NZMATH  1.2.0
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nzmath.algfield Namespace Reference

Classes

class  BasicAlgNumber
 
class  MatAlgNumber
 
class  NumberField
 

Functions

def prime_decomp (p, polynomial)
 
def _easy_prime_decomp (p, polynomial)
 
def _main_prime_decomp (p, polynomial)
 
def changetype (a, polynomial=[0, 1])
 
def disc (A)
 
def qpoly (coeffs)
 
def zpoly (coeffs)
 
def fppoly (coeffs, p)
 

Function Documentation

◆ _easy_prime_decomp()

def nzmath.algfield._easy_prime_decomp (   p,
  polynomial 
)
private
prime decomposition by factoring polynomial

Definition at line 758 of file algfield.py.

References nzmath.algfield.fppoly(), and nzmath.bigrange.range().

Referenced by nzmath.algfield.prime_decomp().

◆ _main_prime_decomp()

def nzmath.algfield._main_prime_decomp (   p,
  polynomial 
)
private
main step of prime decomposition

Definition at line 782 of file algfield.py.

Referenced by nzmath.algfield.prime_decomp().

◆ changetype()

def nzmath.algfield.changetype (   a,
  polynomial = [0, 1] 
)
Change 'a' to be an element of field K defined polynomial

Definition at line 789 of file algfield.py.

References nzmath.bigrange.range().

Referenced by nzmath.algfield.NumberField.POLRED().

◆ disc()

def nzmath.algfield.disc (   A)
Compute the discriminant of a_i, where A=[a_1,...,a_n]

Definition at line 812 of file algfield.py.

References nzmath.bigrange.range().

◆ fppoly()

def nzmath.algfield.fppoly (   coeffs,
  p 
)
Return a Z_p coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 840 of file algfield.py.

Referenced by nzmath.algfield._easy_prime_decomp().

◆ prime_decomp()

def nzmath.algfield.prime_decomp (   p,
  polynomial 
)
Return prime decomposition of (p) over Q[x]/(polynomial).

Definition at line 747 of file algfield.py.

References nzmath.algfield._easy_prime_decomp(), and nzmath.algfield._main_prime_decomp().

◆ qpoly()

def nzmath.algfield.qpoly (   coeffs)
Return a rational coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 825 of file algfield.py.

Referenced by nzmath.algfield.BasicAlgNumber.inverse().

◆ zpoly()

def nzmath.algfield.zpoly (   coeffs)
Return an integer coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 833 of file algfield.py.

Referenced by nzmath.algfield.NumberField.__mul__(), nzmath.algfield.BasicAlgNumber.__mul__(), nzmath.algfield.BasicAlgNumber.__pow__(), nzmath.algfield.BasicAlgNumber.__truediv__(), nzmath.algfield.BasicAlgNumber.norm(), nzmath.algfield.NumberField.POLRED(), and nzmath.algfield.NumberField.signature().