conatus.expert.AzimuthalMFold

class conatus.expert.AzimuthalMFold(coord, m0=2)

Bases: _Z2Generator

Rotation phi -> phi + 2 pi / m0 about the axis (disk, annulus, cylinder, sphere, shell, ball).

Polar/spherical frame components are carried by the rotation (g_* e_r(x) = e_r(g x)), so a field of parity p has every component in the azimuthal class p = +1: m = 0 mod m0 (m0-fold invariant); p = -1 (m0 even): m = m0/2 mod m0 (the rotation by 2 pi / m0 changes its sign). AzimuthalMFold(phi, 2) with EVEN / ODD keeps the even / odd azimuthal wavenumbers. A rotation preserves orientation (det = +1): curls and cross products keep their parity; no frame vector and no derivative is reversed.

Parameters:

• coord (Coordinate)

• m0 (int)

det = 1

property order: int

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.__int__(). For floating-point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by ‘+’ or ‘-’ and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal. >>> int(‘0b100’, base=0) 4

flips(coord)

Parameters:

coord (Coordinate)

Return type:

bool

property key: tuple

residue(p)

Azimuthal class of parity p: kept wavenumbers are m = residue (mod m0).

Parameters:

p (Parity)

Return type:

int

keeps(m, p)

Is azimuthal wavenumber m in the class of parity p?

Parameters:

• m (int)

• p (Parity)

Return type:

bool

centre(basis)

Validates the azimuthal basis (Fourier over 2 pi, size a multiple of m0).

Parameters:

basis (Basis)

Return type:

float

mirror(pos, basis)

Parameters:

• pos (float)

• basis (Basis)

Return type:

float

is_fixed(pos, basis)

Parameters:

• pos (float)

• basis (Basis)

Return type:

bool

explain()

Return type:

str