symexpr

package module
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 Go to latest Published: Feb 18, 2014 License: BSD-3-Clause Imports: 7 Imported by: 4

README

Symbolic Expressions (just math for now)

  • represetation: as an AST tree
  • manipulation: add,rm, simplify, derivative
  • evaluation: explicit, RK4 integration, non-linear regression via levmar->MINPACK
  • printing: String() print, prettyprint, serialization
type exprType int

const (
	NULL      exprType = iota
	CONSTANT           // indexed constant, useful for regression tasks
	CONSTANTF          // floating point constant
	TIME               // useful when looking at time series and RK4 integration
	SYSTEM             // i use this like a variable that changes between experiments, but not with time (mass,size,etc.)
	VAR                // a canonical variable

	NEG
	ABS
	SQRT
	SIN
	COS
	TAN
	EXP
	LOG
	POWI // Expr^Integer
	POWF // Expr^Float

	POWE // Expr^Expr
	DIV

	ADD // these can have more than two child nodes
	MUL // this eases simplification

	EXPR_MAX
	STARTVAR // for serialization reduction of variables
)

// Expr is the interface to all node types for the AST of mathematical expression
// 

type Expr interface {

	// types.go (this file)
	ExprType() exprType
	Clone() Expr

	// stats.go
	Size() int
	Depth() int
	Height() int
	NumChildren() int
	CalcExprStats(currDepth int) (mySize int)

	// compare.go
	AmILess(rhs Expr) bool
	AmIEqual(rhs Expr) bool
	AmISame(rhs Expr) bool       // equality without coefficient values/index
	AmIAlmostSame(rhs Expr) bool // adds flexibility to mul comparison to AmISame
	Sort()

	// has.go
	HasVar() bool
	HasVarI(i int) bool
	NumVar() int

	// DFS for a floating point valued ConstantF
	HasConst() bool
	// DFS for a indexed valued Constant
	HasConstI(i int) bool
	// Counts the number of indexed Constant nodes
	NumConstants() int

	// convert.go

	// Converts indexed Constant nodes to ConstantF nodes
	// using the input slice as the values for replacement 
	ConvertToConstantFs(cs []float64) Expr
	// DFS converting float valued constants to indexed constants
	// the input should be an empty slice
	// the output is an appended slice the size = |ConstantF| in the tree
	ConvertToConstants(cs []float64) ([]float64, Expr)
	//   IndexConstants( ci int ) int

	// getset.go   
	// DFS retrieval of a node by index
	GetExpr(pos *int) Expr
	// DFS replacement of a node and it's subtree
	// replaced is used to discontinue the DFS after replacement
	// replace_me gets triggered when pos == 0 and informs the parent node to replace the respective child node
	SetExpr(pos *int, e Expr) (replace_me, replaced bool)

	// print.go

	// prints the AST 
	String() string

	// creates an integer representation of the AST in ~prefix notation
	// The input is an empty slice, output is the representation.
	// The output is generally the ExprType integer value
	// Associative operators (+ & *) also include the number of children.
	// The terminal nodes include the index when appropriate.
	Serial([]int) []int

	// Pretty print acts like String, but replaces the internal indexed
	// formatting with user specified strings and values
	PrettyPrint(dnames, snames []string, cvals []float64) string
	// 	WriteString( buf *bytes.Buffer )

	// eval.go
	// Evaluates an expression at one point
	// t is a time value
	// x are the input Var values
	// c are the indexed Constant values
	// s are the indexed System values
	// the output is the result of DFS evaluation
	Eval(t float64, x, c, s []float64) float64

	// simp.go
	Simplify(rules SimpRules) Expr

	// deriv.go
	// Calculate the derivative w.r.t. Var_i
	DerivVar(i int) Expr
	// Calculate the derivative w.r.t. Constant_i
	DerivConst(i int) Expr
}

Tony Worm Sept, 2012

Documentation

Overview

Package symexpr implements symbolic equations as an AST. It aims to provide ease of dynamic manipulation of the tree.

This work comes out of my Masters thesis at Binghamton University and is geared towards Symbolic Regression.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func DumpExprTypes 

func DumpExprTypes()

func PRK4 

func PRK4(xn int, eqn Expr, ti, tj float64, x_in, x_out, x_tmp, c, s []float64) float64

func PrintPRK4 

func PrintPRK4(xn int, eqn Expr, ti, to float64, x_in, x_out, x_tmp, c, s []float64) float64

func RK4 

func RK4(eqn []Expr, ti, tj float64, x_in, x_tmp, c, s []float64) (x_out []float64)

Types

type Abs 

type Abs struct {
	Unary
}

func NewAbs 

func NewAbs(e Expr) *Abs

func (*Abs) AmIAlmostSame 

func (u *Abs) AmIAlmostSame(r Expr) bool

func (*Abs) AmIEqual 

func (u *Abs) AmIEqual(r Expr) bool

func (*Abs) AmILess 

func (u *Abs) AmILess(r Expr) bool

func (*Abs) AmISame 

func (u *Abs) AmISame(r Expr) bool

func (*Abs) Clone 

func (u *Abs) Clone() Expr

func (*Abs) ConvertToConstantFs 

func (u *Abs) ConvertToConstantFs(cs []float64) Expr

func (*Abs) ConvertToConstants 

func (u *Abs) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Abs) DerivConst 

func (u *Abs) DerivConst(i int) Expr

func (*Abs) DerivVar 

func (u *Abs) DerivVar(i int) Expr

func (*Abs) Eval 

func (u *Abs) Eval(t float64, x, c, s []float64) float64

func (*Abs) ExprType 

func (u *Abs) ExprType() ExprType

func (*Abs) GetExpr 

func (u *Abs) GetExpr(pos *int) Expr

func (*Abs) Javascript 

func (u *Abs) Javascript(dnames, snames []string, cvals []float64) string

func (*Abs) Latex 

func (u *Abs) Latex(dnames, snames []string, cvals []float64) string

func (*Abs) PrettyPrint 

func (u *Abs) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Abs) Serial 

func (u *Abs) Serial(sofar []int) []int

func (*Abs) SetExpr 

func (u *Abs) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Abs) Simplify 

func (u *Abs) Simplify(rules SimpRules) (ret Expr)

func (*Abs) Sort 

func (u *Abs) Sort()

