| | |
- builtins.object
-
- FiniteFieldArray
-
- ExtensionFieldArray
-
- BinaryFieldArray
- PrimeFieldArray
- FiniteFieldElement
-
- ExtensionFieldElement
-
- BinaryFieldElement
- PrimeFieldElement
class BinaryFieldArray(ExtensionFieldArray) |
| |
BinaryFieldArray(value, check=True, copy=False)
|
| |
- Method resolution order:
- BinaryFieldArray
- ExtensionFieldArray
- FiniteFieldArray
- builtins.object
Data and other attributes defined here:
- __annotations__ = {}
Methods inherited from ExtensionFieldArray:
- __repr__(self)
- Return repr(self).
Data descriptors inherited from ExtensionFieldArray:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Methods inherited from FiniteFieldArray:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __array_ufunc__(self, ufunc, method, *inputs, **kwargs)
- __contains__(self, value)
- __eq__(self, other)
- Elementwise equality as for Numpy arrays.
- __getitem__(self, key)
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imatmul__(self, other)
- In-place matrix multiplication.
- __imul__(self, other)
- In-place multiplication.
- __init__(self, value, check=True, copy=False)
- Initialize self. See help(type(self)) for accurate signature.
- __ipow__(self, other)
- In-place exponentiation.
- __irshift__(self, other)
- In-place right shift.
- __isub__(self, other)
- In-place subtraction.
- __iter__(self)
- __itruediv__(self, other)
- "In-place division.
- __len__(self)
- __lshift__(self, other)
- Left shift.
- __matmul__(self, other)
- Matrix multiplication.
- __mul__(self, other)
- Multiplication.
- __ne__(self, other)
- Elementwise nonequality as for Numpy arrays.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __pow__(self, other)
- Exponentiation.
- __radd__ = __add__(self, other)
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmatmul__(self, other)
- Matrix multiplication (with reflected arguments).
- __rmul__ = __mul__(self, other)
- __rpow__(self, other)
- Exponentiation (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rshift__(self, other)
- Right shift.
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __setitem__(self, key, value)
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- compress(self, *args, **kwargs)
- copy(self, *args, **kwargs)
- diagonal(self, *args, **kwargs)
- flatten(self, *args, **kwargs)
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- nonzero(self, *args, **kwargs)
- prod(self, *args, **kwargs)
- ravel(self, *args, **kwargs)
- reciprocal(self)
- Multiplicative inverse.
- repeat(self, *args, **kwargs)
- reshape(self, *args, **kwargs)
- sqrt(self, INV=False)
- Modular (inverse) square root.
- sum(self, *args, **kwargs)
- swapaxes(self, axis1, axis2)
- take(self, *args, **kwargs)
- tolist(self)
- trace(self, *args, **kwargs)
- transpose(self, *axes)
Static methods inherited from FiniteFieldArray:
- diag(a, k=0)
- gauss_det(a)
- Determinant by Gaussian elimination on (last 2 dimensions of) array a.
- gauss_inv(A)
- Inverse by Gaussian elimination on augmented matrix (A | I).
- gauss_solve(A, B)
- Linear solve by Gaussian elimination on matrix (A | B).
- matrix_pow(A, n)
Readonly properties inherited from FiniteFieldArray:
- T
- flat
- ndim
- shape
- size
Data descriptors inherited from FiniteFieldArray:
- value
Data and other attributes inherited from FiniteFieldArray:
- __hash__ = None
|
class BinaryFieldElement(ExtensionFieldElement) |
| |
BinaryFieldElement(value)
Common base class for binary field elements.
|
| |
- Method resolution order:
- BinaryFieldElement
- ExtensionFieldElement
- FiniteFieldElement
- builtins.object
Data and other attributes defined here:
- __annotations__ = {'modulus': <class 'mpyc.gfpx.BinaryPolynomial'>}
- characteristic = 2
Methods inherited from ExtensionFieldElement:
- __init__(self, value)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
- Extract field element as an integer value.
- __irshift__(self, other)
- In-place right shift.
- __pow__(self, other)
- Exponentiation.
- __reduce__(self)
- Helper for pickle.
- __repr__(self)
- Return repr(self).
- __rshift__(self, other)
- Right shift.
Static methods inherited from ExtensionFieldElement:
- createGF(modulus)
- Create new object for use by pickle module.
Methods inherited from FiniteFieldElement:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __bool__(self)
- Truth value testing.
