ganrac

package module
v0.0.5 Latest Latest
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 Go to latest Published: Nov 10, 2023 License: MIT Imports: 17 Imported by: 1

README

GaNRAC Logo GaNRAC Logo

GaNRAC

Getting started

Requirements
install ox-asir

CentOS

# yum install libX11-devel libXt-devel libXaw-devel
> curl -O "http://www.math.sci.kobe-u.ac.jp/pub/OpenXM/Head/openxm-head.tar.gz"
> tar xf openxm-head.tar.gz
> (cd OpenXM/src; make install)
> (cd OpenXM/rc; make install)
> while :; do ox -ox ox_asir -control 1234 -data 4321; done

Ubuntu

# apt install build-essential m4 bison
# apt install libx11-dev libxt-dev libxaw7-dev
> curl -O "http://www.math.sci.kobe-u.ac.jp/pub/OpenXM/Head/openxm-head.tar.gz"
> tar xf openxm-head.tar.gz
> (cd OpenXM/src; make install)
> (cd OpenXM/rc; make install)
> while :; do ox -ox ox_asir -control 1234 -data 4321; done

Installation

downloading the binary

See https://github.com/hiwane/ganrac/releases

compiling from source code

Required: go (1.18 or newer)

ox-asir version

> go install github.com/hiwane/ganrac/cmd/ganrac-ox@latest
> # go get github.com/hiwane/ganrac/cmd/ganrac-ox

SageMath version

> go install github.com/hiwane/ganrac/cmd/ganrac-sage@latest
> # go get github.com/hiwane/ganrac/cmd/ganrac-sage

Demo

ganrac9

real Quantifier Elimination

See qe.md for details.

ganrac7

F = ex([x], a*x^2+b*x+c==0);
qe(F);
G = example("quad");
H = time(qe(G[0]));
qe(all([x,y,z], equiv(G[1], H)));
real QE by Cylindrical Algebraic Decomposition

See cad.md for details.

ganrac8

vars(c,b,a,x);
F = ex([x], a*x^2+b*x+c <= 0);
F;
C = cadinit(F);
cadproj(C);
print(C, "proj");
print(C, "proj", 3, 0);
cadlift(C);
print(C, "sig");
print(C, "sig", 0);
print(C, "cell", 0, 1);
cadsfc(C);
print(C, "stat");

Documentation

Index

Constants

View Source 
const (
	PF_EVAL_UNKNOWN = -1
	PF_EVAL_NO      = 0
	PF_EVAL_YES     = 1

	PROJ_McCallum = 0
	PROJ_HONG     = 1

	CAD_STAGE_INITED int8 = 0
	CAD_STAGE_PROJED int8 = 1
	CAD_STAGE_LIFTED int8 = 2
)
View Source 
const (
	EVEN_NO   = 0x00
	EVEN_NG   = 0x01
	EVEN_LIN1 = 0x02 // 線形，ただし，主係数は定数
	EVEN_LIN2 = 0x04 // 線形で，主係数が変数
	EVEN_OK   = 0x08 // atom の因数分解した因子すべてが even 例：(x^2+1) * (x^4+3*x^2+1)
	EVEN_OKM  = 0x10 // atom.getPoly() が even 例：(x-1)*(x+1)
	EVEN_LIN  = EVEN_LIN1 | EVEN_LIN2
)
View Source 
const (
	LT       OP = 0x1
	EQ       OP = 0x2
	GT       OP = 0x4
	LE       OP = LT | EQ
	GE       OP = GT | EQ
	NE       OP = GT | LT
	OP_TRUE  OP = GT | EQ | LT
	OP_FALSE OP = 0x0

	FTAG_TRUE  uint = 0x101
	FTAG_FALSE uint = 0x102
	FTAG_ATOM  uint = 0x103
	FTAG_AND   uint = 0x104
	FTAG_OR    uint = 0x105
	FTAG_ALL   uint = 0x106
	FTAG_EX    uint = 0x107
)
View Source 
const (
	TAG_NONE = iota
	TAG_STR
	TAG_NUM
	TAG_POLY
	TAG_FOF
	TAG_LIST
	TAG_CAD

	FORMAT_TEX    = 'P'
	FORMAT_DUMP   = 'V'
	FORMAT_SRC    = 'S'
	FORMAT_QEPCAD = 'Q'
	FORMAT_INDEX  = 'I'
)
View Source 
const (
	NTAG_NONE = iota
	NTAG_INT
	NTAG_RAT
	NTAG_BININT
	NTAG_INTERVAL
	NTAG_MOD
)
View Source 
const (
	QEALGO_VSLIN  = 0x0001
	QEALGO_VSQUAD = 0x0002

	QEALGO_EQLIN  = 0x0010
	QEALGO_EQQUAD = 0x0020

	QEALGO_NEQ = 0x0100 // 非等式制約QE

	QEALGO_ATOM = 0x0200 // ex([x], f(x) <= 0)
	QEALGO_SDC  = 0x0400 // ex([x], x>=0 && f(x) <= 0)

	QEALGO_SMPL_EVEN = 0x100000000
	QEALGO_SMPL_HOMO = 0x200000000
	QEALGO_SMPL_TRAN = 0x400000000
	QEALGO_SMPL_ROTA = 0x800000000
)
View Source 
const (
	// pdq() の復帰
	SFC_PROJ_DEFINABLE   = 0
	SFC_PROJ_UNDEFINABLE = 1
	SFC_PROJ_UNDET       = 2
)
View Source 
const ATOMQE_MAX_DEG = 8
View Source 
const KARATSUBA_DEG_MOD = 4

go test -bench BenchmarkModularMulPoly -run BenchmarkModularMulPoly -o prof/ganrac -count=N 3x20= 34.222 4x20= 30.380 5x20= 31.947

View Source 
const OPVS_SHIFT = 8
View Source 
const SDCQE_MAX_DEG = 8

Variables

View Source 
var DebugCounter map[string]int = make(map[string]int)