func (*Abs) StackSerial 

func (u *Abs) StackSerial(sofar []int) []int

func (*Abs) String 

func (u *Abs) String() string

type Add 

type Add struct {
	N_ary
}

N-ary Operators

func NewAdd 

func NewAdd() *Add

func (*Add) AmIAlmostSame 

func (n *Add) AmIAlmostSame(r Expr) bool

func (*Add) AmIEqual 

func (n *Add) AmIEqual(r Expr) bool

func (*Add) AmILess 

func (n *Add) AmILess(r Expr) bool

func (*Add) AmISame 

func (n *Add) AmISame(r Expr) bool

func (*Add) Clone 

func (n *Add) Clone() Expr

func (*Add) ConvertToConstantFs 

func (n *Add) ConvertToConstantFs(cs []float64) Expr

func (*Add) ConvertToConstants 

func (n *Add) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Add) DerivConst 

func (n *Add) DerivConst(i int) Expr

func (*Add) DerivVar 

func (n *Add) DerivVar(i int) Expr

func (*Add) Eval 

func (n *Add) Eval(t float64, x, c, s []float64) float64

func (*Add) ExprType 

func (n *Add) ExprType() ExprType

func (*Add) GetExpr 

func (n *Add) GetExpr(pos *int) Expr

func (*Add) Insert 

func (a *Add) Insert(e Expr)

func (*Add) Javascript 

func (n *Add) Javascript(dnames, snames []string, cvals []float64) string

func (*Add) Latex 

func (n *Add) Latex(dnames, snames []string, cvals []float64) string

func (*Add) Len 

func (n *Add) Len() int

func (*Add) Less 

func (n *Add) Less(i, j int) bool

func (*Add) PrettyPrint 

func (n *Add) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Add) Serial 

func (n *Add) Serial(sofar []int) []int

func (*Add) SetExpr 

func (n *Add) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Add) Simplify 

func (n *Add) Simplify(rules SimpRules) Expr

func (*Add) Sort 

func (n *Add) Sort()

func (*Add) StackSerial 

func (n *Add) StackSerial(sofar []int) []int

func (*Add) String 

func (n *Add) String() string

func (*Add) Swap 

func (n *Add) Swap(i, j int)

type Binary 

type Binary struct {
	ExprStats
	C1, C2 Expr
}

type Constant 

type Constant struct {
	Leaf
	P int
}

func NewConstant 

func NewConstant(i int) *Constant

func (*Constant) AmIAlmostSame 

func (c *Constant) AmIAlmostSame(r Expr) bool

func (*Constant) AmIEqual 

func (c *Constant) AmIEqual(r Expr) bool

func (*Constant) AmILess 

func (c *Constant) AmILess(r Expr) bool

func (*Constant) AmISame 

func (c *Constant) AmISame(r Expr) bool

func (*Constant) Clone 

func (c *Constant) Clone() Expr

func (*Constant) ConvertToConstantFs 

func (c *Constant) ConvertToConstantFs(cs []float64) Expr

func (*Constant) ConvertToConstants 

func (c *Constant) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Constant) DerivConst 

func (c *Constant) DerivConst(i int) Expr

func (*Constant) Eval 

func (cnst *Constant) Eval(t float64, x, c, s []float64) float64

func (*Constant) ExprType 

func (c *Constant) ExprType() ExprType

func (*Constant) GetExpr 

func (c *Constant) GetExpr(pos *int) Expr

func (*Constant) HasConst 

func (c *Constant) HasConst() bool

func (*Constant) HasConstI 

func (c *Constant) HasConstI(i int) bool

func (*Constant) Javascript 

func (c *Constant) Javascript(dnames, snames []string, cvals []float64) string

func (*Constant) Latex 

func (c *Constant) Latex(dnames, snames []string, cvals []float64) string

func (*Constant) NumConstants 

func (c *Constant) NumConstants() int

func (*Constant) PrettyPrint 

func (c *Constant) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Constant) Serial 

func (c *Constant) Serial(sofar []int) []int

func (*Constant) SetExpr 

func (c *Constant) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Constant) Simplify 

func (c *Constant) Simplify(rules SimpRules) Expr

func (*Constant) Sort 

func (c *Constant) Sort()

func (*Constant) StackSerial 

func (c *Constant) StackSerial(sofar []int) []int

func (*Constant) String 

func (c *Constant) String() string

type ConstantF 

type ConstantF struct {
	Leaf
	F float64
}

func NewConstantF 

func NewConstantF(f float64) *ConstantF

func (*ConstantF) AmIAlmostSame 

func (c *ConstantF) AmIAlmostSame(r Expr) bool

func (*ConstantF) AmIEqual 

func (c *ConstantF) AmIEqual(r Expr) bool

func (*ConstantF) AmILess 

func (c *ConstantF) AmILess(r Expr) bool

func (*ConstantF) AmISame 

func (c *ConstantF) AmISame(r Expr) bool

func (*ConstantF) Clone 

func (c *ConstantF) Clone() Expr

func (*ConstantF) ConvertToConstantFs 

func (c *ConstantF) ConvertToConstantFs(cs []float64) Expr

func (*ConstantF) ConvertToConstants 

func (c *ConstantF) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*ConstantF) Eval 

func (cnst *ConstantF) Eval(t float64, x, c, s []float64) float64

func (*ConstantF) ExprType 

func (c *ConstantF) ExprType() ExprType

func (*ConstantF) GetExpr 

func (c *ConstantF) GetExpr(pos *int) Expr

func (*ConstantF) HasConst 

func (c *ConstantF) HasConst() bool

func (*ConstantF) HasConstI 

func (c *ConstantF) HasConstI(i int) bool

func (*ConstantF) Javascript 

func (c *ConstantF) Javascript(dnames, snames []string, cvals []float64) string

func (*ConstantF) Latex 

func (c *ConstantF) Latex(dnames, snames []string, cvals []float64) string

func (*ConstantF) PrettyPrint 

func (c *ConstantF) PrettyPrint(dnames, snames []string, cvals []float64) string

( we don't output the index since it is unimportant and can be altered )

func (*ConstantF) Serial 

func (c *ConstantF) Serial(sofar []int) []int

func (*ConstantF) SetExpr 

func (c *ConstantF) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*ConstantF) Simplify 

func (c *ConstantF) Simplify(rules SimpRules) Expr

func (*ConstantF) Sort 

func (c *ConstantF) Sort()

func (*ConstantF) StackSerial 

func (c *ConstantF) StackSerial(sofar []int) []int

func (*ConstantF) String 

func (c *ConstantF) String() string

type Cos 

type Cos struct {
	Unary
}

func NewCos 

func NewCos(e Expr) *Cos

func (*Cos) AmIAlmostSame 

func (u *Cos) AmIAlmostSame(r Expr) bool

func (*Cos) AmIEqual 

func (u *Cos) AmIEqual(r Expr) bool

func (*Cos) AmILess 

func (u *Cos) AmILess(r Expr) bool

func (*Cos) AmISame 

func (u *Cos) AmISame(r Expr) bool

func (*Cos) Clone 

func (u *Cos) Clone() Expr

func (*Cos) ConvertToConstantFs 

func (u *Cos) ConvertToConstantFs(cs []float64) Expr

func (*Cos) ConvertToConstants 

func (u *Cos) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Cos) DerivConst 