Return False if this field element is zero, True otherwise.
Field elements can thus be used directly in Boolean formulas.
- __eq__(self, other)
- Equality test.
- __hash__(self)
- Make finite field elements hashable (e.g., for LRU caching).
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imul__(self, other)
- In-place multiplication.
- __isub__(self, other)
- In-place subtraction.
- __itruediv__(self, other)
- In-place division.
- __lshift__(self, other)
- Left shift.
- __mul__(self, other)
- Multiplication.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __radd__(self, other)
- Addition (with reflected arguments).
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmul__(self, other)
- Multiplication (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- reciprocal(self)
- Multiplicative inverse.
- sqrt(self, INV=False)
- Modular (inverse) square root.
Class methods inherited from FiniteFieldElement:
- from_bytes(data) from builtins.type
- Return the list of integers represented by the given byte string.
- to_bytes(x) from builtins.type
- Return byte string representing the given list/ndarray of integers x.
Data descriptors inherited from FiniteFieldElement:
- value
Data and other attributes inherited from FiniteFieldElement:
- byte_length = None
- ext_deg = None
- is_signed = None
- order = None
|
class ExtensionFieldArray(FiniteFieldArray) |
| |
ExtensionFieldArray(value, check=True, copy=False)
|
| |
- Method resolution order:
- ExtensionFieldArray
- FiniteFieldArray
- builtins.object
Methods defined here:
- __repr__(self)
- Return repr(self).
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes defined here:
- __annotations__ = {}
Methods inherited from FiniteFieldArray:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __array_ufunc__(self, ufunc, method, *inputs, **kwargs)
- __contains__(self, value)
- __eq__(self, other)
- Elementwise equality as for Numpy arrays.
- __getitem__(self, key)
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imatmul__(self, other)
- In-place matrix multiplication.
- __imul__(self, other)
- In-place multiplication.
- __init__(self, value, check=True, copy=False)
- Initialize self. See help(type(self)) for accurate signature.
- __ipow__(self, other)
- In-place exponentiation.
- __irshift__(self, other)
- In-place right shift.
- __isub__(self, other)
- In-place subtraction.
- __iter__(self)
- __itruediv__(self, other)
- "In-place division.
- __len__(self)
- __lshift__(self, other)
- Left shift.
- __matmul__(self, other)
- Matrix multiplication.
- __mul__(self, other)
- Multiplication.
- __ne__(self, other)
- Elementwise nonequality as for Numpy arrays.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __pow__(self, other)
- Exponentiation.
- __radd__ = __add__(self, other)
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmatmul__(self, other)
- Matrix multiplication (with reflected arguments).
- __rmul__ = __mul__(self, other)
- __rpow__(self, other)
- Exponentiation (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rshift__(self, other)
- Right shift.
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __setitem__(self, key, value)
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- compress(self, *args, **kwargs)
- copy(self, *args, **kwargs)
- diagonal(self, *args, **kwargs)
- flatten(self, *args, **kwargs)
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- nonzero(self, *args, **kwargs)
- prod(self, *args, **kwargs)
- ravel(self, *args, **kwargs)
- reciprocal(self)
- Multiplicative inverse.
- repeat(self, *args, **kwargs)
- reshape(self, *args, **kwargs)
- sqrt(self, INV=False)
- Modular (inverse) square root.
- sum(self, *args, **kwargs)
- swapaxes(self, axis1, axis2)
- take(self, *args, **kwargs)
- tolist(self)
- trace(self, *args, **kwargs)
- transpose(self, *axes)
Static methods inherited from FiniteFieldArray:
- diag(a, k=0)
- gauss_det(a)
- Determinant by Gaussian elimination on (last 2 dimensions of) array a.
- gauss_inv(A)
- Inverse by Gaussian elimination on augmented matrix (A | I).
- gauss_solve(A, B)
- Linear solve by Gaussian elimination on matrix (A | B).
- matrix_pow(A, n)
Readonly properties inherited from FiniteFieldArray:
- T
- flat
- ndim
- shape
- size
Data descriptors inherited from FiniteFieldArray:
- value
Data and other attributes inherited from FiniteFieldArray:
- __hash__ = None
|
class ExtensionFieldElement(FiniteFieldElement) |
| |
ExtensionFieldElement(value)
Common base class for extension field elements.
|
| |
- Method resolution order:
- ExtensionFieldElement
- FiniteFieldElement
- builtins.object
Methods defined here:
- __init__(self, value)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
- Extract field element as an integer value.
