class to manipulate with Cheng-Wu theorem More...

#include <SD.h>

Static Public Member Functions
static bool	isProjective (const ex fe, const ex delta)
	to check the input fe is Projective or NOT w.r.t. delta More...

static void	Projectivize (ex &fe, const ex delta, const ex xsum=0)
	to Projectivize the input fe, the fe will be updated More...

static void	Scalelize (ex &fe, const lst xs, const ex cy)
	to Scalelize the input fe, the fe will be updated More...

static void	Scalelize (ex &fe, const ex xi, const ex cy)
	to Scalelize the input fe, the fe will be updated, make transformation xi -> cy * yi & yi->xi, the determinant will be added to fe back More...

static exvector	Binarize (ex const fe, ex const eqn)
	Binarize the input fe, w.r.t. the linear eqn. More...

static void	Binarize (ex const fe, ex const eqn, exvector &ovec)
	Binarize the input fe, w.r.t. the linear eqn. More...

static bool	isLinearizable (const ex ft, const ex delta, lst &xcs)
	Linearize w.r.t. F-term. More...

static void	Linearize (const lst xcs, ex &fe, ex &ft)
	Linearize w.r.t. xcs_in. More...

static bool	isPartilizable (const ex ft, const ex delta, lst &xcs, int mode=0)
	isPartilize w.r.t. F-term, generized to isLinearizable More...

static void	Partilize (const lst xcs, const lst delta, const ex fe, exvector &ret_lst)
	Partilize function, generized to Linearize. More...

static exvector	Evaluate (const ex &fe)
	ChengWu Internal, make sure ft in the first term, ONLY appear in ChengWu.cpp. More...

static exvector	WickRotation (const exvector &fe_vec)
	WickRotation, just check WRA exist or NOT to see successful or NOT. Still Experimental. More...

static exvector	Apply (const exvector &fe_vec, const ex &ft=0)
	ChengWu-rized on the vector of fe, note that 1st element of the output, which needs to be droped, its information is used to label the ChengWu is successful or NOT. also check the Evaluate function for more information. More...

static exvector	Apply (const ex &fe, const ex &ft=0)

Detailed Description

class to manipulate with Cheng-Wu theorem

Definition at line 387 of file SD.h.

Member Function Documentation

◆ Apply() [1/2]

static exvector HepLib::SD::ChengWu::Apply	(	const ex &	fe,
		const ex &	ft = `0`
	)

inlinestatic

Definition at line 403 of file SD.h.

◆ Apply() [2/2]

exvector HepLib::SD::ChengWu::Apply	(	const exvector &	fe_vec,
		const ex &	ft = `0`
	)

static

ChengWu-rized on the vector of fe, note that 1st element of the output, which needs to be droped, its information is used to label the ChengWu is successful or NOT. also check the Evaluate function for more information.

Parameters

fe_vec the input vector of fe

Returns: ChengWu-rized vector of fe

Definition at line 61 of file ChengWu.cpp.

◆ Binarize() [1/2]

exvector HepLib::SD::ChengWu::Binarize	(	ex const	fe,
		ex const	eqn
	)

static

Binarize the input fe, w.r.t. the linear eqn.

Parameters

fe	the { function list, exponet list }
eqn	linear equation, line a xi + b xj, e.g. xi-xj can be devide into xi>xj and xi < xj, and then change xi/xj back to 0 to infinity

Returns: 2 elements of { function list, exponet list }, just like fe

Definition at line 219 of file ChengWu.cpp.

◆ Binarize() [2/2]

void HepLib::SD::ChengWu::Binarize	(	ex const	fe,
		ex const	eqn,
		exvector &	ovec
	)

static

Binarize the input fe, w.r.t. the linear eqn.

Parameters

fe	the { function list, exponet list }
eqn	linear equation, line a xi + b xj, e.g. xi-xj can be devide into xi>xj and xi < xj, and then change xi/xj back to 0 to infinity
ovec	will get updated

Definition at line 231 of file ChengWu.cpp.

◆ Evaluate()

exvector HepLib::SD::ChengWu::Evaluate ( const ex & in_fe )

static

ChengWu Internal, make sure ft in the first term, ONLY appear in ChengWu.cpp.

Parameters

in_fe input fe, ft = in_fe.op(0).op(0), and in_fe.op(1).op(0) should be 0

Returns: vector of fe, and fe_op(0).op(0) replaced by 1-ok, 2-nok

Definition at line 648 of file ChengWu.cpp.

◆ isLinearizable()

bool HepLib::SD::ChengWu::isLinearizable	(	const ex	ft,
		const ex	delta,
		lst &	xcs
	)

static

Linearize w.r.t. F-term.

