I have a very big rational function and i want to obtain the numerator and denominator. with .numerator_denominator() it takes forever with .numerator_denominator(False) not every term is expanded. with .expand() and .combine() it takes forever and the result is not a single fraction.
I need a single fraction N(x)/D(x) where N and D are polynomials in x, it is not important how big !
In this case, you can try with
sage: K.<x> = FunctionField(SR)
or
K = FractionField(PolynomialRing(SR, 'x'))
I am not sure how big are your rational functions, but if i do:
sage: f = sum(K.random_element() for i in range(100))
sage: f.numerator()
...
sage: f.denominator()
....
and this is almost instantaneous.
This seems a good idea.
But I have an expression of type 'sage.symbolic.expression.Expression' that contains a variable s of the same type.
When I use your approach I have/handle objects of type 'sage.rings.function_field.function_field_element.FunctionFieldElement_rational' after constructing a Rational function field in s over Symbolic Ring (of type sage.rings.function_field.function_field.RationalFunctionField_with_category')
SO THE ONE s (in the expression) is NOT the s in the function field element...
If I do the conversion with K(expr) the whole expr is considered as a block and is not "parsed" for s... So when then I call denominator I always get 1
How can this be fixed/handled ?
Thanx you !
What happens with your big rational function if, instead of working with symbolic functions, you work in the FunctionField ?
sage: K.<x> = FunctionField(QQ) ; K
Rational function field in x over Rational Field
sage: f = K(3*x/(4*(x^2+1))+ x^2/(3*x^3-5))
sage: f.numerator()
13*x^4 + 4*x^2 - 15*x
sage: f.denominator()
12*x^5 + 12*x^3 - 20*x^2 - 20
Or in the FractionField ?
sage: K = FractionField(PolynomialRing(QQ,'x')) ; K
Fraction Field of Univariate Polynomial Ring in x over Rational Field
sage: f = K(3*x/(4*(x^2+1))+ x^2/(3*x^3-5))
sage: f.numerator()
13*x^4 + 4*x^2 - 15*x
sage: f.denominator()
12*x^5 + 12*x^3 - 20*x^2 - 20
Does one of them work ? Which is faster ? Otherwise, could you give us an example of "big rational function" ?
Asked: 2013-10-16 18:58:48 +0100
Seen: 4,888 times
Last updated: Oct 18 '13
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