Math Namespace Reference

Functions
float	Li2 (float x)
float	Li3 (float x)
complex	CLi2 (Scalar x)
float	Cl2 (float x)
float	H2 (float x, float y)
float	B (float m1, float m2, float Q)
int	kron (int x, int y)
float	integrate (f, float l, float u, float prec=1e-6)
Scalar	c_integrate (f, float l, float u, float prec=1e-6)
float	psi (int n)
float	A0t (float x)
float	F0t (float x)
float	B0t (float x)
float	C0t (float x)
float	D0t (float x)
float	E0t (float x)
float	T (float x)
float	A1t (float x, float l)
float	B1t (float x, float l)
float	C1t (float x, float l)
float	D1t (float x, float l)
float	E1t (float x, float l)
float	F1t (float x, float l)
float	G1t (float x, float l)
float	C7t2mt (float x)
float	C7c2MW (float x)
float	C8t2mt (float x)
float	C8c2MW (float x)
float	F7_1 (float x)
float	F7_2 (float x)
float	F8_1 (float x)
float	F8_2 (float x)
float	G3H (float x, float lu)
float	G4H (float x, float lu)
float	G7H (float x, float lu, float ld)
float	G8H (float x, float lu, float ld)
float	EH (float x, float lu)
float	D9H0 (float x, float lu)
float	D9H1 (float x, float lu, float L)
float	Delta3H (float x, float lu)
float	Delta4H (float x, float lu)
float	Delta7H (float x, float lu, float ld)
float	Delta8H (float x, float lu, float ld)
float	C9llH0 (float x, float y, float lu)
float	C9llH1 (float x, float y, float lu, float L)
float	C10Wt2mt (float x)
float	C10Wc2MW (float x)
float	C10Zt2mt (float x)
float	C10Z2tri (float x)
float	F0SP (float xt)

Variables
	PI = mb.PI
	E = mb.E
	ZETA3 = mb.ZETA3
	GAMMA = mb.GAMMA

Detailed Description

Python wrapper for C++ bindings generated using Pybind11.
Each function corresponds to a mathematical or numerical utility available in the C++ backend.

Function Documentation

A0t()

float Math.A0t

(

float

x

)

Wilson coefficient A0t.

Args:
    x: A real parameter.

Returns:
    Value of A0t(x).

Definition at line 152 of file Math.py.

A1t()

float Math.A1t	(	float	x,
		float	l
	)

Wilson coefficient A1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of A1t(x, l).

Definition at line 194 of file Math.py.

B()

float Math.B	(	float	m1,
		float	m2,
		float	Q
	)

Compute the B-function of two masses and a scale Q.

Args:
    m1: First mass.
    m2: Second mass.
    Q: Renormalization scale.

Returns:
    Value of B(m1, m2, Q).

Definition at line 75 of file Math.py.

B0t()

float Math.B0t

(

float

x

)

Wilson coefficient B0t.

Definition at line 169 of file Math.py.

B1t()

float Math.B1t	(	float	x,
		float	l
	)

Wilson coefficient B1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of B1t(x, l).

Definition at line 207 of file Math.py.

C0t()

float Math.C0t

(

float

x

)

Wilson coefficient C0t.

Definition at line 174 of file Math.py.

C10Wc2MW()

float Math.C10Wc2MW

(

float

x

)

Wilson coefficient C10Wc at M_W scale.

Args:
    x: A real parameter.

Returns:
    Value of C10Wc2MW(x).

Definition at line 570 of file Math.py.

C10Wt2mt()

float Math.C10Wt2mt

(

float

x

)

Wilson coefficient C10Wt at 2m_t scale.

Args:
    x: A real parameter.

Returns:
    Value of C10Wt2mt(x).

Definition at line 558 of file Math.py.

C10Z2tri()

float Math.C10Z2tri

(

float

x

)

Wilson coefficient C10Z from triangle diagrams.

Args:
    x: A real parameter.

Returns:
    Value of C10Z2tri(x).

Definition at line 594 of file Math.py.

C10Zt2mt()

float Math.C10Zt2mt

(

float

x

)

Wilson coefficient C10Zt at 2m_t scale.

Args:
    x: A real parameter.

Returns:
    Value of C10Zt2mt(x).

Definition at line 582 of file Math.py.

C1t()

float Math.C1t	(	float	x,
		float	l
	)

Wilson coefficient C1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of C1t(x, l).

Definition at line 220 of file Math.py.

C7c2MW()

float Math.C7c2MW

(

float

x

)

Wilson coefficient C7c at M_W scale.

Args:
    x: A real parameter.