func (u *Cos) DerivConst(i int) Expr

func (*Cos) DerivVar 

func (u *Cos) DerivVar(i int) Expr

func (*Cos) Eval 

func (u *Cos) Eval(t float64, x, c, s []float64) float64

func (*Cos) ExprType 

func (u *Cos) ExprType() ExprType

func (*Cos) GetExpr 

func (u *Cos) GetExpr(pos *int) Expr

func (*Cos) Javascript 

func (u *Cos) Javascript(dnames, snames []string, cvals []float64) string

func (*Cos) Latex 

func (u *Cos) Latex(dnames, snames []string, cvals []float64) string

func (*Cos) PrettyPrint 

func (u *Cos) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Cos) Serial 

func (u *Cos) Serial(sofar []int) []int

func (*Cos) SetExpr 

func (u *Cos) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Cos) Simplify 

func (u *Cos) Simplify(rules SimpRules) (ret Expr)

func (*Cos) Sort 

func (u *Cos) Sort()

func (*Cos) StackSerial 

func (u *Cos) StackSerial(sofar []int) []int

func (*Cos) String 

func (u *Cos) String() string

type Div 

type Div struct {
	ExprStats
	Numer Expr
	Denom Expr
}

func NewDiv 

func NewDiv(n, d Expr) *Div

func (*Div) AmIAlmostSame 

func (n *Div) AmIAlmostSame(r Expr) bool

func (*Div) AmIEqual 

func (n *Div) AmIEqual(r Expr) bool

func (*Div) AmILess 

func (n *Div) AmILess(r Expr) bool

func (*Div) AmISame 

func (n *Div) AmISame(r Expr) bool

func (*Div) CalcExprStats 

func (n *Div) CalcExprStats()

func (*Div) Clone 

func (n *Div) Clone() Expr

func (*Div) ConvertToConstantFs 

func (n *Div) ConvertToConstantFs(cs []float64) Expr

func (*Div) ConvertToConstants 

func (n *Div) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Div) DerivConst 

func (n *Div) DerivConst(i int) Expr

func (*Div) DerivVar 

func (n *Div) DerivVar(i int) Expr

func (*Div) Eval 

func (n *Div) Eval(t float64, x, c, s []float64) float64

func (*Div) ExprType 

func (n *Div) ExprType() ExprType

func (*Div) GetExpr 

func (n *Div) GetExpr(pos *int) Expr

func (*Div) HasConst 

func (n *Div) HasConst() bool

func (*Div) HasConstI 

func (n *Div) HasConstI(i int) bool

func (*Div) HasVar 

func (n *Div) HasVar() bool

func (*Div) HasVarI 

func (n *Div) HasVarI(i int) bool

func (*Div) Javascript 

func (n *Div) Javascript(dnames, snames []string, cvals []float64) string

func (*Div) Latex 

func (n *Div) Latex(dnames, snames []string, cvals []float64) string

func (*Div) NumConstants 

func (n *Div) NumConstants() int

func (*Div) NumVar 

func (n *Div) NumVar() int

func (*Div) PrettyPrint 

func (n *Div) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Div) Serial 

func (n *Div) Serial(sofar []int) []int

func (*Div) SetExpr 

func (n *Div) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Div) Simplify 

func (n *Div) Simplify(rules SimpRules) Expr

func (*Div) Sort 

func (n *Div) Sort()

func (*Div) StackSerial 

func (n *Div) StackSerial(sofar []int) []int

func (*Div) String 

func (n *Div) String() string

type Exp 

type Exp struct {
	Unary
}

func NewExp 

func NewExp(e Expr) *Exp

func (*Exp) AmIAlmostSame 

func (u *Exp) AmIAlmostSame(r Expr) bool

func (*Exp) AmIEqual 

func (u *Exp) AmIEqual(r Expr) bool

func (*Exp) AmILess 

func (u *Exp) AmILess(r Expr) bool

func (*Exp) AmISame 

func (u *Exp) AmISame(r Expr) bool

func (*Exp) Clone 

func (u *Exp) Clone() Expr

func (*Exp) ConvertToConstantFs 

func (u *Exp) ConvertToConstantFs(cs []float64) Expr

func (*Exp) ConvertToConstants 

func (u *Exp) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Exp) DerivConst 

func (u *Exp) DerivConst(i int) Expr

func (*Exp) DerivVar 

func (u *Exp) DerivVar(i int) Expr

func (*Exp) Eval 

func (u *Exp) Eval(t float64, x, c, s []float64) float64

func (*Exp) ExprType 

func (u *Exp) ExprType() ExprType

func (*Exp) GetExpr 

func (u *Exp) GetExpr(pos *int) Expr

func (*Exp) Javascript 

func (u *Exp) Javascript(dnames, snames []string, cvals []float64) string

func (*Exp) Latex 

func (u *Exp) Latex(dnames, snames []string, cvals []float64) string

func (*Exp) PrettyPrint 

func (u *Exp) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Exp) Serial 

func (u *Exp) Serial(sofar []int) []int

func (*Exp) SetExpr 

func (u *Exp) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Exp) Simplify 

func (u *Exp) Simplify(rules SimpRules) (ret Expr)

func (*Exp) Sort 

func (u *Exp) Sort()

func (*Exp) StackSerial 

func (u *Exp) StackSerial(sofar []int) []int

func (*Exp) String 

func (u *Exp) String() string

type Expr 

type Expr interface {

	// types.go (this file)
	ExprType() ExprType
	Clone() Expr

	// stats.go
	Size() int
	Depth() int
	Height() int
	NumChildren() int
	CalcExprStats()

	// compare.go
	AmILess(rhs Expr) bool
	AmIEqual(rhs Expr) bool
	AmISame(rhs Expr) bool       // equality without coefficient values/index
	AmIAlmostSame(rhs Expr) bool // adds flexibility to mul comparison to AmISame
	Sort()

	// has.go
	HasVar() bool
	HasVarI(i int) bool
	NumVar() int

	// DFS for a floating point valued ConstantF
	HasConst() bool
	// DFS for a indexed valued Constant
	HasConstI(i int) bool
	// Counts the number of indexed Constant nodes
	NumConstants() int

	// Converts indexed Constant nodes to ConstantF nodes
	// using the input slice as the values for replacement
	ConvertToConstantFs(cs []float64) Expr
	// DFS converting float valued constants to indexed constants
	// the input should be an empty slice
	// the output is an appended slice the size = |ConstantF| in the tree
	ConvertToConstants(cs []float64) ([]float64, Expr)