Functions

func ExampleNames added in v0.0.4 

func ExampleNames() []string

func GetColordFml 

func GetColordFml() bool

func IncDebugCounter added in v0.0.3 

func IncDebugCounter(f string, n int) int

func MaxPrec 

func MaxPrec(x, y *Interval) uint

func NewCadErrorWO added in v0.0.4 

func NewCadErrorWO(cell *Cell) error

func NewFofQuadEq added in v0.0.3 

func NewFofQuadEq(g *Ganrac, p *Poly, lv Level) *fof_quad_eq

func NewQeCond added in v0.0.3 

func NewQeCond() *qeCond

func NewReduceInfo added in v0.0.3 

func NewReduceInfo(g *Ganrac, c, neccon, sufcon Fof) *reduce_info

neccon: 必要条件 sufcon: 十分条件

func QEOptionNames added in v0.0.4 

func QEOptionNames() []string

func SetColordFml 

func SetColordFml(b bool)

func VarNum added in v0.0.2 

func VarNum() int

func VarStr added in v0.0.2 

func VarStr(lv Level) string

Types

type Atom 

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

func (*Atom) Clone added in v0.0.4 

func (p *Atom) Clone() *Atom

func (*Atom) Deg 

func (p *Atom) Deg(lv Level) int

func (*Atom) Equals 

func (p *Atom) Equals(qq interface{}) bool

func (*Atom) FmlLess 

func (p *Atom) FmlLess(qq Fof) bool

func (*Atom) Format 

func (p *Atom) Format(b fmt.State, format rune)

func (*Atom) Indets 

func (p *Atom) Indets(b []bool)

func (*Atom) IsQff 

func (p *Atom) IsQff() bool

func (*Atom) IsQuantifier 

func (p *Atom) IsQuantifier() bool

func (*Atom) Not 

func (p *Atom) Not() Fof

func (*Atom) String 

func (p *Atom) String() string

func (*Atom) Subst 

func (p *Atom) Subst(xs RObj, lvs Level) Fof

func (*Atom) Tag 

func (p *Atom) Tag() uint

type AtomF 

type AtomF struct {
	FofTFbase
}

func (*AtomF) Deg 

func (p *AtomF) Deg(lv Level) int

func (*AtomF) Equals 

func (p *AtomF) Equals(qq interface{}) bool

func (*AtomF) FmlLess 

func (p *AtomF) FmlLess(q Fof) bool

func (*AtomF) Format 

func (p *AtomF) Format(s fmt.State, format rune)

func (*AtomF) Indets 

func (p *AtomF) Indets(b []bool)

func (*AtomF) IsQff 

func (p *AtomF) IsQff() bool

func (*AtomF) IsQuantifier 

func (p *AtomF) IsQuantifier() bool

func (*AtomF) Not 

func (p *AtomF) Not() Fof

func (*AtomF) String 

func (p *AtomF) String() string

func (*AtomF) Subst 

func (p *AtomF) Subst(xs RObj, lvs Level) Fof

func (*AtomF) Tag 

func (p *AtomF) Tag() uint

type AtomProj 

type AtomProj struct {
	Atom
	// contains filtered or unexported fields
}

type AtomT 

type AtomT struct {
	FofTFbase
}

func (*AtomT) Deg 

func (p *AtomT) Deg(lv Level) int

func (*AtomT) Equals 

func (p *AtomT) Equals(qq interface{}) bool

func (*AtomT) FmlLess 

func (p *AtomT) FmlLess(q Fof) bool

func (*AtomT) Format 

func (p *AtomT) Format(s fmt.State, format rune)

func (*AtomT) Indets 

func (p *AtomT) Indets(b []bool)

func (*AtomT) IsQff 

func (p *AtomT) IsQff() bool

func (*AtomT) IsQuantifier 

func (p *AtomT) IsQuantifier() bool

func (*AtomT) Not 

func (p *AtomT) Not() Fof

func (*AtomT) String 

func (p *AtomT) String() string

func (*AtomT) Subst 

func (p *AtomT) Subst(xs RObj, lvs Level) Fof

func (*AtomT) Tag 

func (p *AtomT) Tag() uint

type BinInt 

type BinInt struct {
	Number
	// contains filtered or unexported fields
}

BinInt is an NObj

func NewBinInt 

func NewBinInt(n *big.Int, m int) *BinInt

func (*BinInt) Abs 

func (z *BinInt) Abs() NObj

func (*BinInt) Add 

func (x *BinInt) Add(yy RObj) RObj

func (*BinInt) AddInt 

func (x *BinInt) AddInt(y *Int) RObj

func (*BinInt) Cmp 

func (z *BinInt) Cmp(xx NObj) int

func (*BinInt) CmpAbs 

func (z *BinInt) CmpAbs(xx NObj) int

func (*BinInt) Div 

func (x *BinInt) Div(yy NObj) RObj

func (*BinInt) Equals 

func (x *BinInt) Equals(yy interface{}) bool

func (*BinInt) Float 

func (z *BinInt) Float() float64

func (*BinInt) Format 

func (x *BinInt) Format(s fmt.State, format rune)

func (*BinInt) IsMinusOne 

func (x *BinInt) IsMinusOne() bool

func (*BinInt) IsOne 

func (x *BinInt) IsOne() bool

func (*BinInt) IsZero 

func (x *BinInt) IsZero() bool

func (*BinInt) Mul 

func (x *BinInt) Mul(yy RObj) RObj

func (*BinInt) MulInt 

func (x *BinInt) MulInt(y *Int) RObj

func (*BinInt) Neg 

func (x *BinInt) Neg() RObj

func (*BinInt) Pow 

func (x *BinInt) Pow(r *Int) RObj

func (*BinInt) Sign 

func (x *BinInt) Sign() int

func (*BinInt) String 

func (x *BinInt) String() string

func (*BinInt) Sub 

func (x *BinInt) Sub(yy RObj) RObj

func (*BinInt) Subst 

func (z *BinInt) Subst(x RObj, lv Level) RObj

func (*BinInt) ToInt added in v0.0.5 

func (z *BinInt) ToInt(p *Int) *Int

整数に丸める. input z = (x+p) * 2^m return integer y s.t. t <= z < t+1 Params: p = 0 or 1 is expected