- __irshift__(self, other)
- In-place right shift.
- __pow__(self, other)
- Exponentiation.
- __reduce__(self)
- Helper for pickle.
- __repr__(self)
- Return repr(self).
- __rshift__(self, other)
- Right shift.
Static methods defined here:
- createGF(modulus)
- Create new object for use by pickle module.
Data and other attributes defined here:
- __annotations__ = {'modulus': <class 'mpyc.gfpx.Polynomial'>}
Methods inherited from FiniteFieldElement:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __bool__(self)
- Truth value testing.
Return False if this field element is zero, True otherwise.
Field elements can thus be used directly in Boolean formulas.
- __eq__(self, other)
- Equality test.
- __hash__(self)
- Make finite field elements hashable (e.g., for LRU caching).
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imul__(self, other)
- In-place multiplication.
- __isub__(self, other)
- In-place subtraction.
- __itruediv__(self, other)
- In-place division.
- __lshift__(self, other)
- Left shift.
- __mul__(self, other)
- Multiplication.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __radd__(self, other)
- Addition (with reflected arguments).
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmul__(self, other)
- Multiplication (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- reciprocal(self)
- Multiplicative inverse.
- sqrt(self, INV=False)
- Modular (inverse) square root.
Class methods inherited from FiniteFieldElement:
- from_bytes(data) from builtins.type
- Return the list of integers represented by the given byte string.
- to_bytes(x) from builtins.type
- Return byte string representing the given list/ndarray of integers x.
Data descriptors inherited from FiniteFieldElement:
- value
Data and other attributes inherited from FiniteFieldElement:
- byte_length = None
- characteristic = None
- ext_deg = None
- is_signed = None
- order = None
|
class FiniteFieldArray(builtins.object) |
| |
FiniteFieldArray(value, check=True, copy=False)
Common base class for finite field arrays.
An array over finite field F behaves much like a NumPy array with dtype=F.
Conceptually, an array a over F can be thought of as, for example
"a = np.array([[F(1), F(2)], [F(0), F(3)]], dtype=F)"
Internally, however, arrays over a finite field F are represented by NumPy
arrays with dtype=object storing just the values of the finite field elements:
"a = (field=F, value=np.array([[1, 2], [0, 3]], dtype=object))"
Invariant: elements of array 'value' are reduced w.r.t. modulus.
|
| |
Methods defined here:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __array_ufunc__(self, ufunc, method, *inputs, **kwargs)
- __contains__(self, value)
- __eq__(self, other)
- Elementwise equality as for Numpy arrays.
- __getitem__(self, key)
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imatmul__(self, other)
- In-place matrix multiplication.
- __imul__(self, other)
- In-place multiplication.
- __init__(self, value, check=True, copy=False)
- Initialize self. See help(type(self)) for accurate signature.
- __ipow__(self, other)
- In-place exponentiation.
- __irshift__(self, other)
- In-place right shift.
- __isub__(self, other)
- In-place subtraction.
- __iter__(self)
- __itruediv__(self, other)
- "In-place division.
- __len__(self)
- __lshift__(self, other)
- Left shift.
- __matmul__(self, other)
- Matrix multiplication.
- __mul__(self, other)
- Multiplication.
- __ne__(self, other)
- Elementwise nonequality as for Numpy arrays.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __pow__(self, other)
- Exponentiation.
- __radd__ = __add__(self, other)
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmatmul__(self, other)
- Matrix multiplication (with reflected arguments).
- __rmul__ = __mul__(self, other)
- __rpow__(self, other)
- Exponentiation (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rshift__(self, other)
- Right shift.
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __setitem__(self, key, value)
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- compress(self, *args, **kwargs)
- copy(self, *args, **kwargs)
- diagonal(self, *args, **kwargs)
- flatten(self, *args, **kwargs)
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- nonzero(self, *args, **kwargs)
- prod(self, *args, **kwargs)
- ravel(self, *args, **kwargs)
- reciprocal(self)
- Multiplicative inverse.
- repeat(self, *args, **kwargs)
- reshape(self, *args, **kwargs)
- sqrt(self, INV=False)
- Modular (inverse) square root.
