Module: sage.rings.fraction_field_element
Author: William Stein (input from David Joyner, David Kohel, and Joe Wetherell)
Module-level Functions
x) |
Class: FractionFieldElement
sage: K, x = FractionField(PolynomialRing(Q)).objgen() sage: K Fraction Field of Univariate Polynomial Ring in x over Rational Field sage: loads(K.dumps()) == K True sage: f = (x^3 + x)/(17 - x^19); f (x^3 + x)/(-x^19 + 17) sage: loads(f.dumps()) == f True
self, parent, numerator, [denominator=True], [coerce=True], [reduce=1]) |
Functions: copy,
denominator,
numerator,
reduce,
valuation
self) |
Return the valuation of self, assuming that the numerator and denominator have valuation functions defined on them.
sage: x = PolynomialRing(RationalField()).gen() sage: f = (x**3 + x)/(x**2 - 2*x**3) sage: f (x^2 + 1)/(-2*x^2 + x) sage: f.valuation() -1
Special Functions: __abs__,
__call__,
__cmp__,
__float__,
__int__,
__invert__,
__long__,
__neg__,
__pos__,
__pow__,
__repr__,
_add_,
_div_,
_integer_,
_is_atomic,
_latex_,
_mul_,
_rational_,
_sub_
self) |
Evaluate the fraction at the given arguments. This assumes that a call function is defined for the numerator and denominator.
sage: x = MPolynomialRing(RationalField(),3).gens() sage: f = x[0] + x[1] - 2*x[1]*x[2] sage: f x1 - 2*x1*x2 + x0 sage: f(1,2,5) -17 sage: h = f /(x[1] + x[2]) sage: h (x1 - 2*x1*x2 + x0)/(x2 + x1) sage: h(1,2,5) -17/7
self) |
Return a latex representation of this rational function.
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