func (*BinInt) ToIntRat 

func (z *BinInt) ToIntRat() NObj

type CAD 

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

func NewCAD 

func NewCAD(prenex_formula Fof, g *Ganrac) (*CAD, error)

func (*CAD) Fprint 

func (cad *CAD) Fprint(b io.Writer, args ...interface{}) error

func (*CAD) FprintInput 

func (cad *CAD) FprintInput(b io.Writer, args ...interface{}) error

func (*CAD) FprintProj 

func (cad *CAD) FprintProj(b io.Writer, args ...interface{}) error

func (*CAD) FprintProjs 

func (cad *CAD) FprintProjs(b io.Writer, lv Level)

func (*CAD) InitProj added in v0.0.3 

func (c *CAD) InitProj(algo ProjectionAlgo)

func (*CAD) InitRoot added in v0.0.3 

func (c *CAD) InitRoot()

func (*CAD) Lift 

func (cad *CAD) Lift(index ...int) error

func (*CAD) Print 

func (cad *CAD) Print(args ...interface{}) error

func (*CAD) PrintProj 

func (cad *CAD) PrintProj(args ...interface{})

func (*CAD) Projection 

func (cad *CAD) Projection(algo ProjectionAlgo) (*List, error)

func (*CAD) Root added in v0.0.3 

func (c *CAD) Root() *Cell

func (*CAD) Sfc 

func (cad *CAD) Sfc() (Fof, error)

func (*CAD) String 

func (c *CAD) String() string

func (*CAD) Tag 

func (c *CAD) Tag() uint

type CADSfc 

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

func NewCADSfc 

func NewCADSfc(cad *CAD) *CADSfc

type CADStat 

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

func (CADStat) Fprint 

func (stat CADStat) Fprint(b io.Writer, cad *CAD)

type CAD_error_wo added in v0.0.4 

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

func (*CAD_error_wo) Error added in v0.0.4 

func (e *CAD_error_wo) Error() string

type CAS added in v0.0.2 

type CAS interface {
	Gcd(p, q *Poly) RObj

	/* asir format
	 * Factor(p) = [[c, 1], [q2, n2], [q3, n3], ..., [qm, nm]]
	 *  where
	 *     c in Q and
	 * 	   q2, ..., qm in Q[X] and
	 * 	   n2, ..., nm in N and
	 *     p = c* q2^n2 * q3^n3 * ... * qm^nm
	 */
	Factor(p *Poly) *List

	Discrim(p *Poly, lv Level) RObj
	Resultant(p *Poly, q *Poly, lv Level) RObj

	/* principal subresultant coefficient */
	Psc(p *Poly, q *Poly, lv Level, j int32) RObj

	/*
	 * slope resultant
	 * H. Hong. Quantifier elimination for formulas constrained by quadratic equations
	 */
	Slope(p *Poly, q *Poly, lv Level, k int32) RObj

	// Subresultant seq.
	// cc の値により, psc 等に変える
	//   0: subresultant seq.
	//   1: principal subresultant seq.
	//   2: constant term
	//   3: 1+2
	Sres(p *Poly, q *Poly, lv Level, cc int32) *List

	// groebner basis
	// vars 変数順序を表す
	// 束縛変数と自由変数を分けるために block order を用いる. n はそのための区切りの位置を表す.
	// 区切りが必要のない場合は，n=0 を用いる
	GB(p *List, vars *List, n int) *List

	// returns reduce(p, gb), sgn < 0
	// (vars, n) については，GB を参照
	Reduce(p *Poly, gb *List, vars *List, n int) (RObj, bool)

	Eval(p string) (GObj, error)

	Close() error

	SetLogger(logger *log.Logger)
}

type Cell 

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

func NewCell 

func NewCell(cad *CAD, parent *Cell, idx uint) *Cell

func (*Cell) Fprint 

func (cell *Cell) Fprint(b io.Writer, args ...interface{}) error

func (*Cell) Index 

func (cell *Cell) Index() []uint

インデックスを返す. 論文等は 1 始まりだが，0 始まりであることに注意 つまり， section は奇数である

func (*Cell) Neg 

func (cell *Cell) Neg() *Cell

func (*Cell) Prec 

func (cell *Cell) Prec() uint

func (*Cell) Precs 

func (cell *Cell) Precs() []uint

func (*Cell) Print 

func (cell *Cell) Print(args ...interface{}) error

func (*Cell) Sign 

func (cell *Cell) Sign() int

returns the sign of the sample point

func (*Cell) Square 

func (cell *Cell) Square(even int)

func (*Cell) Truth added in v0.0.3 

func (cell *Cell) Truth() int8

type Cellmod 

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

func NewCellmod 

func NewCellmod(cell *Cell) *Cellmod

type Dict 

type Dict struct {
	GObj
	// contains filtered or unexported fields
}

func NewDict 

func NewDict() *Dict

func (*Dict) Equals 

func (z *Dict) Equals(vv interface{}) bool

func (*Dict) Format 

func (z *Dict) Format(s fmt.State, format rune)

func (*Dict) Get 

func (z *Dict) Get(k string) (GObj, error)

func (*Dict) Indets 

func (z *Dict) Indets(b []bool)

