an error if q is zero.

func (*Element) IsEqualTo 

func (q *Element) IsEqualTo(r *Element) bool

IsEqualTo returns true iff q = r.

func (*Element) IsEqualToInt64 

func (q *Element) IsEqualToInt64(r int64) bool

IsEqualToInt64 returns true iff q = r.

func (*Element) IsEqualToInteger 

func (q *Element) IsEqualToInteger(r *integer.Element) bool

IsEqualToInteger returns true iff q = r.

func (*Element) IsEqualToUint64 

func (q *Element) IsEqualToUint64(r uint64) bool

IsEqualToUint64 returns true iff q = r.

func (*Element) IsGreaterThan 

func (q *Element) IsGreaterThan(r *Element) bool

IsGreaterThan returns true iff q > r.

func (*Element) IsGreaterThanInt64 

func (q *Element) IsGreaterThanInt64(r int64) bool

IsGreaterThanInt64 returns true iff q > r.

func (*Element) IsGreaterThanInteger 

func (q *Element) IsGreaterThanInteger(r *integer.Element) bool

IsGreaterThanInteger returns true iff q > r.

func (*Element) IsGreaterThanOrEqualTo 

func (q *Element) IsGreaterThanOrEqualTo(r *Element) bool

IsGreaterThanOrEqualTo returns true iff q >= r.

func (*Element) IsGreaterThanOrEqualToInt64 

func (q *Element) IsGreaterThanOrEqualToInt64(r int64) bool

IsGreaterThanOrEqualToInt64 returns true iff q >= r.

func (*Element) IsGreaterThanOrEqualToInteger 

func (q *Element) IsGreaterThanOrEqualToInteger(r *integer.Element) bool

IsGreaterThanOrEqualToInteger returns true iff q >= r.

func (*Element) IsInt64 

func (q *Element) IsInt64() bool

IsInt64 returns true iff the rational can be expressed as an int64.

func (*Element) IsIntegral 

func (q *Element) IsIntegral() bool

IsIntegral returns true iff q can be represented by an integer.

func (*Element) IsLessThan 

func (q *Element) IsLessThan(r *Element) bool

IsLessThan returns true iff q < r.

func (*Element) IsLessThanInt64 

func (q *Element) IsLessThanInt64(r int64) bool

IsLessThanInt64 returns true iff q < r.

func (*Element) IsLessThanInteger 

func (q *Element) IsLessThanInteger(r *integer.Element) bool

IsLessThanInteger returns true iff q < r.

func (*Element) IsLessThanOrEqualTo 

func (q *Element) IsLessThanOrEqualTo(r *Element) bool

IsLessThanOrEqualTo returns true iff q <= r.

func (*Element) IsLessThanOrEqualToInt64 

func (q *Element) IsLessThanOrEqualToInt64(r int64) bool

IsLessThanOrEqualToInt64 returns true iff q <= r.

func (*Element) IsLessThanOrEqualToInteger 

func (q *Element) IsLessThanOrEqualToInteger(r *integer.Element) bool

IsLessThanOrEqualToInteger returns true iff q <= r.

func (*Element) IsNegative 

func (q *Element) IsNegative() bool

IsNegative returns true iff q < 0.

func (*Element) IsOne 

func (q *Element) IsOne() bool

IsOne returns true iff q is one.

func (*Element) IsPositive 

func (q *Element) IsPositive() bool

IsPositive returns true iff q > 0.

func (*Element) IsUint64 

func (q *Element) IsUint64() bool

IsUint64 returns true iff the rational can be expressed as a uint64.

func (*Element) IsZero 

func (q *Element) IsZero() bool

IsZero returns true iff q is zero.

func (*Element) Negate 

func (q *Element) Negate() *Element

Negate return -q.

func (*Element) Numerator 

func (q *Element) Numerator() *integer.Element

Numerator returns the numerator of q as an integer.

func (*Element) Parent 

func (q *Element) Parent() object.Parent

Parent returns the field of rational numbers as a object.Parent. This can safely be coerced to type Parent.