	// getset.go
	// DFS retrieval of a node by index
	GetExpr(pos *int) Expr
	// DFS replacement of a node and it's subtree
	// replaced is used to discontinue the DFS after replacement
	// replace_me gets triggered when pos == 0 and informs the parent node to replace the respective child node
	SetExpr(pos *int, e Expr) (replace_me, replaced bool)

	// prints the AST
	String() string

	// creates an integer representation of the AST in ~prefix notation
	// The input is an empty slice, output is the representation.
	// The output is generally the ExprType integer value
	// Associative operators (+ & *) also include the number of children.
	// The terminal nodes include the index when appropriate.
	Serial([]int) []int
	StackSerial([]int) []int

	// Pretty print acts like String, but replaces the internal indexed
	// formatting with user specified strings and values
	PrettyPrint(dnames, snames []string, cvals []float64) string

	// Similar to PrettyPrint, but in latex format
	Latex(dnames, snames []string, cvals []float64) string
	Javascript(dnames, snames []string, cvals []float64) string

	// eval.go
	// Evaluates an expression at one point
	// t is a time value
	// x are the input Var values
	// c are the indexed Constant values
	// s are the indexed System values
	// the output is the result of DFS evaluation
	Eval(t float64, x, c, s []float64) float64

	// simp.go
	Simplify(rules SimpRules) Expr

	// deriv.go
	// Calculate the derivative w.r.t. Var_i
	DerivVar(i int) Expr
	// Calculate the derivative w.r.t. Constant_i
	DerivConst(i int) Expr
	// contains filtered or unexported methods
}

Expr is the interface to all node types for the AST of mathematical expression

func ParseFunc 

func ParseFunc(text string, varNames []string) Expr

func SwapExpr 

func SwapExpr(orig, newt Expr, pos int) (ret Expr)

type ExprArray 

type ExprArray []Expr

func (ExprArray) Len 

func (p ExprArray) Len() int

func (ExprArray) Less 

func (p ExprArray) Less(i, j int) bool

func (ExprArray) Swap 

func (p ExprArray) Swap(i, j int)

type ExprParams 

type ExprParams struct {

	// bounds on tree
	MaxS, MaxD,
	MinS, MinD int

	// bounds on some operators
	NumDim, NumSys, NumCoeff int

	// usable terms at each location
	Roots, Nodes, Leafs, NonTrig []Expr
}

type ExprStats 

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

func (*ExprStats) Depth 

func (es *ExprStats) Depth() int

func (*ExprStats) Height 

func (es *ExprStats) Height() int

func (*ExprStats) NumChildren 

func (es *ExprStats) NumChildren() int

func (*ExprStats) Pos 

func (es *ExprStats) Pos() int

func (*ExprStats) Size 

func (es *ExprStats) Size() int

type ExprType 

type ExprType int
const (
	NULL ExprType = iota

	STARTLEAF
	CONSTANT  // indexed constant, useful for non-linear regression tasks
	CONSTANTF // floating point constant
	TIME      // useful when looking at time series and RK4 integration
	SYSTEM    // i use this like a variable that changes between experiments, but not with time (mass,size,etc.)
	VAR       // a canonical variable
	LASTLEAF

	STARTFUNC
	NEG
	ABS
	SQRT
	SIN
	COS
	TAN
	EXP
	LOG
	LASTFUNC

	POWI // Expr^Integer
	POWF // Expr^Float
	POWE // Expr^Expr
	DIV  // Expr/Expr

	ADD // these can have more than two child nodes
	MUL // this eases sorting and simplification

	EXPR_MAX
	STARTVAR // for serialization reduction of variables
)

func (ExprType) String 

func (e ExprType) String() string

type Leaf 

type Leaf struct {
	ExprStats
}

func (*Leaf) CalcExprStats 

func (t *Leaf) CalcExprStats()

func (*Leaf) DerivConst 

func (l *Leaf) DerivConst(i int) Expr

func (*Leaf) DerivVar 

func (l *Leaf) DerivVar(i int) Expr

func (*Leaf) HasConst 

func (l *Leaf) HasConst() bool

func (*Leaf) HasConstI 

func (l *Leaf) HasConstI(i int) bool

func (*Leaf) HasVar 

func (l *Leaf) HasVar() bool

func (*Leaf) HasVarI 

func (l *Leaf) HasVarI(i int) bool

func (*Leaf) NumConstants 

func (l *Leaf) NumConstants() int

func (*Leaf) NumVar 

func (l *Leaf) NumVar() int

func (*Leaf) Simplify 

func (l *Leaf) Simplify(rules SimpRules) Expr

type Log 

type Log struct {
	Unary
}

func NewLog 

func NewLog(e Expr) *Log

func (*Log) AmIAlmostSame 

func (u *Log) AmIAlmostSame(r Expr) bool

func (*Log) AmIEqual 

func (u *Log) AmIEqual(r Expr) bool

func (*Log) AmILess 

func (u *Log) AmILess(r Expr) bool

func (*Log) AmISame 

func (u *Log) AmISame(r Expr) bool

func (*Log) Clone 

func (u *Log) Clone() Expr

func (*Log) ConvertToConstantFs 

func (u *Log) ConvertToConstantFs(cs []float64) Expr

func (*Log) ConvertToConstants 

func (u *Log) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Log) DerivConst 

func (u *Log) DerivConst(i int) Expr

func (*Log) DerivVar 

func (u *Log) DerivVar(i int) Expr

func (*Log) Eval 

func (u *Log) Eval(t float64, x, c, s []float64) float64

func (*Log) ExprType 

func (u *Log) ExprType() ExprType

func (*Log) GetExpr 

func (u *Log) GetExpr(pos *int) Expr

func (*Log) Javascript 

func (u *Log) Javascript(dnames, snames []string, cvals []float64) string

func (*Log) Latex 

func (u *Log) Latex(dnames, snames []string, cvals []float64) string

func (*Log) PrettyPrint 

func (u *Log) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Log) Serial 

func (u *Log) Serial(sofar []int) []int

func (*Log) SetExpr 

func (u *Log) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Log) Simplify 

func (u *Log) Simplify(rules SimpRules) (ret Expr)

func (*Log) Sort 

func (u *Log) Sort()

func (*Log) StackSerial 

func (u *Log) StackSerial(sofar []int) []int

func (*Log) String 

func (u *Log) String() string

type Mul 

type Mul struct {
	N_ary
}

func NewMul 

func NewMul() *Mul

func (*Mul) AmIAlmostSame 

func (n *Mul) AmIAlmostSame(r Expr) bool

func (*Mul) AmIEqual 

func (n *Mul) AmIEqual(r Expr) bool

func (*Mul) AmILess 

func (n *Mul) AmILess(r Expr) bool

func (*Mul) AmISame 

func (n *Mul) AmISame(r Expr) bool

func (*Mul) Clone 

func (n *Mul) Clone() Expr

func (*Mul) ConvertToConstantFs 

func (n *Mul) ConvertToConstantFs(cs []float64) Expr

func (*Mul) ConvertToConstants 

func (n *Mul) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Mul) DerivConst 