func (*Dict) Len 

func (z *Dict) Len() int

func (*Dict) Set 

func (z *Dict) Set(k string, v GObj) error

setser

func (*Dict) String 

func (z *Dict) String() string

func (*Dict) Tag 

func (z *Dict) Tag() uint

type Exists 

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

func (*Exists) Deg 

func (p *Exists) Deg(lv Level) int

func (*Exists) Equals 

func (p *Exists) Equals(qq interface{}) bool

func (*Exists) Fml 

func (p *Exists) Fml() Fof

func (*Exists) FmlLess 

func (p *Exists) FmlLess(q Fof) bool

func (*Exists) Format 

func (p *Exists) Format(b fmt.State, format rune)

func (*Exists) Get 

func (p *Exists) Get(idx *Int) (interface{}, error)

func (*Exists) Indets 

func (p *Exists) Indets(b []bool)

func (*Exists) IsQff 

func (p *Exists) IsQff() bool

func (*Exists) IsQuantifier 

func (p *Exists) IsQuantifier() bool

func (*Exists) Not 

func (p *Exists) Not() Fof

func (*Exists) Qs 

func (p *Exists) Qs() []Level

func (*Exists) String 

func (p *Exists) String() string

func (*Exists) Subst 

func (p *Exists) Subst(xs RObj, lvs Level) Fof

func (*Exists) Tag 

func (p *Exists) Tag() uint

type FmlAnd 

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

func (*FmlAnd) Deg 

func (p *FmlAnd) Deg(lv Level) int

func (*FmlAnd) Equals 

func (p *FmlAnd) Equals(qq interface{}) bool

func (*FmlAnd) FmlLess 

func (p *FmlAnd) FmlLess(q Fof) bool

func (*FmlAnd) Fmls 

func (p *FmlAnd) Fmls() []Fof

func (*FmlAnd) Format 

func (p *FmlAnd) Format(b fmt.State, format rune)

func (*FmlAnd) Get 

func (p *FmlAnd) Get(idx *Int) (Fof, error)

func (*FmlAnd) Indets 

func (p *FmlAnd) Indets(b []bool)

func (*FmlAnd) IsQff 

func (p *FmlAnd) IsQff() bool

func (*FmlAnd) IsQuantifier 

func (p *FmlAnd) IsQuantifier() bool

func (*FmlAnd) Len 

func (p *FmlAnd) Len() int

func (*FmlAnd) Not 

func (p *FmlAnd) Not() Fof

func (*FmlAnd) String 

func (p *FmlAnd) String() string

func (*FmlAnd) Subst 

func (p *FmlAnd) Subst(xs RObj, lvs Level) Fof

func (*FmlAnd) Tag 

func (p *FmlAnd) Tag() uint

type FmlOr 

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

func (*FmlOr) Deg 

func (p *FmlOr) Deg(lv Level) int

func (*FmlOr) Equals 

func (p *FmlOr) Equals(qq interface{}) bool

func (*FmlOr) FmlLess 

func (p *FmlOr) FmlLess(q Fof) bool

func (*FmlOr) Fmls 

func (p *FmlOr) Fmls() []Fof

func (*FmlOr) Format 

func (p *FmlOr) Format(b fmt.State, format rune)

func (*FmlOr) Get 

func (p *FmlOr) Get(idx *Int) (Fof, error)

func (*FmlOr) Indets 

func (p *FmlOr) Indets(b []bool)

func (*FmlOr) IsQff 

func (p *FmlOr) IsQff() bool

func (*FmlOr) IsQuantifier 

func (p *FmlOr) IsQuantifier() bool

func (*FmlOr) Len 

func (p *FmlOr) Len() int

func (*FmlOr) Not 

func (p *FmlOr) Not() Fof

func (*FmlOr) String 

func (p *FmlOr) String() string

func (*FmlOr) Subst 

func (p *FmlOr) Subst(xs RObj, lvs Level) Fof

func (*FmlOr) Tag 

func (p *FmlOr) Tag() uint

type Fof 

type Fof interface {
	GObj
	fmt.Formatter

	IsQff() bool        // quantifier free formula
	IsQuantifier() bool // ForAll か Exists なら true

	Not() Fof // 否定

	Subst(xs RObj, lv Level) Fof

	Deg(lv Level) int
	FmlLess(a Fof) bool // normalize() でのソート用
	// contains filtered or unexported methods
}

first-order formula

func NewAtom 

func NewAtom(p RObj, op OP) Fof

func NewAtoms 

func NewAtoms(pp []RObj, op OP) Fof

func NewBool 

func NewBool(b bool) Fof

func NewExists 

func NewExists(lv []Level, fml Fof) Fof

func NewFmlAnd 

func NewFmlAnd(pp Fof, qq Fof) Fof

func NewFmlAnds added in v0.0.3 

func NewFmlAnds(pp ...Fof) Fof

func NewFmlEquiv added in v0.0.3 

func NewFmlEquiv(f1, f2 Fof) Fof

func NewFmlImpl added in v0.0.4 

func NewFmlImpl(f1, f2 Fof) Fof

func NewFmlOr 

func NewFmlOr(pp Fof, qq Fof) Fof

func NewFmlOrs added in v0.0.3 

func NewFmlOrs(pp ...Fof) Fof

func NewForAll added in v0.0.4 

func NewForAll(lv []Level, fml Fof) Fof

func NewQuantifier 

func NewQuantifier(forex bool, lvv []Level, fml Fof) Fof

type FofAO 

type FofAO interface {
	// and/or
	Fof

	Fmls() []Fof

	Len() int
	// contains filtered or unexported methods
}

type FofQ 

type FofQ interface {
	// quantifier
	Fof

	Qs() []Level
	Fml() Fof
	// contains filtered or unexported methods
}

type FofTFbase 

type FofTFbase struct {
	Fof
}

type ForAll 

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

func (*ForAll) Deg 

func (p *ForAll) Deg(lv Level) int

func (*ForAll) Equals 

func (p *ForAll) Equals(qq interface{}) bool

func (*ForAll) Fml 

func (p *ForAll) Fml() Fof

func (*ForAll) FmlLess 

func (p *ForAll) FmlLess(q Fof) bool

func (*ForAll) Format 

func (p *ForAll) Format(b fmt.State, format rune)