func (*Element) Power 

func (q *Element) Power(k *integer.Element) (*Element, error)

Power returns q^k.

func (*Element) PowerInt64 

func (q *Element) PowerInt64(k int64) (*Element, error)

PowerInt64 returns q^k.

func (*Element) ScalarMultiplyByInt64 

func (q *Element) ScalarMultiplyByInt64(a int64) *Element

ScalarMultiplyByInt64 returns the product a * q.

func (*Element) ScalarMultiplyByInteger 

func (q *Element) ScalarMultiplyByInteger(a *integer.Element) *Element

ScalarMultiplyByInteger returns the product a * q.

func (*Element) ScalarMultiplyByRational 

func (q *Element) ScalarMultiplyByRational(a *Element) *Element

ScalarMultiplyByRational returns the product a * q.

func (*Element) ScalarMultiplyByUint64 

func (q *Element) ScalarMultiplyByUint64(a uint64) *Element

ScalarMultiplyByUint64 returns the product a * q.

func (*Element) Sign 

func (q *Element) Sign() int

Sign returns the sign of q, i.e. -1 if q < 0; 0 if n == 0; +1 if q > 0.

func (*Element) String 

func (q *Element) String() string

String returns a string representation of the given rational.

func (*Element) ToInteger 

func (q *Element) ToInteger() (*integer.Element, error)

ToInteger return the rational as an integer, or an error if this is not possible.

func (*Element) Uint64 

func (q *Element) Uint64() (uint64, error)

Uint64 returns the rational as a uint64, or an error if this is not possible.

type Parent 

type Parent struct{}

Parent represents the (unique) field of rational numbers.

func Field 

func Field() Parent

Field returns the (unique) field of rational numbers

func (Parent) Add 

func (R Parent) Add(x object.Element, y object.Element) (object.Element, error)

Add returns x + y.

func (Parent) AreEqual 

func (R Parent) AreEqual(x object.Element, y object.Element) (bool, error)

AreEqual returns true iff x equals y.

func (Parent) Cmp 

func (R Parent) Cmp(x object.Element, y object.Element) (int, error)

Cmp returns -1 if x < y, 0 if x == y, and +1 if x > y.

func (Parent) Contains 

func (R Parent) Contains(x object.Element) bool

Contains returns true iff x is a rational number, or can naturally be regarded as a rational number.

func (Parent) Divide 

func (R Parent) Divide(x object.Element, y object.Element) (object.Element, error)

Divide returns the quotient x / y. Returns a errors.DivisionByZero error if y is zero.

func (Parent) DotProduct 

func (R Parent) DotProduct(S1 []object.Element, S2 []object.Element) (object.Element, error)

DotProduct returns the dot-product of the slices S1 and S2. That is, it returns S1[0] * S2[0] + ... + S1[k] * S2[k], where k+1 is the minimum of len(S1) and len(S2). The dot-product of two empty slices is the zero element.

func (Parent) FromInteger 

func (R Parent) FromInteger(n *integer.Element) object.Element

FromInteger returns n as rational number.

func (Parent) FromRational 

func (R Parent) FromRational(q *Element) (object.Element, error)

FromRational returns q.

func (Parent) Inverse 

func (R Parent) Inverse(q object.Element) (object.Element, error)

Inverse returns 1/q. Returns an errors.DivisionByZero error if q is zero.

func (Parent) IsOne 

func (R Parent) IsOne(x object.Element) (bool, error)

IsOne returns true iff x is the rational number 1.

func (Parent) IsUnit 

func (R Parent) IsUnit(q object.Element) (bool, object.Element, error)

IsUnit returns true iff q is a multiplicative unit (i.e. q is non-zero). If true, also returns the inverse element 1/q.

func (Parent) IsZero 

func (R Parent) IsZero(x object.Element) (bool, error)

IsZero returns true iff x is the rational number 0.