func (n *Mul) DerivConst(i int) Expr

func (*Mul) DerivVar 

func (n *Mul) DerivVar(i int) Expr

func (*Mul) Eval 

func (n *Mul) Eval(t float64, x, c, s []float64) float64

func (*Mul) ExprType 

func (n *Mul) ExprType() ExprType

func (*Mul) GetExpr 

func (n *Mul) GetExpr(pos *int) Expr

func (*Mul) Insert 

func (a *Mul) Insert(e Expr)

func (*Mul) Javascript 

func (n *Mul) Javascript(dnames, snames []string, cvals []float64) string

func (*Mul) Latex 

func (n *Mul) Latex(dnames, snames []string, cvals []float64) string

func (*Mul) Len 

func (n *Mul) Len() int

func (*Mul) Less 

func (n *Mul) Less(i, j int) bool

func (*Mul) PrettyPrint 

func (n *Mul) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Mul) Serial 

func (n *Mul) Serial(sofar []int) []int

func (*Mul) SetExpr 

func (n *Mul) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Mul) Simplify 

func (n *Mul) Simplify(rules SimpRules) Expr

func (*Mul) Sort 

func (n *Mul) Sort()

func (*Mul) StackSerial 

func (n *Mul) StackSerial(sofar []int) []int

func (*Mul) String 

func (n *Mul) String() string

func (*Mul) Swap 

func (n *Mul) Swap(i, j int)

type N_ary 

type N_ary struct {
	ExprStats
	CS []Expr
}

func (*N_ary) CalcExprStats 

func (n *N_ary) CalcExprStats()

func (*N_ary) DerivConst 

func (n *N_ary) DerivConst(i int) Expr

func (*N_ary) DerivVar 

func (n *N_ary) DerivVar(i int) Expr

func (*N_ary) HasConst 

func (n *N_ary) HasConst() bool

func (*N_ary) HasConstI 

func (n *N_ary) HasConstI(i int) bool

func (*N_ary) HasVar 

func (n *N_ary) HasVar() bool

func (*N_ary) HasVarI 

func (n *N_ary) HasVarI(i int) bool

func (*N_ary) NumConstants 

func (n *N_ary) NumConstants() int

func (*N_ary) NumVar 

func (n *N_ary) NumVar() int

func (*N_ary) Simplify 

func (n *N_ary) Simplify(rules SimpRules) Expr

type Neg 

type Neg struct {
	Unary
}

Unary Operators

func NewNeg 

func NewNeg(e Expr) *Neg

func (*Neg) AmIAlmostSame 

func (u *Neg) AmIAlmostSame(r Expr) bool

func (*Neg) AmIEqual 

func (u *Neg) AmIEqual(r Expr) bool

func (*Neg) AmILess 

func (u *Neg) AmILess(r Expr) bool

func (*Neg) AmISame 

func (u *Neg) AmISame(r Expr) bool

func (*Neg) Clone 

func (u *Neg) Clone() Expr

func (*Neg) ConvertToConstantFs 

func (u *Neg) ConvertToConstantFs(cs []float64) Expr

func (*Neg) ConvertToConstants 

func (u *Neg) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Neg) DerivConst 

func (u *Neg) DerivConst(i int) Expr

func (*Neg) DerivVar 

func (u *Neg) DerivVar(i int) Expr

func (*Neg) Eval 

func (u *Neg) Eval(t float64, x, c, s []float64) float64

func (*Neg) ExprType 

func (u *Neg) ExprType() ExprType

func (*Neg) GetExpr 

func (u *Neg) GetExpr(pos *int) Expr

func (*Neg) Javascript 

func (u *Neg) Javascript(dnames, snames []string, cvals []float64) string

func (*Neg) Latex 

func (u *Neg) Latex(dnames, snames []string, cvals []float64) string

func (*Neg) PrettyPrint 

func (u *Neg) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Neg) Serial 

func (u *Neg) Serial(sofar []int) []int

func (*Neg) SetExpr 

func (u *Neg) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Neg) Simplify 

func (u *Neg) Simplify(rules SimpRules) (ret Expr)

func (*Neg) Sort 

func (u *Neg) Sort()

func (*Neg) StackSerial 

func (u *Neg) StackSerial(sofar []int) []int

func (*Neg) String 

func (u *Neg) String() string

type Null 

type Null struct {
	ExprStats
}

Null Leaf (shouldn't really appear) This is a sample for the other node types

func NewNull 

func NewNull() *Null

func (*Null) AmIAlmostSame 

func (n *Null) AmIAlmostSame(r Expr) bool

func (*Null) AmIEqual 

func (n *Null) AmIEqual(r Expr) bool

func (*Null) AmILess 

func (n *Null) AmILess(r Expr) bool

func (*Null) AmISame 

func (n *Null) AmISame(r Expr) bool

func (*Null) CalcExprStats 

func (n *Null) CalcExprStats()

func (*Null) Clone 

func (n *Null) Clone() Expr

func (*Null) ConvertToConstantFs 

func (n *Null) ConvertToConstantFs(cs []float64) Expr

func (*Null) ConvertToConstants 

func (n *Null) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Null) DerivConst 

func (n *Null) DerivConst(i int) Expr

func (*Null) DerivVar 

func (n *Null) DerivVar(i int) Expr

func (*Null) Eval 

func (n *Null) Eval(t float64, x, c, s []float64) float64

func (*Null) ExprType 

func (n *Null) ExprType() ExprType

func (*Null) GetExpr 

func (n *Null) GetExpr(pos *int) Expr

func (*Null) HasConst 

func (n *Null) HasConst() bool

func (*Null) HasConstI 

func (n *Null) HasConstI(i int) bool

func (*Null) HasVar 

func (n *Null) HasVar() bool

func (*Null) HasVarI 

func (n *Null) HasVarI(i int) bool

func (*Null) Javascript 

func (n *Null) Javascript(dnames, snames []string, cvals []float64) string

func (*Null) Latex 

func (n *Null) Latex(dnames, snames []string, cvals []float64) string

func (*Null) NumConstants 

func (n *Null) NumConstants() int

func (*Null) NumVar 

func (n *Null) NumVar() int

func (*Null) PrettyPrint 

func (n *Null) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Null) Serial 

func (n *Null) Serial(sofar []int) []int

func (*Null) SetExpr 

func (n *Null) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Null) Simplify 