func (*ForAll) Get 

func (p *ForAll) Get(idx *Int) (interface{}, error)

func (*ForAll) Indets 

func (p *ForAll) Indets(b []bool)

func (*ForAll) IsQff 

func (p *ForAll) IsQff() bool

func (*ForAll) IsQuantifier 

func (p *ForAll) IsQuantifier() bool

func (*ForAll) Not 

func (p *ForAll) Not() Fof

func (*ForAll) Qs 

func (p *ForAll) Qs() []Level

func (*ForAll) String 

func (p *ForAll) String() string

func (*ForAll) Subst 

func (p *ForAll) Subst(xs RObj, lvs Level) Fof

func (*ForAll) Tag 

func (p *ForAll) Tag() uint

type GObj 

type GObj interface {
	fmt.Formatter
	String() string
	Tag() uint
}

ganrac object RObj, NObj, Fof, List, *String

type Ganrac 

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

func NewGANRAC 

func NewGANRAC() *Ganrac

func (*Ganrac) Close added in v0.0.3 

func (g *Ganrac) Close()

func (*Ganrac) Eval 

func (g *Ganrac) Eval(r io.Reader) (interface{}, error)

func (*Ganrac) FunctionNames added in v0.0.4 

func (g *Ganrac) FunctionNames() []string

func (*Ganrac) InitVarList 

func (g *Ganrac) InitVarList(vlist []string) error

func (*Ganrac) Logger added in v0.0.2 

func (g *Ganrac) Logger() *log.Logger

func (*Ganrac) QE 

func (g *Ganrac) QE(fof Fof, qeopt *QEopt) Fof

func (*Ganrac) SetCAS added in v0.0.2 

func (g *Ganrac) SetCAS(cas CAS)

func (*Ganrac) SetLogger 

func (g *Ganrac) SetLogger(logger *log.Logger)

func (*Ganrac) SetParaNum added in v0.0.4 

func (g *Ganrac) SetParaNum(n int)

type Int 

type Int struct {
	Number
	// contains filtered or unexported fields
}

Int is an NObj

func NewInt 

func NewInt(n int64) *Int

func NewIntZ 

func NewIntZ(z *big.Int) *Int

func ParseInt 

func ParseInt(s string, base int) *Int

func (*Int) Abs 

func (z *Int) Abs() NObj

func (*Int) Add 

func (x *Int) Add(y RObj) RObj

func (*Int) Bit 

func (x *Int) Bit(i int) uint

func (*Int) Cmp 

func (z *Int) Cmp(xx NObj) int

func (*Int) CmpAbs 

func (z *Int) CmpAbs(xx NObj) int

func (*Int) Div 

func (x *Int) Div(yy NObj) RObj

func (*Int) Equals 

func (x *Int) Equals(y interface{}) bool

func (*Int) Float 

func (z *Int) Float() float64

func (*Int) Format 

func (x *Int) Format(s fmt.State, format rune)

func (*Int) Gcd 

func (x *Int) Gcd(y *Int) *Int

func (*Int) GcdEx 

func (x *Int) GcdEx(y *Int) (*Int, *Int, *Int)

func (*Int) Int64 

func (x *Int) Int64() int64

func (*Int) IsInt64 

func (x *Int) IsInt64() bool

func (*Int) IsMinusOne 

func (x *Int) IsMinusOne() bool

func (*Int) IsOne 

func (x *Int) IsOne() bool

func (*Int) IsZero 

func (x *Int) IsZero() bool

func (*Int) Mul 

func (x *Int) Mul(y RObj) RObj

func (*Int) N added in v0.0.2 

func (x *Int) N() *big.Int

func (*Int) Neg 

func (x *Int) Neg() RObj

func (*Int) Pow 

func (x *Int) Pow(y *Int) RObj

func (*Int) QuoRem added in v0.0.4 

func (x *Int) QuoRem(y *Int) (*Int, *Int)

func (*Int) Set 

func (x *Int) Set(y RObj) RObj

func (*Int) Sign 

func (x *Int) Sign() int

func (*Int) String 

func (x *Int) String() string

func (*Int) Sub 

func (x *Int) Sub(y RObj) RObj

func (*Int) Subst 

func (z *Int) Subst(x RObj, lv Level) RObj

type Interval 

type Interval struct {
	Number
	// contains filtered or unexported fields
}

Interval is an NObj

func FRealRoot 

func FRealRoot(prec uint, lmax int, poly []*big.Float, rand float64) []*Interval

func NewIntervalFloat 

func NewIntervalFloat(n *big.Float, prec uint) *Interval

func NewIntervalInt64 

func NewIntervalInt64(n int64, prec uint) *Interval

func (*Interval) Abs 

func (x *Interval) Abs() NObj

func (*Interval) Add 

func (x *Interval) Add(yy RObj) RObj

func (*Interval) AddFloat 

func (x *Interval) AddFloat(y *big.Float) *Interval

func (*Interval) Cmp 

func (x *Interval) Cmp(y NObj) int

func (*Interval) CmpAbs 

func (x *Interval) CmpAbs(y NObj) int

func (*Interval) ContainsZero 

func (c *Interval) ContainsZero() bool

func (*Interval) Div 

func (x *Interval) Div(yy NObj) RObj

func (*Interval) Equals 

func (x *Interval) Equals(v interface{}) bool

func (*Interval) Float 

func (x *Interval) Float() float64

func (*Interval) Format 

func (x *Interval) Format(s fmt.State, format rune)

