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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 | discriminant (self) |
| def | to_field_polynomial (self) |
| def | __pow__ (self, index, mod=None) |
 Public Member Functions inherited from nzmath.poly.uniutil.PseudoDivisionProvider | |
| def | pseudo_divmod (self, other) |
| def | pseudo_floordiv (self, other) |
| def | pseudo_mod (self, other) |
| def | __truediv__ (self, other) |
| def | exact_division (self, other) |
| def | scalar_exact_division (self, scale) |
| def | monic_divmod (self, other) |
| def | monic_floordiv (self, other) |
| def | monic_mod (self, other) |
| def | monic_pow (self, index, mod) |
| 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 domain coefficients.
Definition at line 1280 of file uniutil.py.
| def nzmath.poly.uniutil.DomainPolynomial.__init__ | ( | self, | |
| coefficients, | |||
coeffring = None, |
|||
_sorted = False, |
|||
| ** | kwds | ||
| ) |
Initialize the polynomial. - coefficients: initializer for polynomial coefficients - coeffring: domain
Reimplemented from nzmath.poly.uniutil.RingPolynomial.
Reimplemented in nzmath.poly.uniutil.IntegerPolynomial, and nzmath.poly.uniutil.UniqueFactorizationDomainPolynomial.
Definition at line 1284 of file uniutil.py.
| def nzmath.poly.uniutil.DomainPolynomial.__pow__ | ( | self, | |
| index, | |||
mod = None |
|||
| ) |
self ** index (% mod) It overrides the method from SortedPolynomial. The mod MUST be monic, otherwise the method raises ValueError.
Definition at line 1325 of file uniutil.py.
References nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow().
| def nzmath.poly.uniutil.DomainPolynomial.discriminant | ( | self | ) |
Return discriminant of the polynomial.
Definition at line 1298 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.DomainPolynomial.to_field_polynomial | ( | self | ) |
Return a FieldPolynomial object obtained by embedding the polynomial ring over the domain D to over the quatient field of D.
Definition at line 1316 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(), nzmath.poly.uniutil.RingPolynomial.getCoefficientRing(), nzmath.poly.formalsum.FormalSumContainerInterface.iterterms(), and nzmath.poly.uniutil.polynomial().
1.8.16