func (n *Null) Simplify(rules SimpRules) Expr

func (*Null) Sort 

func (n *Null) Sort()

func (*Null) StackSerial 

func (n *Null) StackSerial(sofar []int) []int

func (*Null) String 

func (n *Null) String() string

type PowE 

type PowE struct {
	ExprStats
	Base  Expr
	Power Expr
}

func NewPowE 

func NewPowE(b, p Expr) *PowE

func (*PowE) AmIAlmostSame 

func (n *PowE) AmIAlmostSame(r Expr) bool

func (*PowE) AmIEqual 

func (n *PowE) AmIEqual(r Expr) bool

func (*PowE) AmILess 

func (n *PowE) AmILess(r Expr) bool

func (*PowE) AmISame 

func (n *PowE) AmISame(r Expr) bool

func (*PowE) CalcExprStats 

func (n *PowE) CalcExprStats()

func (*PowE) Clone 

func (n *PowE) Clone() Expr

func (*PowE) ConvertToConstantFs 

func (n *PowE) ConvertToConstantFs(cs []float64) Expr

func (*PowE) ConvertToConstants 

func (n *PowE) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*PowE) DerivConst 

func (n *PowE) DerivConst(i int) Expr

func (*PowE) DerivVar 

func (n *PowE) DerivVar(i int) Expr

TODO TODO TODO fix me and the next one

func (*PowE) Eval 

func (n *PowE) Eval(t float64, x, c, s []float64) float64

func (*PowE) ExprType 

func (n *PowE) ExprType() ExprType

func (*PowE) GetExpr 

func (n *PowE) GetExpr(pos *int) Expr

func (*PowE) HasConst 

func (n *PowE) HasConst() bool

func (*PowE) HasConstI 

func (n *PowE) HasConstI(i int) bool

func (*PowE) HasVar 

func (n *PowE) HasVar() bool

func (*PowE) HasVarI 

func (n *PowE) HasVarI(i int) bool

func (*PowE) Javascript 

func (u *PowE) Javascript(dnames, snames []string, cvals []float64) string

func (*PowE) Latex 

func (u *PowE) Latex(dnames, snames []string, cvals []float64) string

func (*PowE) NumConstants 

func (n *PowE) NumConstants() int

func (*PowE) NumVar 

func (n *PowE) NumVar() int

func (*PowE) PrettyPrint 

func (u *PowE) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*PowE) Serial 

func (n *PowE) Serial(sofar []int) []int

func (*PowE) SetExpr 

func (n *PowE) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*PowE) Simplify 

func (n *PowE) Simplify(rules SimpRules) Expr

func (*PowE) Sort 

func (n *PowE) Sort()

func (*PowE) StackSerial 

func (n *PowE) StackSerial(sofar []int) []int

func (*PowE) String 

func (n *PowE) String() string

type PowF 

type PowF struct {
	ExprStats
	Base  Expr
	Power float64
}

func NewPowF 

func NewPowF(b Expr, f float64) *PowF

func (*PowF) AmIAlmostSame 

func (u *PowF) AmIAlmostSame(r Expr) bool

func (*PowF) AmIEqual 

func (u *PowF) AmIEqual(r Expr) bool

func (*PowF) AmILess 

func (u *PowF) AmILess(r Expr) bool

func (*PowF) AmISame 

func (u *PowF) AmISame(r Expr) bool

func (*PowF) CalcExprStats 

func (u *PowF) CalcExprStats()

func (*PowF) Clone 

func (u *PowF) Clone() Expr

func (*PowF) ConvertToConstantFs 

func (u *PowF) ConvertToConstantFs(cs []float64) Expr

func (*PowF) ConvertToConstants 

func (u *PowF) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*PowF) DerivConst 

func (u *PowF) DerivConst(i int) Expr

func (*PowF) DerivVar 

func (u *PowF) DerivVar(i int) Expr

func (*PowF) Eval 

func (u *PowF) Eval(t float64, x, c, s []float64) float64

func (*PowF) ExprType 

func (u *PowF) ExprType() ExprType

func (*PowF) GetExpr 

func (u *PowF) GetExpr(pos *int) Expr

func (*PowF) HasConst 

func (u *PowF) HasConst() bool

func (*PowF) HasConstI 

func (u *PowF) HasConstI(i int) bool

func (*PowF) HasVar 

func (u *PowF) HasVar() bool

func (*PowF) HasVarI 

func (u *PowF) HasVarI(i int) bool

func (*PowF) Javascript 

func (u *PowF) Javascript(dnames, snames []string, cvals []float64) string

func (*PowF) Latex 

func (u *PowF) Latex(dnames, snames []string, cvals []float64) string

func (*PowF) NumConstants 

func (u *PowF) NumConstants() int

func (*PowF) NumVar 

func (u *PowF) NumVar() int

func (*PowF) PrettyPrint 

func (u *PowF) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*PowF) Serial 

func (u *PowF) Serial(sofar []int) []int

func (*PowF) SetExpr 

func (u *PowF) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*PowF) Simplify 

func (u *PowF) Simplify(rules SimpRules) Expr

func (*PowF) Sort 

func (u *PowF) Sort()

func (*PowF) StackSerial 

func (u *PowF) StackSerial(sofar []int) []int

func (*PowF) String 

func (u *PowF) String() string

type PowI 

type PowI struct {
	ExprStats
	Base  Expr
	Power int
}

Hmmm... Operators

func NewPowI 

func NewPowI(e Expr, i int) *PowI

func (*PowI) AmIAlmostSame 

func (u *PowI) AmIAlmostSame(r Expr) bool

func (*PowI) AmIEqual 

func (u *PowI) AmIEqual(r Expr) bool

func (*PowI) AmILess 

func (u *PowI) AmILess(r Expr) bool

func (*PowI) AmISame 

func (u *PowI) AmISame(r Expr) bool

func (*PowI) CalcExprStats 

func (u *PowI) CalcExprStats()

func (*PowI) Clone 

func (u *PowI) Clone() Expr

func (*PowI) ConvertToConstantFs 

func (u *PowI) ConvertToConstantFs(cs []float64) Expr

func (*PowI) ConvertToConstants 

func (u *PowI) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*PowI) DerivConst 