func (*Interval) IsMinusOne 

func (x *Interval) IsMinusOne() bool

func (*Interval) IsOne 

func (x *Interval) IsOne() bool

func (*Interval) IsZero 

func (x *Interval) IsZero() bool

func (*Interval) Mul 

func (x *Interval) Mul(yy RObj) RObj

func (*Interval) Mul2Exp 

func (x *Interval) Mul2Exp(m uint) NObj

func (*Interval) MulFloat 

func (x *Interval) MulFloat(y *big.Float) *Interval

func (*Interval) MulInt64 

func (x *Interval) MulInt64(y int64) *Interval

func (*Interval) Neg 

func (x *Interval) Neg() RObj

func (*Interval) Pow 

func (x *Interval) Pow(yy *Int) RObj

func (*Interval) Prec 

func (z *Interval) Prec() uint

func (*Interval) SetFloat 

func (z *Interval) SetFloat(n *big.Float)

func (*Interval) SetFloat64 

func (z *Interval) SetFloat64(n float64)

func (*Interval) SetInt64 

func (z *Interval) SetInt64(n int64)

func (*Interval) SetPrec 

func (z *Interval) SetPrec(prec uint)

func (*Interval) Sign 

func (x *Interval) Sign() int

func (*Interval) String 

func (z *Interval) String() string

func (*Interval) Sub 

func (x *Interval) Sub(yy RObj) RObj

func (*Interval) SubFloat 

func (x *Interval) SubFloat(y *big.Float) *Interval

func (*Interval) Subst 

func (x *Interval) Subst(v RObj, lv Level) RObj

type Level 

type Level int8

func VarStr2Lv added in v0.0.2 

func VarStr2Lv(s string) (Level, bool)

type Levels 

type Levels []Level

type List 

type List struct {
	GObj
	// contains filtered or unexported fields
}

func NewList 

func NewList(args ...interface{}) *List

func NewListN added in v0.0.4 

func NewListN(n int, args ...interface{}) *List

func (*List) Append 

func (z *List) Append(a GObj)

func (*List) Equals 

func (z *List) Equals(vv interface{}) bool

func (*List) Format 

func (z *List) Format(s fmt.State, format rune)

func (*List) Get 

func (z *List) Get(ii *Int) (GObj, error)

func (*List) Geti 

func (z *List) Geti(idx ...int) (GObj, error)

func (*List) Indets 

func (z *List) Indets(b []bool)

func (*List) Iter 

func (z *List) Iter() []GObj

func (*List) Len 

func (z *List) Len() int

func (*List) Set 

func (z *List) Set(ii *Int, v GObj) error

func (*List) Seti added in v0.0.2 

func (z *List) Seti(i int, v GObj) error

func (*List) String 

func (z *List) String() string

func (*List) Subst 

func (z *List) Subst(xs RObj, lvs Level) *List

func (*List) Swap added in v0.0.2 

func (z *List) Swap(i, j int) error

func (*List) Tag 

func (z *List) Tag() uint

type Moder 

type Moder interface {
	// modular arithmetic
	RObj
	// contains filtered or unexported methods
}

type NObj 

type NObj interface {
	RObj

	Float() float64
	Cmp(x NObj) int
	CmpAbs(x NObj) int
	Abs() NObj
	Sign() int
	// contains filtered or unexported methods
}

numeric *Int, *Rat, *BinInt, *Interval, Uint

type NumRegion 

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

nil は empty set を表す.

func NewNumRegion added in v0.0.3 

func NewNumRegion() *NumRegion

func (*NumRegion) Format 

func (m *NumRegion) Format(s fmt.State, format rune)

type Number 

type Number struct {
	NObj
}

func (*Number) Deg added in v0.0.5 

func (x *Number) Deg(lv Level) int

func (*Number) IsNumeric 

func (x *Number) IsNumeric() bool

func (*Number) String 

func (x *Number) String() string

func (*Number) Tag 

func (x *Number) Tag() uint

type OP 

type OP uint8

func (OP) Format added in v0.0.4 

func (op OP) Format(b fmt.State, format rune)

func (OP) String 

func (op OP) String() string

type Poly 

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

poly in K[x_lv,...,x_n]

func NewPoly 

func NewPoly(lv Level, deg_plus_1 int) *Poly

func NewPolyCoef 

func NewPolyCoef(lv Level, coeffs ...interface{}) *Poly

func NewPolyInts 

func NewPolyInts(lv Level, coeffs ...int64) *Poly

func NewPolyVar 

func NewPolyVar(lv Level) *Poly

func NewPolyVarn added in v0.0.2 

func NewPolyVarn(lv Level, deg int) *Poly

func VarPoly added in v0.0.2 

func VarPoly(lv Level) *Poly

func (*Poly) Add 

func (x *Poly) Add(y RObj) RObj

func (*Poly) Clone 

func (z *Poly) Clone() *Poly

func (*Poly) Cmp 

func (p *Poly) Cmp(q *Poly) int

func (*Poly) Coef 

func (z *Poly) Coef(lv Level, deg uint) RObj

func (*Poly) Deg 

func (z *Poly) Deg(lv Level) int

func (*Poly) Diff added in v0.0.2 

func (z *Poly) Diff(lv Level) RObj

func (*Poly) Div 

func (x *Poly) Div(y NObj) RObj

func (*Poly) Equals 

func (z *Poly) Equals(x interface{}) bool

func (*Poly) Format 

func (z *Poly) Format(s fmt.State, format rune)

func (*Poly) Indets 

func (z *Poly) Indets(b []bool)

func (*Poly) IsMinusOne 

func (z *Poly) IsMinusOne() bool

func (*Poly) IsNumeric 

func (z *Poly) IsNumeric() bool

func (*Poly) IsOne 

func (z *Poly) IsOne() bool

func (*Poly) IsZZ added in v0.0.4 

func (x *Poly) IsZZ() bool

整数係数多項式か

func (*Poly) IsZero 

func (z *Poly) IsZero() bool

func (*Poly) LeadinfCoef 

func (z *Poly) LeadinfCoef() NObj

func (*Poly) Less 

func (p *Poly) Less(q *Poly) bool

func (*Poly) Level added in v0.0.2 

func (z *Poly) Level() Level

func (*Poly) Mul 

func (x *Poly) Mul(yy RObj) RObj

func (*Poly) Neg 

func (z *Poly) Neg() RObj

func (*Poly) NegX added in v0.0.4 

func (f *Poly) NegX(lv Level) *Poly

returns f(-x)