Parameters

ft	the F-term
delta	the delta list
xcs	a list of format: { {x1,c1}, {x2,c2} ... }, will be updated by its append method

Returns: true for success

Definition at line 300 of file ChengWu.cpp.

◆ isPartilizable()

bool HepLib::SD::ChengWu::isPartilizable	(	const ex	ft,
		const ex	delta,
		lst &	xcs,
		int	mode = `0`
	)

static

isPartilize w.r.t. F-term, generized to isLinearizable

Parameters

ft	the F-term
delta	the delta list
xcs	a list of format: { {x1,c1}, {x2,c2} ... }, will be updated by its append method
mode	in the following, the repeated i implies summation on it. mode=0: x_i P_i, with P_i same-sign mode=1: x_i P_i + G_0, with P_i and G_0 same-sign mode=2: x_i P_i + G_0, with P-i same-sign, G_0 ~ (xm-xn)^n mode=3: x_i P_i + x_0 G_0 + Q_0, with P-i same-sign, G_0 ~ (xm-xn)^n & Q_0 same-sign mode=4: x_i P_i + x_0 G_0 + Q_0, with P-i same-sign, G_0/Q_0 ~ (xm-xn)^n

Returns: 2 elements of { function list, exponet list }, just like fe

Definition at line 396 of file ChengWu.cpp.

◆ isProjective()

bool HepLib::SD::ChengWu::isProjective	(	const ex	fe,
		const ex	delta
	)

static

to check the input fe is Projective or NOT w.r.t. delta

Parameters

fe	is the { function list, exponet list }
delta	is a list of x's in Delta function

Returns: true if fe is Projective

Definition at line 94 of file ChengWu.cpp.

◆ Linearize()

void HepLib::SD::ChengWu::Linearize	(	const lst	xcs_in,
		ex &	fe,
		ex &	ft
	)

static

Linearize w.r.t. xcs_in.

Parameters

xcs_in	from isLinerizable function
fe	the input/ouput fe
ft	other expression needs to be transformed

Definition at line 327 of file ChengWu.cpp.

◆ Partilize()

void HepLib::SD::ChengWu::Partilize	(	const lst	xcs,
		const lst	delta_in,
		const ex	fe_in,
		exvector &	ret_lst
	)

static

Partilize function, generized to Linearize.

Parameters

xcs	just from isPartilizable
delta_in	the delta list
fe_in	the original fe
ret_lst	will be updated by push_back

Definition at line 488 of file ChengWu.cpp.

◆ Projectivize()

void HepLib::SD::ChengWu::Projectivize	(	ex &	fe,
		const ex	delta,
		const ex	xsum_in = `0`
	)

static

to Projectivize the input fe, the fe will be updated

Parameters

fe	is the { function list, exponet list }
delta	is a list of x's in Delta function
xsum_in	is used to balance the powers, xsum refers to Delta(1-xsum), if xsum=0, then xsum=SUM(delta list)

Definition at line 118 of file ChengWu.cpp.

◆ Scalelize() [1/2]

void HepLib::SD::ChengWu::Scalelize	(	ex &	fe,
		const ex	xi,
		const ex	cy
	)

static

to Scalelize the input fe, the fe will be updated, make transformation xi -> cy * yi & yi->xi, the determinant will be added to fe back

Parameters

fe	is the { function list, exponet list }
xi	the variable
cy	the coefficient

Definition at line 158 of file ChengWu.cpp.

◆ Scalelize() [2/2]

void HepLib::SD::ChengWu::Scalelize	(	ex &	fe,
		const lst	xs,
		const ex	cy
	)

static

to Scalelize the input fe, the fe will be updated

Parameters

fe	is the { function list, exponet list }
xs	the list of { xi }, make transformation for each xi -> cy * yi & yi->xi, the determinant will be added to fe back
cy	the coefficient

Definition at line 169 of file ChengWu.cpp.

◆ WickRotation()

exvector HepLib::SD::ChengWu::WickRotation ( const exvector & fe_vec )

static

WickRotation, just check WRA exist or NOT to see successful or NOT. Still Experimental.

Parameters

fe_vec input fe vector

Returns: vector of fe

Definition at line 743 of file ChengWu.cpp.

The documentation for this class was generated from the following files:

/home/runner/work/HepLib/HepLib/SD/SD.h
/home/runner/work/HepLib/HepLib/SD/ChengWu.cpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ Apply() [1/2]

◆ Apply() [2/2]

◆ Binarize() [1/2]

◆ Binarize() [2/2]

◆ Evaluate()

◆ isLinearizable()

◆ isPartilizable()

◆ isProjective()

◆ Linearize()

◆ Partilize()

◆ Projectivize()

◆ Scalelize() [1/2]

◆ Scalelize() [2/2]

◆ WickRotation()