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2014-07-27 01:53:51 -0500 commented question !f2py not working

I provided further clarification to my question.

2014-07-26 13:03:48 -0500 asked a question !f2py not working

Why is the command line F2PY tool not working with my sage installation?

The command !f2py on the sage shell returns

f2py*
-bash: f2py*: command not found

Do I have to be in the right folder for the tool to work?

I run sage in a virtual machine under Windows 7.

Sage 6.2 Documentation referring to f2py (the section referring to the command line tool is at the very bottom

2014-07-26 06:34:05 -0500 commented answer Summing polynomials

Sorry if that wasn't clear. I understood N to be a finite integer.

2014-07-26 04:00:15 -0500 asked a question Summing polynomials

I have a ┬┤Univariate Polynomial Ring in t over Symbolic Ring┬┤

sage: cj_t = (-1)**(j-1)/factorial(j-1)*(-j+a)**(j-1/2)*exp(-j)*(t+j)**(-1)

How can I compute the sum over j from 1 to N?

sage: sum(cj_t,1,N)

doesn't work.

sage: sum([cj_t for j in [1..N]])

(Python syntax) doesn't work either.

2014-07-26 01:41:39 -0500 commented answer Convert symbolic expressions like sqrt(2) or exp(1) to rational numbers

I'll maybe post a separate question for the precision issue. Thank you for your answer.

2014-07-25 14:37:55 -0500 commented answer Convert symbolic expressions like sqrt(2) or exp(1) to rational numbers

That sounds good. Is there an advantage in the additional step to working over a field of real numbers? What if I wanted to invert a power series with those coefficients, are rational coeffients better than real numbers?

2014-07-25 14:37:05 -0500 answered a question Convert symbolic expressions like sqrt(2) or exp(1) to rational numbers

That sounds good. Is there an advantage in the additional step to working over a field of real numbers? What if I wanted to invert a power series with those coefficients, are rational coeffients better than real numbers?

2014-07-25 12:35:04 -0500 asked a question Convert symbolic expressions like sqrt(2) or exp(1) to rational numbers

I have coefficents of a rational polynomial f(x) in terms of symbolic expressions like sqrt(2) and exp(1).

How can I convert these coefficients to rational number approximations of them, so that I can work in a structure like a polynomial ring?

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2014-07-23 13:38:52 -0500 commented answer Series Reversion

Thanks a lot for your help. I think I got the hang of it.

2014-07-22 14:48:39 -0500 answered a question Series Reversion

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 approimation)

How do I get separate polynomials for the numerator and the denominator that are defined in the right algebraic structure?

2014-07-21 14:50:23 -0500 commented question Series Reversion

see above for the instructions

2014-07-20 09:43:13 -0500 commented question Series Reversion

I added a line with what y(x) looks like.

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2014-07-20 08:46:18 -0500 commented answer Series Reversion

`y(x).power_series(SR)` gives `TypeError: denominator must be a unit'

2014-07-20 05:43:52 -0500 asked a question 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?