NZMATH
1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
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Public Member Functions | |
def | __init__ (self) |
def | createElement (self, *args) |
def | isfield (self) |
def | gcd (self, a, b) |
def | getQuotientField (self) |
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def | isdomain (self) |
def | isnoetherian (self) |
def | isufd (self) |
def | ispid (self) |
def | iseuclidean (self) |
def | registerModuleAction (self, action_ring, action) |
def | hasaction (self, action_ring) |
def | getaction (self, action_ring) |
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def | createElement (self, seed) |
def | getCharacteristic (self) |
def | issubring (self, other) |
def | issuperring (self, other) |
def | getCommonSuperring (self, other) |
def | __eq__ (self, other) |
def | __hash__ (self) |
def | __ne__ (self, other) |
Additional Inherited Members | |
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properties | |
Field is an abstract class which expresses that the derived classes are (in mathematical meaning) fields.
def nzmath.ring.Field.__init__ | ( | self | ) |
Set field flag True of 'properties' attribute.
Reimplemented from nzmath.ring.CommutativeRing.
Reimplemented in nzmath.rational.RationalField, nzmath.imaginary.ComplexField, and nzmath.real.RealField.
Definition at line 196 of file ring.py.
References nzmath.ring.CommutativeRing.properties.
def nzmath.ring.Field.createElement | ( | self, | |
* | args | ||
) |
createElement returns an element of the field.
Reimplemented in nzmath.algfield.NumberField.
def nzmath.ring.Field.gcd | ( | self, | |
a, | |||
b | |||
) |
A field is trivially a ufd and shuold provide gcd.
Definition at line 218 of file ring.py.
References nzmath.real.RealField.one, nzmath.poly.ring.PolynomialRing.one, nzmath.imaginary.ComplexField.one, nzmath.intresidue.IntegerResidueClassRing.one, nzmath.algfield.NumberField.one, nzmath.finitefield.FinitePrimeField.one, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.one, nzmath.ring.ResidueClassRing.one, nzmath.poly.ring.RationalFunctionField.one, nzmath.rational.RationalField.one, nzmath.finitefield.ExtendedField.one, nzmath.rational.IntegerRing.one, nzmath.matrix.MatrixRing.one, nzmath.real.RealField.zero, nzmath.poly.ring.PolynomialRing.zero, nzmath.imaginary.ComplexField.zero, nzmath.intresidue.IntegerResidueClassRing.zero, nzmath.algfield.NumberField.zero, nzmath.finitefield.FinitePrimeField.zero, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.zero, nzmath.ring.ResidueClassRing.zero, nzmath.poly.ring.RationalFunctionField.zero, nzmath.rational.RationalField.zero, nzmath.finitefield.ExtendedField.zero, nzmath.rational.IntegerRing.zero, and nzmath.matrix.MatrixRing.zero.
def nzmath.ring.Field.getQuotientField | ( | self | ) |
getQuotientField returns the quotient field of the field. It is, of course, itself.
Reimplemented from nzmath.ring.CommutativeRing.
Reimplemented in nzmath.rational.RationalField, and nzmath.poly.ring.RationalFunctionField.
def nzmath.ring.Field.isfield | ( | self | ) |
Field overrides isfield of CommutativeRing.
Reimplemented from nzmath.ring.CommutativeRing.