- sum(self, *args, **kwargs)
- swapaxes(self, axis1, axis2)
- take(self, *args, **kwargs)
- tolist(self)
- trace(self, *args, **kwargs)
- transpose(self, *axes)
Static methods defined here:
- diag(a, k=0)
- gauss_det(a)
- Determinant by Gaussian elimination on (last 2 dimensions of) array a.
- gauss_inv(A)
- Inverse by Gaussian elimination on augmented matrix (A | I).
- gauss_solve(A, B)
- Linear solve by Gaussian elimination on matrix (A | B).
- matrix_pow(A, n)
Readonly properties defined here:
- T
- flat
- ndim
- shape
- size
Data descriptors defined here:
- value
Data and other attributes defined here:
- __annotations__ = {'_mix_types': <class 'type'>, 'field': <class 'type'>}
- __hash__ = None
|
class FiniteFieldElement(builtins.object) |
| |
FiniteFieldElement(value)
Abstract base class for finite field elements.
Invariant: 'value' is reduced w.r.t. modulus.
|
| |
Methods defined here:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __bool__(self)
- Truth value testing.
Return False if this field element is zero, True otherwise.
Field elements can thus be used directly in Boolean formulas.
- __eq__(self, other)
- Equality test.
- __hash__(self)
- Make finite field elements hashable (e.g., for LRU caching).
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imul__(self, other)
- In-place multiplication.
- __init__(self, value)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
- Extract field element as an integer value.
- __irshift__(self, other)
- In-place right shift.
- __isub__(self, other)
- In-place subtraction.
- __itruediv__(self, other)
- In-place division.
- __lshift__(self, other)
- Left shift.
- __mul__(self, other)
- Multiplication.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __pow__(self, other)
- Exponentiation.
- __radd__(self, other)
- Addition (with reflected arguments).
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmul__(self, other)
- Multiplication (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rshift__(self, other)
- Right shift.
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- reciprocal(self)
- Multiplicative inverse.
- sqrt(self, INV=False)
- Modular (inverse) square root.
Class methods defined here:
- from_bytes(data) from builtins.type
- Return the list of integers represented by the given byte string.
- to_bytes(x) from builtins.type
- Return byte string representing the given list/ndarray of integers x.
Data descriptors defined here:
- value
Data and other attributes defined here:
- __annotations__ = {'_mix_types': <class 'type'>, 'array': <class 'type'>, 'modulus': <class 'type'>}
- byte_length = None
- characteristic = None
- ext_deg = None
- is_signed = None
- order = None
|
class PrimeFieldArray(FiniteFieldArray) |
| |
PrimeFieldArray(value, check=True, copy=False)
|
| |
- Method resolution order:
- PrimeFieldArray
- FiniteFieldArray
- builtins.object
Methods defined here:
- __abs__(self)
- Absolute value of (signed) value.
- __int__(self)
- Extract (signed) integer value for size-1 arrays only.
- __repr__(self)
- Return repr(self).
- signed_(self)
- Return signed integer representation, symmetric around zero.
- unsigned_(self)
- Return unsigned integer representation.
Class methods defined here:
- intarray(a) from builtins.type
- Extract finite field array as a (signed) integer array.
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes defined here:
- __annotations__ = {}
Methods inherited from FiniteFieldArray:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __array_ufunc__(self, ufunc, method, *inputs, **kwargs)
- __contains__(self, value)
- __eq__(self, other)
- Elementwise equality as for Numpy arrays.
- __getitem__(self, key)
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imatmul__(self, other)
- In-place matrix multiplication.
- __imul__(self, other)
- In-place multiplication.
- __init__(self, value, check=True, copy=False)
- Initialize self. See help(type(self)) for accurate signature.
- __ipow__(self, other)
- In-place exponentiation.
- __irshift__(self, other)
- In-place right shift.
- __isub__(self, other)
- In-place subtraction.
- __iter__(self)
- __itruediv__(self, other)
- "In-place division.
- __len__(self)
- __lshift__(self, other)
- Left shift.
- __matmul__(self, other)
- Matrix multiplication.
- __mul__(self, other)
- Multiplication.
- __ne__(self, other)
- Elementwise nonequality as for Numpy arrays.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __pow__(self, other)
- Exponentiation.
- __radd__ = __add__(self, other)
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmatmul__(self, other)
- Matrix multiplication (with reflected arguments).
- __rmul__ = __mul__(self, other)
- __rpow__(self, other)
- Exponentiation (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rshift__(self, other)
- Right shift.