func (*Poly) NewPoly added in v0.0.4 

func (p *Poly) NewPoly() *Poly

func (*Poly) PPC added in v0.0.2 

func (p *Poly) PPC() (*Poly, *Int)

func (*Poly) Pow 

func (x *Poly) Pow(y *Int) RObj

func (*Poly) RealRootIsolation 

func (p *Poly) RealRootIsolation(prec int) (*List, error)

func (*Poly) RootBound 

func (z *Poly) RootBound() (NObj, error)

func (*Poly) Sdiv added in v0.0.2 

func (xorg *Poly) Sdiv(y *Poly) RObj

func (*Poly) Set 

func (z *Poly) Set(x RObj) RObj

func (*Poly) Sign 

func (z *Poly) Sign() int

func (*Poly) String 

func (z *Poly) String() string

func (*Poly) Sub 

func (p *Poly) Sub(y RObj) RObj

func (*Poly) SubsXinv added in v0.0.3 

func (q *Poly) SubsXinv() *Poly

func (*Poly) Subst 

func (z *Poly) Subst(xs RObj, lv Level) RObj

func (*Poly) SubstIntv 

func (z *Poly) SubstIntv(x *Interval, lv Level, prec uint) RObj

区間の代入なので 2 乗を利用したい．

func (*Poly) SubstXinvLv added in v0.0.4 

func (f *Poly) SubstXinvLv(lv Level, n int) RObj

return x^n f(1/x) assume f(0) != 0, deg(f) <= n

func (*Poly) Tag 

func (z *Poly) Tag() uint

type ProjFactor 

type ProjFactor interface {
	P() *Poly
	Lv() Level
	Deg() int

	Index() uint
	SetIndex(i uint)

	// 入力の論理式に含まれるなら true
	Input() bool
	SetInputT(b bool)

	// 数値手法による評価
	Sign() sign_t
	SetSign(sgn sign_t)

	// 表示用
	FprintProjFactor(b io.Writer, cad *CAD)
	// contains filtered or unexported methods
}

type ProjFactorBase 

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

func (*ProjFactorBase) Deg 

func (pfb *ProjFactorBase) Deg() int

func (*ProjFactorBase) Index 

func (pfb *ProjFactorBase) Index() uint

func (*ProjFactorBase) Input 

func (pfb *ProjFactorBase) Input() bool

func (*ProjFactorBase) Lv 

func (pfb *ProjFactorBase) Lv() Level

func (*ProjFactorBase) P 

func (pfb *ProjFactorBase) P() *Poly

func (*ProjFactorBase) SetIndex 

func (pfb *ProjFactorBase) SetIndex(i uint)

func (*ProjFactorBase) SetInputT 

func (pfb *ProjFactorBase) SetInputT(b bool)

func (*ProjFactorBase) SetSign 

func (pfb *ProjFactorBase) SetSign(b sign_t)

func (*ProjFactorBase) Sign 

func (pfb *ProjFactorBase) Sign() sign_t

type ProjFactorHH 

type ProjFactorHH struct {
	ProjFactorBase
	// contains filtered or unexported fields
}

func (*ProjFactorHH) FprintProjFactor 

func (pf *ProjFactorHH) FprintProjFactor(b io.Writer, cad *CAD)

type ProjFactorMC 

type ProjFactorMC struct {
	ProjFactorBase
	// contains filtered or unexported fields
}

func (*ProjFactorMC) FprintProjFactor 

func (pf *ProjFactorMC) FprintProjFactor(b io.Writer, cad *CAD)

type ProjFactors 

type ProjFactors interface {
	Len() int
	// contains filtered or unexported methods
}

type ProjFactorsHH 

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

func (*ProjFactorsHH) Len 

func (pfs *ProjFactorsHH) Len() int

type ProjFactorsMC 

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

func (*ProjFactorsMC) Len 

func (pfs *ProjFactorsMC) Len() int
type ProjLink struct {
	// contains filtered or unexported fields
}

func (*ProjLink) Fprint 

func (pl *ProjLink) Fprint(b io.Writer)

type ProjectionAlgo 

type ProjectionAlgo int

type QEopt 

type QEopt struct {
	Algo algo_t
	// contains filtered or unexported fields
}

func NewQEopt 

func NewQEopt() *QEopt

func (*QEopt) AddAlgo added in v0.0.3 

func (qeopt *QEopt) AddAlgo(algo algo_t)

func (*QEopt) DelAlgo added in v0.0.3 

func (qeopt *QEopt) DelAlgo(algo algo_t)

func (*QEopt) SetAlgo 

func (qeopt *QEopt) SetAlgo(algo algo_t, v bool)

type QeExample 

type QeExample struct {
	Input  Fof
	Output Fof
	Ref    string
	DOI    string
}

func GetExampleFof 

func GetExampleFof(name string) *QeExample

type RObj 

type RObj interface {
	GObj

	Add(x RObj) RObj // z+x
	Sub(x RObj) RObj // z-x
	Mul(x RObj) RObj
	Div(x NObj) RObj
	Pow(x *Int) RObj
	Subst(x RObj, lv Level) RObj
	Neg() RObj
	Deg(lv Level) int // 次数を返す. zero の場合も 0 になる
	//	Set(x RObj) RObj
	Sign() int
	IsZero() bool
	IsOne() bool
	IsMinusOne() bool
	IsNumeric() bool
	// contains filtered or unexported methods
}