func (u *PowI) DerivConst(i int) Expr

func (*PowI) DerivVar 

func (u *PowI) DerivVar(i int) Expr

func (*PowI) Eval 

func (u *PowI) Eval(t float64, x, c, s []float64) float64

func (*PowI) ExprType 

func (u *PowI) ExprType() ExprType

func (*PowI) GetExpr 

func (u *PowI) GetExpr(pos *int) Expr

func (*PowI) HasConst 

func (u *PowI) HasConst() bool

func (*PowI) HasConstI 

func (u *PowI) HasConstI(i int) bool

func (*PowI) HasVar 

func (u *PowI) HasVar() bool

func (*PowI) HasVarI 

func (u *PowI) HasVarI(i int) bool

func (*PowI) Javascript 

func (u *PowI) Javascript(dnames, snames []string, cvals []float64) string

func (*PowI) Latex 

func (u *PowI) Latex(dnames, snames []string, cvals []float64) string

func (*PowI) NumConstants 

func (u *PowI) NumConstants() int

func (*PowI) NumVar 

func (u *PowI) NumVar() int

func (*PowI) PrettyPrint 

func (u *PowI) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*PowI) Serial 

func (u *PowI) Serial(sofar []int) []int

func (*PowI) SetExpr 

func (u *PowI) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*PowI) Simplify 

func (u *PowI) Simplify(rules SimpRules) Expr

func (*PowI) Sort 

func (u *PowI) Sort()

func (*PowI) StackSerial 

func (u *PowI) StackSerial(sofar []int) []int

func (*PowI) String 

func (u *PowI) String() string

type SimpRules 

type SimpRules struct {
	GroupAddTerms bool
	ConvertConsts bool
	MulToPow      bool
	MaxPowPow     int

	MulInCoeff int // add must be >= to size, 0 == No

	// state tracking
	InTrig bool
}

func DefaultRules 

func DefaultRules() SimpRules

type Sin 

type Sin struct {
	Unary
}

func NewSin 

func NewSin(e Expr) *Sin

func (*Sin) AmIAlmostSame 

func (u *Sin) AmIAlmostSame(r Expr) bool

func (*Sin) AmIEqual 

func (u *Sin) AmIEqual(r Expr) bool

func (*Sin) AmILess 

func (u *Sin) AmILess(r Expr) bool

func (*Sin) AmISame 

func (u *Sin) AmISame(r Expr) bool

func (*Sin) Clone 

func (u *Sin) Clone() Expr

func (*Sin) ConvertToConstantFs 

func (u *Sin) ConvertToConstantFs(cs []float64) Expr

func (*Sin) ConvertToConstants 

func (u *Sin) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Sin) DerivConst 

func (u *Sin) DerivConst(i int) Expr

func (*Sin) DerivVar 

func (u *Sin) DerivVar(i int) Expr

func (*Sin) Eval 

func (u *Sin) Eval(t float64, x, c, s []float64) float64

func (*Sin) ExprType 

func (u *Sin) ExprType() ExprType

func (*Sin) GetExpr 

func (u *Sin) GetExpr(pos *int) Expr

func (*Sin) Javascript 

func (u *Sin) Javascript(dnames, snames []string, cvals []float64) string

func (*Sin) Latex 

func (u *Sin) Latex(dnames, snames []string, cvals []float64) string

func (*Sin) PrettyPrint 

func (u *Sin) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Sin) Serial 

func (u *Sin) Serial(sofar []int) []int

func (*Sin) SetExpr 

func (u *Sin) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Sin) Simplify 

func (u *Sin) Simplify(rules SimpRules) (ret Expr)

func (*Sin) Sort 

func (u *Sin) Sort()

func (*Sin) StackSerial 

func (u *Sin) StackSerial(sofar []int) []int

func (*Sin) String 

func (u *Sin) String() string

type Sqrt 

type Sqrt struct {
	Unary
}

func NewSqrt 

func NewSqrt(e Expr) *Sqrt

func (*Sqrt) AmIAlmostSame 

func (u *Sqrt) AmIAlmostSame(r Expr) bool

func (*Sqrt) AmIEqual 

func (u *Sqrt) AmIEqual(r Expr) bool

func (*Sqrt) AmILess 

func (u *Sqrt) AmILess(r Expr) bool

func (*Sqrt) AmISame 

func (u *Sqrt) AmISame(r Expr) bool

func (*Sqrt) Clone 

func (u *Sqrt) Clone() Expr

func (*Sqrt) ConvertToConstantFs 

func (u *Sqrt) ConvertToConstantFs(cs []float64) Expr

func (*Sqrt) ConvertToConstants 

func (u *Sqrt) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Sqrt) DerivConst 

func (u *Sqrt) DerivConst(i int) Expr

func (*Sqrt) DerivVar 

func (u *Sqrt) DerivVar(i int) Expr

func (*Sqrt) Eval 

func (u *Sqrt) Eval(t float64, x, c, s []float64) float64

func (*Sqrt) ExprType 

func (u *Sqrt) ExprType() ExprType

func (*Sqrt) GetExpr 

func (u *Sqrt) GetExpr(pos *int) Expr

func (*Sqrt) Javascript 

func (u *Sqrt) Javascript(dnames, snames []string, cvals []float64) string

func (*Sqrt) Latex 

func (u *Sqrt) Latex(dnames, snames []string, cvals []float64) string

func (*Sqrt) PrettyPrint 

func (u *Sqrt) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Sqrt) Serial 

func (u *Sqrt) Serial(sofar []int) []int

func (*Sqrt) SetExpr 

func (u *Sqrt) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Sqrt) Simplify 

func (u *Sqrt) Simplify(rules SimpRules) (ret Expr)

func (*Sqrt) Sort 

func (u *Sqrt) Sort()

func (*Sqrt) StackSerial 

func (u *Sqrt) StackSerial(sofar []int) []int

func (*Sqrt) String 

func (u *Sqrt) String() string

type System 

type System struct {
	Leaf
	P int
}

func NewSystem 

func NewSystem(i int) *System

func (*System) AmIAlmostSame 

func (s *System) AmIAlmostSame(r Expr) bool

func (*System) AmIEqual 

func (s *System) AmIEqual(r Expr) bool

func (*System) AmILess 

func (s *System) AmILess(r Expr) bool

func (*System) AmISame 

func (s *System) AmISame(r Expr) bool

func (*System) Clone 

func (s *System) Clone() Expr

func (*System) ConvertToConstantFs 

func (s *System) ConvertToConstantFs(cs []float64) Expr

func (*System) ConvertToConstants 

func (s *System) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*System) Eval 

func (sys *System) Eval(t float64, x, c, s []float64) float64

func (*System) ExprType 

func (s *System) ExprType() ExprType

func (*System) GetExpr 

func (s *System) GetExpr(pos *int) Expr

func (*System) Javascript 

func (s *System) Javascript(dnames, snames []string, cvals []float64) string

func (*System) Latex 

func (s *System) Latex(dnames, snames []string, cvals []float64) string

func (*System) PrettyPrint 

func (s *System) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*System) Serial 

func (s *System) Serial(sofar []int) []int

func (*System) SetExpr 

func (s *System) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*System) Simplify 

