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NZMATH
1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
 Fossies Dox: NZMATH-1.2.0.tar.gz ("inofficial" and yet experimental doxygen-generated source code documentation)  |
|
NZMATH
1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
Fossies Dox: NZMATH-1.2.0.tar.gz ("inofficial" and yet experimental doxygen-generated source code documentation) |
Public Member Functions | |
| def | __init__ (self, coefficients, coeffring=None, _sorted=False, **kwds) |
| def | __pow__ (self, index, mod=None) |
| def | resultant (self, other) |
| def | discriminant (self) |
 Public Member Functions inherited from nzmath.poly.uniutil.DivisionProvider | |
| def | __init__ (self) |
| def | __divmod__ (self, other) |
| def | __floordiv__ (self, other) |
| def | __mod__ (self, other) |
| def | mod (self, dividend) |
| def | mod_pow (self, polynom, index) |
| def | __truediv__ (self, other) |
| def | scalar_exact_division (self, scale) |
| def | gcd (self, other) |
| def | extgcd (self, other) |
| Public Member Functions inherited from nzmath.poly.uniutil.ContentProvider | |
| def | content (self) |
| def | primitive_part (self) |
| Public Member Functions inherited from nzmath.poly.uniutil.RingPolynomial | |
| def | getRing (self) |
| def | getCoefficientRing (self) |
| def | __repr__ (self) |
| def | __add__ (self, other) |
| def | __radd__ (self, other) |
| def | __sub__ (self, other) |
| def | __rsub__ (self, other) |
| def | ismonic (self) |
| def | __getitem__ (self, degree) |
| Public Member Functions inherited from nzmath.poly.uniutil.OrderProvider | |
| def | __init__ (self, order=termorder.ascending_order) |
| def | shift_degree_to (self, degree) |
| def | split_at (self, degree) |
| Public Member Functions inherited from nzmath.poly.univar.SortedPolynomial | |
| def | __init__ (self, coefficients, _sorted=False, **kwds) |
| def | __pos__ (self) |
| def | __neg__ (self) |
| def | __mul__ (self, other) |
| def | __rmul__ (self, other) |
| def | ring_mul_karatsuba (self, other) |
| def | scalar_mul (self, scale) |
| def | square (self) |
| def | __pow__ (self, index) |
| def | degree (self) |
| def | leading_coefficient (self) |
| def | leading_term (self) |
| def | iterterms (self) |
| def | iterbases (self) |
| def | itercoefficients (self) |
| def | __contains__ (self, degree) |
| def | __len__ (self) |
| def | __eq__ (self, other) |
| def | __hash__ (self) |
| def | __call__ (self, val) |
| Public Member Functions inherited from nzmath.poly.univar.PolynomialInterface | |
| def | __init__ (self, coefficients, **kwds) |
| def | ring_mul (self, other) |
| def | term_mul (self, term) |
| def | differentiate (self) |
| def | upshift_degree (self, slide) |
| def | downshift_degree (self, slide) |
| def | terms_map (self, func) |
| def | construct_with_default (self, terms) |
| Public Member Functions inherited from nzmath.poly.formalsum.FormalSumContainerInterface | |
| def | __iter__ (self) |
| def | __ne__ (self, other) |
| def | __nonzero__ (self) |
| def | terms (self) |
| def | coefficients (self) |
| def | bases (self) |
| def | coefficients_map (self, func) |
| def | bases_map (self, func) |
| Public Member Functions inherited from nzmath.poly.uniutil.RingElementProvider | |
| def | __init__ (self) |
| def | set_coefficient_ring (self, coeffring) |
| Public Member Functions inherited from nzmath.ring.CommutativeRingElement | |
| def | mul_module_action (self, other) |
| def | exact_division (self, other) |
| Public Member Functions inherited from nzmath.ring.RingElement | |
| def | __init__ (self, *args, **kwd) |
| def | __eq__ (self, other) |
| def | __hash__ (self) |
| def | __ne__ (self, other) |
Additional Inherited Members | |
| Public Attributes inherited from nzmath.poly.uniutil.OrderProvider | |
| order | |
| Public Attributes inherited from nzmath.poly.univar.SortedPolynomial | |
| sorted | |
| Public Attributes inherited from nzmath.poly.univar.PolynomialInterface | |
| number_of_variables | |
Polynomial with field coefficients.
