 | 1 | initial version |
I have a rational polynomial y(x) = P(x)/Q(x) which I want to revert (I'm trying to find the inverse of y).
y(x) is a symbolic expression in SAGE. In order to use g = y.reversion() I have to convert the symbolic expression to a power series.
y(x).power_series(QQ) SAGE returns[sage]: TypeError: unable to convert 45*(256*sqrt(2))*e to a rational
y(x).power_series(RR) it tells me[sage]: TypeError: denominator must be a unit
Am I missing some algebra?
| | 2 | No.2 Revision |
I have a rational polynomial y(x) = P(x)/Q(x) which I want to revert (I'm trying to find the inverse of y).
y(x) is a symbolic expression in SAGE. Sage. In order to use g = y.reversion() I have to convert the symbolic expression to a power series.
When I do y(x).power_series(QQ) SAGE Sage returns
[sage]: TypeError: unable to convert 45*(256*sqrt(2))*e to arationalrational
When I try y(x).power_series(RR) it tells me
[sage]: TypeError: denominator must be aunitunit
Am I missing some algebra?
| | 3 | No.3 Revision |
I have a rational polynomial y(x) = P(x)/Q(x) which I want to revert (I'm trying to find the inverse of y).
y(x) is a symbolic expression in Sage. SAGE. In order to use g = y.reversion() I have to convert the symbolic expression to a power series.
y(x) looks like this
x^2*f1((3/x-1)^n,(1/x-1)^n) / (const + f2((3/x-1)^n,(1/x-1)^n)))
The numerator has higher degree than the denominator.
When I do y(x).power_series(QQ) Sage SAGE returns
[sage]: TypeError: unable to convert 45*(256*sqrt(2))*e to arationalrational
When I try y(x).power_series(RR) it tells me
[sage]: TypeError: denominator must be aunitunit
Am I missing some algebra?
| | 4 | No.4 Revision |
I have a rational polynomial y(x) = P(x)/Q(x) which I want to revert (I'm trying to find the inverse of y).
y(x) is a symbolic expression in SAGE. In order to use g = y.reversion() I have to convert the symbolic expression to a power series.
y(x) looks like this
x^2*f1((3/x-1)^n,(1/x-1)^n) x^2*f1((3/x-1)^m,(1/x-1)^m) / (const + f2((3/x-1)^n,(1/x-1)^n)))
The numerator has higher degree than the denominator.
y(x).power_series(QQ) SAGE returns[sage]: TypeError: unable to convert 45*(256*sqrt(2))*e to a rational
y(x).power_series(RR) it tells me[sage]: TypeError: denominator must be a unit
Am I missing some algebra?
| | 5 | No.5 Revision |
I have a rational polynomial y(x) = P(x)/Q(x) f(z) = P(z)/Q(z) which I want to revert (I'm trying to find the inverse of y).
y(x) is a symbolic expression f).
I'll pick a simple example, the function f(z) = (1/z-1)^4
[sage:] z = var('z');
[sage:] z = FractionField(PolynomialRing(QQ, 'z')).objgen();
[sage:] f(z) = (1/z-1)^4;
[sage:] g = f(z).taylor(x,2,4); #I expand f in SAGE. In order to use g = y.reversion() I have to convert the symbolic expression to a power series. y(x) looks like this
x^2*f1((3/x-1)^m,(1/x-1)^m) / (const + f2((3/x-1)^n,(1/x-1)^n)))
The numerator a Taylor series just to make sure it's a series
[sage:] f.expand().reversion();
AttributeError: 'sage.symbolic.expression.Expression' object has higher degree than the denominator.
- When I do
y(x).power_series(QQ) SAGE returns
[sage]: TypeError: unable to convert 45*(256*sqrt(2))*e to a rational
- When I try
y(x).power_series(RR) it tells me
[sage]: no
attribute 'reversion'
[sage:] g1 = g.power_series(QQ);
TypeError: denominator must be a unitunit
[sage:] g.reversion();
AttributeError: 'sage.symbolic.expression.Expression' object has no
attribute 'reversion'
Am
A power series P(z) is not a rational function P(z)/Q(z). That's why the TypeError: denominator must be a unit appears.
Is it possible that SAGE cannot invert rational polynomials? In the SAGE help text the computation is passed to pari first, before using Lagrangian inversion.
I missing some algebra?thought SAGE uses FLINT. Why is it not used for computing the inverse of rational polynomials?
6 No.6 Revision
Series Reversion
I have a rational polynomial f(z) = P(z)/Q(z) which I want to revert (I'm trying to find the inverse of f).
I'll pick a simple example, the function f(z) = (1/z-1)^4
[sage:] sage: z = var('z');
[sage:] var('z')
sage: z = FractionField(PolynomialRing(QQ, 'z')).objgen();
[sage:] 'z')).objgen()
sage: f(z) = (1/z-1)^4;
[sage:] (1/z-1)^4
sage: g = f(z).taylor(x,2,4); #I expand f in a Taylor series just to make sure it's a series
[sage:] f.expand().reversion();
sage: f.expand().reversion()
AttributeError: 'sage.symbolic.expression.Expression' object has no
no attribute 'reversion'
[sage:] sage: g1 = g.power_series(QQ);
g.power_series(QQ)
TypeError: denominator must be a unit
[sage:] g.reversion();
sage: g.reversion()
AttributeError: 'sage.symbolic.expression.Expression' object has no
no attribute 'reversion'
A power series P(z) is not a rational function P(z)/Q(z). That's why the TypeError: denominator must be a unit unit appears.
Is it possible that SAGE Sage cannot invert rational polynomials? In the SAGE Sage help text the computation is passed to pari first, before using Lagrangian inversion.
I thought SAGE Sage uses FLINT. Why is it not used for computing the inverse of rational polynomials?
7 No.7 Revision
Series Reversion
I have a rational polynomial f(z) = P(z)/Q(z) which I want to revert (I'm trying to find the inverse of f).
I'll pick a simple example, the function f(z) = (1/z-1)^4
sage: z = var('z')
sage: z = FractionField(PolynomialRing(QQ, 'z')).objgen()
sage: f(z) = (1/z-1)^4
sage: g = f(z).taylor(x,2,4); #I expand f in a Taylor series just to make sure it's a series
sage: f.expand().reversion()
AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'reversion'
sage: g1 = g.power_series(QQ)
TypeError: denominator must be a unit
sage: g.reversion()
AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'reversion'
A power series P(z) is not a rational function P(z)/Q(z). That's why the TypeError: denominator must be a unit appears.
Is it possible that Sage cannot invert rational polynomials? In the Sage help text the computation is passed to pari first, before using Lagrangian inversion.
I thought Sage uses FLINT. Why is it not used for computing the inverse of rational polynomials?
EDIT (after answer by slelievre):
My problem now is how to avoid using the Symbolic Ring. I'm trying to do the following:
I want to invert an approximation formula for the Gamma-function. I am using Spouge's approximation. It has terms in the numerator and the denominator. Ithink I can compute them separetely per se, but what if I wanted to do a Pade approximation of the function
sage: f = (z+13)^(z+1/2)*exp(z)
sage: g = f.pade(5,5)
(it's the term ahead of the sum term in Spouge's approximation)
How do I get separate polynomials for the numerator and the denominator that are defined in the right algebraic structure?
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