func (s *System) Simplify(rules SimpRules) Expr

func (*System) Sort 

func (s *System) Sort()

func (*System) StackSerial 

func (s *System) StackSerial(sofar []int) []int

func (*System) String 

func (s *System) String() string

type Tan 

type Tan struct {
	Unary
}

func NewTan 

func NewTan(e Expr) *Tan

func (*Tan) AmIAlmostSame 

func (u *Tan) AmIAlmostSame(r Expr) bool

func (*Tan) AmIEqual 

func (u *Tan) AmIEqual(r Expr) bool

func (*Tan) AmILess 

func (u *Tan) AmILess(r Expr) bool

func (*Tan) AmISame 

func (u *Tan) AmISame(r Expr) bool

func (*Tan) Clone 

func (u *Tan) Clone() Expr

func (*Tan) ConvertToConstantFs 

func (u *Tan) ConvertToConstantFs(cs []float64) Expr

func (*Tan) ConvertToConstants 

func (u *Tan) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Tan) DerivVar 

func (u *Tan) DerivVar(i int) Expr

func (*Tan) Eval 

func (u *Tan) Eval(t float64, x, c, s []float64) float64

func (*Tan) ExprType 

func (u *Tan) ExprType() ExprType

func (*Tan) GetExpr 

func (u *Tan) GetExpr(pos *int) Expr

func (*Tan) Javascript 

func (u *Tan) Javascript(dnames, snames []string, cvals []float64) string

func (*Tan) Latex 

func (u *Tan) Latex(dnames, snames []string, cvals []float64) string

func (*Tan) PrettyPrint 

func (u *Tan) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Tan) Serial 

func (u *Tan) Serial(sofar []int) []int

func (*Tan) SetExpr 

func (u *Tan) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Tan) Simplify 

func (u *Tan) Simplify(rules SimpRules) (ret Expr)

func (*Tan) Sort 

func (u *Tan) Sort()

func (*Tan) StackSerial 

func (u *Tan) StackSerial(sofar []int) []int

func (*Tan) String 

func (u *Tan) String() string

type Time 

type Time struct {
	Leaf
}

Leaf Nodes

func NewTime 

func NewTime() *Time

func (*Time) AmIAlmostSame 

func (n *Time) AmIAlmostSame(r Expr) bool

func (*Time) AmIEqual 

func (n *Time) AmIEqual(r Expr) bool

func (*Time) AmILess 

func (n *Time) AmILess(r Expr) bool

func (*Time) AmISame 

func (n *Time) AmISame(r Expr) bool

func (*Time) Clone 

func (t *Time) Clone() Expr

func (*Time) ConvertToConstantFs 

func (n *Time) ConvertToConstantFs(cs []float64) Expr

func (*Time) ConvertToConstants 

func (n *Time) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Time) Eval 

func (*Time) Eval(t float64, x, c, s []float64) float64

func (*Time) ExprType 

func (t *Time) ExprType() ExprType

func (*Time) GetExpr 

func (n *Time) GetExpr(pos *int) Expr

func (*Time) Javascript 

func (t *Time) Javascript(dnames, snames []string, cvals []float64) string

func (*Time) Latex 

func (t *Time) Latex(dnames, snames []string, cvals []float64) string

func (*Time) PrettyPrint 

func (t *Time) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Time) Serial 

func (t *Time) Serial(sofar []int) []int

func (*Time) SetExpr 

func (n *Time) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Time) Simplify 

func (n *Time) Simplify(rules SimpRules) Expr

func (*Time) Sort 

func (n *Time) Sort()

func (*Time) StackSerial 

func (t *Time) StackSerial(sofar []int) []int

func (*Time) String 

func (n *Time) String() string

type Unary 

type Unary struct {
	ExprStats
	C Expr
}

func (*Unary) CalcExprStats 

func (u *Unary) CalcExprStats()

func (*Unary) DerivConst 

func (u *Unary) DerivConst(i int) Expr

func (*Unary) DerivVar 

func (u *Unary) DerivVar(i int) Expr

func (*Unary) HasConst 

func (u *Unary) HasConst() bool

func (*Unary) HasConstI 

func (u *Unary) HasConstI(i int) bool

func (*Unary) HasVar 

func (u *Unary) HasVar() bool

func (*Unary) HasVarI 

func (u *Unary) HasVarI(i int) bool

func (*Unary) NumConstants 

func (u *Unary) NumConstants() int

func (*Unary) NumVar 

func (u *Unary) NumVar() int

func (*Unary) Simplify 

func (u *Unary) Simplify(rules SimpRules) Expr

type Var 

type Var struct {
	Leaf
	P int
}

func NewVar 

func NewVar(i int) *Var

func (*Var) AmIAlmostSame 

func (v *Var) AmIAlmostSame(r Expr) bool

func (*Var) AmIEqual 

func (v *Var) AmIEqual(r Expr) bool

func (*Var) AmILess 

func (v *Var) AmILess(r Expr) bool

func (*Var) AmISame 

func (v *Var) AmISame(r Expr) bool

func (*Var) Clone 

func (v *Var) Clone() Expr

func (*Var) ConvertToConstantFs 

func (v *Var) ConvertToConstantFs(cs []float64) Expr

func (*Var) ConvertToConstants 

func (v *Var) ConvertToConstants(cs []float64) ([]float64, Expr)

func (*Var) DerivVar 

func (v *Var) DerivVar(i int) Expr

func (*Var) Eval 

func (v *Var) Eval(t float64, x, c, s []float64) float64

func (*Var) ExprType 

func (v *Var) ExprType() ExprType

func (*Var) GetExpr 

func (v *Var) GetExpr(pos *int) Expr

func (*Var) HasVar 

func (v *Var) HasVar() bool

func (*Var) HasVarI 

func (v *Var) HasVarI(i int) bool

func (*Var) Javascript 

func (v *Var) Javascript(dnames, snames []string, cvals []float64) string

func (*Var) Latex 

func (v *Var) Latex(dnames, snames []string, cvals []float64) string

func (*Var) NumVar 

func (v *Var) NumVar() int

func (*Var) PrettyPrint 

func (v *Var) PrettyPrint(dnames, snames []string, cvals []float64) string

func (*Var) Serial 

func (v *Var) Serial(sofar []int) []int

func (*Var) SetExpr 

func (v *Var) SetExpr(pos *int, e Expr) (replace_me, replaced bool)

func (*Var) Simplify 

func (v *Var) Simplify(rules SimpRules) Expr

func (*Var) Sort 

func (v *Var) Sort()

func (*Var) StackSerial 

func (v *Var) StackSerial(sofar []int) []int

func (*Var) String 

func (v *Var) String() string

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