Definition at line 1386 of file uniutil.py.
| def nzmath.poly.uniutil.FieldPolynomial.__init__ | ( | self, | |
| coefficients, | |||
coeffring = None, |
|||
_sorted = False, |
|||
| ** | kwds | ||
| ) |
Initialize the polynomial. - coefficients: initializer for polynomial coefficients - coeffring: field
Reimplemented from nzmath.poly.uniutil.RingPolynomial.
Reimplemented in nzmath.poly.uniutil.FinitePrimeFieldPolynomial, and nzmath.poly.uniutil.FiniteFieldPolynomial.
Definition at line 1390 of file uniutil.py.
| def nzmath.poly.uniutil.FieldPolynomial.__pow__ | ( | self, | |
| index, | |||
mod = None |
|||
| ) |
self ** index (% mod).
Definition at line 1405 of file uniutil.py.
References nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), nzmath.imaginary.Complex.getRing(), nzmath.intresidue.IntegerResidueClass.getRing(), nzmath.poly.multiutil.RingPolynomial.getRing(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.matrix.RingSquareMatrix.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), nzmath.poly.univar.PolynomialInterface.square(), nzmath.poly.multivar.BasicPolynomial.square(), and nzmath.poly.uniutil.FinitePrimeFieldPolynomial.square().
| def nzmath.poly.uniutil.FieldPolynomial.discriminant | ( | self | ) |
Return discriminant of the polynomial.
Definition at line 1466 of file uniutil.py.
References nzmath.algfield.NumberField.degree, nzmath.poly.array.ArrayPoly.degree, nzmath.poly.termorder.UnivarTermOrder.degree(), nzmath.algfield.BasicAlgNumber.degree, nzmath.finitefield.ExtendedField.degree, nzmath.algfield.MatAlgNumber.degree, nzmath.poly.univar.SortedPolynomial.degree(), nzmath.poly.univar.PolynomialInterface.differentiate(), nzmath.poly.ring.PolynomialRing.getCoefficientRing(), nzmath.poly.multiutil.RingElementProvider.getCoefficientRing(), nzmath.poly.multiutil.RingPolynomial.getCoefficientRing(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCoefficientRing(), nzmath.poly.ring.RationalFunctionField.getCoefficientRing(), nzmath.matrix.RingMatrix.getCoefficientRing(), nzmath.poly.uniutil.RingPolynomial.getCoefficientRing(), nzmath.poly.termorder.TermOrderInterface.leading_coefficient(), nzmath.poly.termorder.UnivarTermOrder.leading_coefficient(), nzmath.poly.termorder.MultivarTermOrder.leading_coefficient(), nzmath.poly.univar.SortedPolynomial.leading_coefficient(), nzmath.poly.multiutil.UniqueFactorizationDomainPolynomial.resultant(), nzmath.poly.uniutil.SubresultantGcdProvider.resultant(), and nzmath.poly.uniutil.FieldPolynomial.resultant().
| def nzmath.poly.uniutil.FieldPolynomial.resultant | ( | self, | |
| other | |||
| ) |
Return the resultant of self and other.
Definition at line 1435 of file uniutil.py.
References nzmath.poly.ring.PolynomialRing.getCoefficientRing(), nzmath.poly.multiutil.RingElementProvider.getCoefficientRing(), nzmath.poly.multiutil.RingPolynomial.getCoefficientRing(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCoefficientRing(), nzmath.poly.ring.RationalFunctionField.getCoefficientRing(), nzmath.matrix.RingMatrix.getCoefficientRing(), and nzmath.poly.uniutil.RingPolynomial.getCoefficientRing().
Referenced by nzmath.poly.uniutil.DomainPolynomial.discriminant(), and nzmath.poly.uniutil.FieldPolynomial.discriminant().
1.8.16