func (Parent) Max 

func (R Parent) Max(S ...object.Element) (object.Element, error)

Max returns the maximum element in the slice S. If S is empty then an error is returned.

func (Parent) MaxAndIndex 

func (R Parent) MaxAndIndex(S []object.Element) (object.Element, int, error)

MaxAndIndex returns the maximum element in the slice S, along with the index of the first occurrence of that element in S. If S is empty then an error is returned.

func (Parent) Min 

func (R Parent) Min(S ...object.Element) (object.Element, error)

Min returns the maximum element in the slice S. If S is empty then an error is returned.

func (Parent) MinAndIndex 

func (R Parent) MinAndIndex(S []object.Element) (object.Element, int, error)

MinAndIndex returns the minimum element in the slice S, along with the index of the first occurrence of that element in S. If S is empty then an error is returned.

func (Parent) Multiply 

func (R Parent) Multiply(x object.Element, y object.Element) (object.Element, error)

Multiply returns the product x * y.

func (Parent) Negate 

func (R Parent) Negate(q object.Element) (object.Element, error)

Negate returns -q.

func (Parent) One 

func (R Parent) One() object.Element

One returns 1.

func (Parent) Power 

func (R Parent) Power(q object.Element, k *integer.Element) (object.Element, error)

Power returns q^k.

func (Parent) Product 

func (R Parent) Product(S ...object.Element) (object.Element, error)

Product returns the product of the elements in the slice S. The product of the empty slice is one.

func (Parent) ScalarMultiplyByInteger 

func (R Parent) ScalarMultiplyByInteger(n *integer.Element, x object.Element) (object.Element, error)

ScalarMultiplyByInteger returns nx, where this is defined to be x + ... + x (n times) if n is positive, and -x - ... - x (|n| times) if n is negative.

func (Parent) Sort 

func (R Parent) Sort(S []object.Element) ([]object.Element, error)

Sort non-destructively sorts the given slice of integers. The sorted slice is returned.

func (Parent) String 

func (R Parent) String() string

String returns a string representation of the field of rational numbers.

func (Parent) Subtract 

func (R Parent) Subtract(x object.Element, y object.Element) (object.Element, error)

Subtract returns x - y.

func (Parent) Sum 

func (R Parent) Sum(S ...object.Element) (object.Element, error)

Sum returns the sum of the elements in the slice S. The sum of the empty slice is the zero element.

func (Parent) ToElement 

func (R Parent) ToElement(x object.Element) (object.Element, error)

ToElement returns x as an element of this parent, or an error if x cannot naturally be regarded as an element of this parent.

func (Parent) Zero 

func (R Parent) Zero() object.Element

Zero returns 0.

type Slice 

type Slice []*Element

Slice wraps an []*Element, implementing slice.Interface.

func (Slice) Entry 

func (S Slice) Entry(i int) object.Element

Entry returns the i-th element in the slice. This will panic if i is out of range.

func (Slice) Hash 

func (S Slice) Hash() hash.Value

Hash returns a hash value for this slice.

func (Slice) Len 

func (S Slice) Len() int

Len returns the length of the slice.

func (Slice) Slice 

func (S Slice) Slice(k int, m int) slice.Interface

Slice returns a subslice starting at index k and of length m - k. The returned subslice will be of the same underlying type. This will panic if the arguments are out of range.

type SortableSlice 

type SortableSlice []*Element

SortableSlice implements the sort.Interface interface.

func (SortableSlice) Len 

func (S SortableSlice) Len() int

Len is the number of elements in the slice.

func (SortableSlice) Less 

func (S SortableSlice) Less(i int, j int) bool

Less reports whether the element with index i should sort before the element with index j.

func (SortableSlice) Sort 

func (S SortableSlice) Sort()

Sort sorts the slice in place.

func (SortableSlice) Swap 

func (S SortableSlice) Swap(i int, j int)

Swap swaps the elements with indexes i and j.

Source Files

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Directories

Path Synopsis
internal
bigratfactory

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