Returns:
    Value of C7c2MW(x).

Definition at line 297 of file Math.py.

C7t2mt()

float Math.C7t2mt

(

float

x

)

Wilson coefficient C7t at 2m_t scale.

Args:
    x: A real parameter.

Returns:
    Value of C7t2mt(x).

Definition at line 285 of file Math.py.

C8c2MW()

float Math.C8c2MW

(

float

x

)

Wilson coefficient C8c at M_W scale.

Args:
    x: A real parameter.

Returns:
    Value of C8c2MW(x).

Definition at line 321 of file Math.py.

C8t2mt()

float Math.C8t2mt

(

float

x

)

Wilson coefficient C8t at 2m_t scale.

Args:
    x: A real parameter.

Returns:
    Value of C8t2mt(x).

Definition at line 309 of file Math.py.

C9llH0()

float Math.C9llH0	(	float	x,
		float	y,
		float	lu
	)

Wilson coefficient C9llH0.

Args:
    x: First real parameter.
    y: Second real parameter.
    lu: Logarithmic scale.

Returns:
    Value of C9llH0(x, y, lu).

Definition at line 529 of file Math.py.

C9llH1()

float Math.C9llH1	(	float	x,
		float	y,
		float	lu,
		float	L
	)

Wilson coefficient C9llH1.

Args:
    x: First real parameter.
    y: Second real parameter.
    lu: Logarithmic scale.
    L: Additional scale.

Returns:
    Value of C9llH1(x, y, lu, L).

Definition at line 543 of file Math.py.

c_integrate()

Scalar Math.c_integrate	(		f,
		float	l,
		float	u,
		float	prec = 1e-6
	)

Integrate a complex-valued function f over [l, u].

Args:
    f: Callable complex function.
    l: Lower bound.
    u: Upper bound.
    prec: Precision.

Returns:
    Complex integral value.

Definition at line 117 of file Math.py.

Cl2()

float Math.Cl2

(

float

x

)

Compute the Clausen function Cl2.

Args:
    x: A real number.

Returns:
    Value of Cl2(x).

Definition at line 50 of file Math.py.

CLi2()

complex Math.CLi2

(

Scalar

x

)

Compute the complex dilogarithm function.

Args:
    x: A complex number.

Returns:
    Complex dilogarithm value.

Definition at line 35 of file Math.py.

D0t()

float Math.D0t

(

float

x

)

Wilson coefficient D0t.

Definition at line 179 of file Math.py.

D1t()

float Math.D1t	(	float	x,
		float	l
	)

Wilson coefficient D1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of D1t(x, l).

Definition at line 233 of file Math.py.

D9H0()

float Math.D9H0	(	float	x,
		float	lu
	)

Wilson coefficient D9H0.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of D9H0(x, lu).

Definition at line 448 of file Math.py.

D9H1()

float Math.D9H1	(	float	x,
		float	lu,
		float	L
	)

Wilson coefficient D9H1.

Args:
    x: A real parameter.
    lu: Logarithmic scale.
    L: Additional parameter.

Returns:
    Value of D9H1(x, lu, L).

Definition at line 461 of file Math.py.

Delta3H()

float Math.Delta3H	(	float	x,
		float	lu
	)

Wilson coefficient Delta3H.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of Delta3H(x, lu).

Definition at line 475 of file Math.py.

Delta4H()

float Math.Delta4H	(	float	x,
		float	lu
	)

Wilson coefficient Delta4H.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of Delta4H(x, lu).

Definition at line 488 of file Math.py.

Delta7H()

float Math.Delta7H	(	float	x,
		float	lu,
		float	ld
	)

Wilson coefficient Delta7H.

Args:
    x: A real parameter.
    lu: Upper log scale.
    ld: Lower log scale.

Returns:
    Value of Delta7H(x, lu, ld).

Definition at line 501 of file Math.py.

Delta8H()

float Math.Delta8H	(	float	x,
		float	lu,
		float	ld
	)

Wilson coefficient Delta8H.

Args:
    x: A real parameter.
    lu: Upper log scale.
    ld: Lower log scale.

Returns:
    Value of Delta8H(x, lu, ld).

Definition at line 515 of file Math.py.

E0t()

float Math.E0t

(

float

x

)

Wilson coefficient E0t.

Definition at line 184 of file Math.py.

E1t()

float Math.E1t	(	float	x,
		float	l
	)

Wilson coefficient E1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of E1t(x, l).

Definition at line 246 of file Math.py.

EH()

float Math.EH	(	float	x,
		float	lu
	)

Wilson coefficient EH.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of EH(x, lu).

Definition at line 435 of file Math.py.