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __setitem__(self, key, value)
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- compress(self, *args, **kwargs)
- copy(self, *args, **kwargs)
- diagonal(self, *args, **kwargs)
- flatten(self, *args, **kwargs)
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- nonzero(self, *args, **kwargs)
- prod(self, *args, **kwargs)
- ravel(self, *args, **kwargs)
- reciprocal(self)
- Multiplicative inverse.
- repeat(self, *args, **kwargs)
- reshape(self, *args, **kwargs)
- sqrt(self, INV=False)
- Modular (inverse) square root.
- sum(self, *args, **kwargs)
- swapaxes(self, axis1, axis2)
- take(self, *args, **kwargs)
- tolist(self)
- trace(self, *args, **kwargs)
- transpose(self, *axes)
Static methods inherited from FiniteFieldArray:
- diag(a, k=0)
- gauss_det(a)
- Determinant by Gaussian elimination on (last 2 dimensions of) array a.
- gauss_inv(A)
- Inverse by Gaussian elimination on augmented matrix (A | I).
- gauss_solve(A, B)
- Linear solve by Gaussian elimination on matrix (A | B).
- matrix_pow(A, n)
Readonly properties inherited from FiniteFieldArray:
- T
- flat
- ndim
- shape
- size
Data descriptors inherited from FiniteFieldArray:
- value
Data and other attributes inherited from FiniteFieldArray:
- __hash__ = None
|
class PrimeFieldElement(FiniteFieldElement) |
| |
PrimeFieldElement(value)
Common base class for prime field elements.
|
| |
- Method resolution order:
- PrimeFieldElement
- FiniteFieldElement
- builtins.object
Methods defined here:
- __abs__(self)
- Absolute value of (signed) value.
- __init__(self, value)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
- Extract field element as a (signed) integer value.
- __irshift__(self, other)
- In-place right shift.
- __pow__(self, other)
- Exponentiation.
- __reduce__(self)
- Helper for pickle.
- __repr__(self)
- Return repr(self).
- __rshift__(self, other)
- Right shift.
- signed_(self)
- Return signed integer representation, symmetric around zero.
- unsigned_(self)
- Return unsigned integer representation.
Static methods defined here:
- createGF(p, n, w)
- Create new object for use by pickle module.
Data and other attributes defined here:
- __annotations__ = {'modulus': <class 'int'>}
- is_signed = None
- nth = None
- root = None
Methods inherited from FiniteFieldElement:
- __add__(self, other)
- Addition.
- __array_function__(self, func, types, args, kwargs)
- __bool__(self)
- Truth value testing.
Return False if this field element is zero, True otherwise.
Field elements can thus be used directly in Boolean formulas.
- __eq__(self, other)
- Equality test.
- __hash__(self)
- Make finite field elements hashable (e.g., for LRU caching).
- __iadd__(self, other)
- In-place addition.
- __ilshift__(self, other)
- In-place left shift.
- __imul__(self, other)
- In-place multiplication.
- __isub__(self, other)
- In-place subtraction.
- __itruediv__(self, other)
- In-place division.
- __lshift__(self, other)
- Left shift.
- __mul__(self, other)
- Multiplication.
- __neg__(self)
- Negation.
- __pos__(self)
- Unary +.
- __radd__(self, other)
- Addition (with reflected arguments).
- __rlshift__(self, other)
- Left shift (with reflected arguments).
- __rmul__(self, other)
- Multiplication (with reflected arguments).
- __rrshift__(self, other)
- Right shift (with reflected arguments).
- __rsub__(self, other)
- Subtraction (with reflected arguments).
- __rtruediv__(self, other)
- Division (with reflected arguments).
- __sub__(self, other)
- Subtraction.
- __truediv__(self, other)
- Division.
- is_sqr(self)
- Test for quadratic residuosity (0 is also square).
- reciprocal(self)
- Multiplicative inverse.
- sqrt(self, INV=False)
- Modular (inverse) square root.
Class methods inherited from FiniteFieldElement:
- from_bytes(data) from builtins.type
- Return the list of integers represented by the given byte string.
- to_bytes(x) from builtins.type
- Return byte string representing the given list/ndarray of integers x.
Data descriptors inherited from FiniteFieldElement:
- value
Data and other attributes inherited from FiniteFieldElement:
- byte_length = None
- characteristic = None
- ext_deg = None
- order = None
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