ring ring in R[x], in R *Poly, *Int, *Rat, *BinInt, *Interval, Uint

func Add 

func Add(x, y RObj) RObj

func Mul 

func Mul(x, y RObj) RObj

func Sub 

func Sub(x, y RObj) RObj

type RObjSample 

type RObjSample struct {
}

func (*RObjSample) Add 

func (z *RObjSample) Add(x RObj) RObj

func (*RObjSample) Deg added in v0.0.4 

func (z *RObjSample) Deg(lv Level) int

func (*RObjSample) Div 

func (z *RObjSample) Div(x NObj) RObj

func (*RObjSample) Equals 

func (z *RObjSample) Equals(x interface{}) bool

func (*RObjSample) Format 

func (z *RObjSample) Format(s fmt.State, format rune)

func (*RObjSample) IsMinusOne 

func (z *RObjSample) IsMinusOne() bool

func (*RObjSample) IsNumeric 

func (z *RObjSample) IsNumeric() bool

func (*RObjSample) IsOne 

func (z *RObjSample) IsOne() bool

func (*RObjSample) IsZero 

func (z *RObjSample) IsZero() bool

func (*RObjSample) Mul 

func (z *RObjSample) Mul(x RObj) RObj

func (*RObjSample) Neg 

func (z *RObjSample) Neg() RObj

func (*RObjSample) Pow 

func (z *RObjSample) Pow(x *Int) RObj

func (*RObjSample) Set 

func (z *RObjSample) Set(x RObj) RObj

func (*RObjSample) Sign 

func (z *RObjSample) Sign() int

func (*RObjSample) String 

func (z *RObjSample) String() string

func (*RObjSample) Sub 

func (z *RObjSample) Sub(x RObj) RObj

func (*RObjSample) Subst 

func (z *RObjSample) Subst(x RObj, lv Level) RObj

func (*RObjSample) Tag 

func (z *RObjSample) Tag() uint

type Rat 

type Rat struct {
	Number
	// contains filtered or unexported fields
}

Rat is an NObj

func NewRat added in v0.0.2 

func NewRat(c *big.Rat) *Rat

func NewRatFrac 

func NewRatFrac(num, den *Int) *Rat

func NewRatInt64 

func NewRatInt64(num, den int64) *Rat

func (*Rat) Abs 

func (z *Rat) Abs() NObj

func (*Rat) Add 

func (x *Rat) Add(yy RObj) RObj

func (*Rat) Cmp 

func (z *Rat) Cmp(xx NObj) int

func (*Rat) CmpAbs 

func (z *Rat) CmpAbs(xx NObj) int

func (*Rat) Div 

func (x *Rat) Div(yy NObj) RObj

func (*Rat) Equals 

func (x *Rat) Equals(y interface{}) bool

func (*Rat) Float 

func (z *Rat) Float() float64

func (*Rat) Format 

func (x *Rat) Format(s fmt.State, format rune)

func (*Rat) IsMinusOne 

func (x *Rat) IsMinusOne() bool

func (*Rat) IsOne 

func (x *Rat) IsOne() bool

func (*Rat) IsZero 

func (x *Rat) IsZero() bool

func (*Rat) Mul 

func (x *Rat) Mul(yy RObj) RObj

func (*Rat) N added in v0.0.2 

func (x *Rat) N() *big.Rat

func (*Rat) Neg 

func (x *Rat) Neg() RObj

func (*Rat) Pow 

func (x *Rat) Pow(y *Int) RObj

func (*Rat) Sign 

func (x *Rat) Sign() int

func (*Rat) String 

func (x *Rat) String() string

func (*Rat) Sub 

func (x *Rat) Sub(yy RObj) RObj

func (*Rat) Subst 

func (z *Rat) Subst(x RObj, lv Level) RObj

func (*Rat) ToInt added in v0.0.5 

func (z *Rat) ToInt() *Int

ToInt returns the quotient x/y for y != 0. If y == 0, a division-by-zero run-time panic occurs.

type String 

type String struct {
	GObj
	// contains filtered or unexported fields
}

func NewString 

func NewString(s string) *String

func (*String) Format 

func (z *String) Format(s fmt.State, format rune)

func (*String) S added in v0.0.2 

func (s *String) S() string

func (*String) String 

func (s *String) String() string

func (*String) Tag 

func (s *String) Tag() uint

type Uint 

type Uint uint32

Uint is an NObj

func (Uint) Abs 

func (p Uint) Abs() NObj

func (Uint) Add 

func (p Uint) Add(x RObj) RObj

func (Uint) Cmp 

func (p Uint) Cmp(x NObj) int

func (Uint) CmpAbs 

func (p Uint) CmpAbs(x NObj) int

func (Uint) Deg added in v0.0.4 

func (x Uint) Deg(lv Level) int

func (Uint) Div 

func (p Uint) Div(x NObj) RObj

func (Uint) Equals 

func (p Uint) Equals(v interface{}) bool

func (Uint) Float 

func (p Uint) Float() float64

func (Uint) Format 

func (p Uint) Format(s fmt.State, format rune)

func (Uint) IsMinusOne 

func (p Uint) IsMinusOne() bool

func (Uint) IsNumeric 

func (p Uint) IsNumeric() bool

func (Uint) IsOne 

func (p Uint) IsOne() bool

func (Uint) IsZero 

func (p Uint) IsZero() bool

func (Uint) Mul 

func (p Uint) Mul(x RObj) RObj

func (Uint) Neg 

func (p Uint) Neg() RObj

func (Uint) Pow 

func (p Uint) Pow(x *Int) RObj

func (Uint) Sign 

func (p Uint) Sign() int

func (Uint) String 

func (p Uint) String() string

func (Uint) Sub 

func (p Uint) Sub(x RObj) RObj

func (Uint) Subst 

func (p Uint) Subst(x RObj, lv Level) RObj

func (Uint) Tag 

func (p Uint) Tag() uint

Source Files

View all Source files

Directories

Path Synopsis
cas
ox
para
sage
test
cmd
esp
ganrac-ox
ganrac-sage
sdc

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