F0SP()

float Math.F0SP

(

float

xt

)

Wilson coefficient F0SP.

Args:
    xt: A real parameter.

Returns:
    Value of F0SP(xt).

Definition at line 606 of file Math.py.

F0t()

float Math.F0t

(

float

x

)

Wilson coefficient F0t.

Definition at line 164 of file Math.py.

F1t()

float Math.F1t	(	float	x,
		float	l
	)

Wilson coefficient F1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of F1t(x, l).

Definition at line 259 of file Math.py.

F7_1()

float Math.F7_1

(

float

x

)

Wilson coefficient F7_1.

Args:
    x: A real parameter.

Returns:
    Value of F7_1(x).

Definition at line 333 of file Math.py.

F7_2()

float Math.F7_2

(

float

x

)

Wilson coefficient F7_2.

Args:
    x: A real parameter.

Returns:
    Value of F7_2(x).

Definition at line 345 of file Math.py.

F8_1()

float Math.F8_1

(

float

x

)

Wilson coefficient F8_1.

Args:
    x: A real parameter.

Returns:
    Value of F8_1(x).

Definition at line 357 of file Math.py.

F8_2()

float Math.F8_2

(

float

x

)

Wilson coefficient F8_2.

Args:
    x: A real parameter.

Returns:
    Value of F8_2(x).

Definition at line 369 of file Math.py.

G1t()

float Math.G1t	(	float	x,
		float	l
	)

Wilson coefficient G1t.

Args:
    x: A real parameter.
    l: Logarithmic scale.

Returns:
    Value of G1t(x, l).

Definition at line 272 of file Math.py.

G3H()

float Math.G3H	(	float	x,
		float	lu
	)

Wilson coefficient G3H.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of G3H(x, lu).

Definition at line 381 of file Math.py.

G4H()

float Math.G4H	(	float	x,
		float	lu
	)

Wilson coefficient G4H.

Args:
    x: A real parameter.
    lu: Logarithmic scale.

Returns:
    Value of G4H(x, lu).

Definition at line 394 of file Math.py.

G7H()

float Math.G7H	(	float	x,
		float	lu,
		float	ld
	)

Wilson coefficient G7H.

Args:
    x: A real parameter.
    lu: Upper log scale.
    ld: Lower log scale.

Returns:
    Value of G7H(x, lu, ld).

Definition at line 407 of file Math.py.

G8H()

float Math.G8H	(	float	x,
		float	lu,
		float	ld
	)

Wilson coefficient G8H.

Args:
    x: A real parameter.
    lu: Upper log scale.
    ld: Lower log scale.

Returns:
    Value of G8H(x, lu, ld).

Definition at line 421 of file Math.py.

H2()

float Math.H2	(	float	x,
		float	y
	)

Compute the H2(x, y) special function.

Args:
    x: First input value.
    y: Second input value.

Returns:
    Value of H2(x, y).

Definition at line 62 of file Math.py.

integrate()

float Math.integrate	(		f,
		float	l,
		float	u,
		float	prec = 1e-6
	)

Integrate a real-valued function f from l to u.

Args:
    f: Callable real function.
    l: Lower integration bound.
    u: Upper integration bound.
    prec: Desired precision.

Returns:
    Integral value.

Definition at line 102 of file Math.py.

kron()

int Math.kron	(	int	x,
		int	y
	)

Kronecker delta function.

Args:
    x: First integer.
    y: Second integer.

Returns:
    1 if x == y, else 0.

Definition at line 89 of file Math.py.

Li2()

float Math.Li2

(

float

x

)

Compute the dilogarithm function.

Args:
    x: A real number.

Returns:
    The value of Li2(x).

Definition at line 11 of file Math.py.

Li3()

float Math.Li3

(

float

x

)

Compute the trilogarithm function.

Args:
    x: A real number.

Returns:
    The value of Li3(x).

Definition at line 23 of file Math.py.

psi()

float Math.psi

(

int

n

)

Compute the digamma function ψ(n) for integer input.

Args:
    n: Integer input (n > 0).

Returns:
    Value of ψ(n).

Definition at line 132 of file Math.py.

T()

float Math.T

(

float

x

)

Wilson coefficient T.

Definition at line 189 of file Math.py.

Variable Documentation

E

Math.E = mb.E

Definition at line 146 of file Math.py.

GAMMA

Math.GAMMA = mb.GAMMA

Definition at line 148 of file Math.py.

PI

Math.PI = mb.PI

Definition at line 145 of file Math.py.

ZETA3

Math.ZETA3 = mb.ZETA3

Definition at line 147 of file Math.py.