Hi Simon,
Simon King wrote:
> Coincidentally, William Stein today advertised a multi author book on
> doing computations with Sage, and it has a chapter on solving
> recurrences, also pointing to sympy.
Well, I'm not responsible for that part ;-)
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Simon King wrote:
> What about
> a more complicated recurrence, such as the one given by
> x_(n+1) = 1 + x_n*2/n
> Any chances to solve those and similar recurrences automatically?
You can try sympy's rsolve() or Maxima's solve_rec(). I don't know how
powerful they are.
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Simon King wrote:
> That's not what I am looking for. No data are given. Given is some
> recursion formula; what we want to know is a corresponding closed
> formula. Example: The recursion x_0=1 and x_(n+1) := f(x_n) = 2*x_n
> should result in the closed formula x_n = 2^n.
ore_algebra also has som
Hi,
Can anyone explain why the following works:
- 8< - 8< - 8< - 8< - 8< - 8< - 8< - 8< -
$ ~/co/sage/sage --version
SageMath version 8.2.beta8, Release Date: 2018-03-10
$ head foo.pyx setup.py
==> foo.pyx <==
from sage.libs.gmp.types cimport mpz_t
==> setup.
John H Palmieri wrote:
> This question comes from
> http://stackoverflow.com/questions/41638257/graphics-in-sage-script:
> if I have a file "foo.sage" and I want to run "sage foo.sage" and have
> it pop up a window displaying a plot, how do I do this?
Running sage < foo.sage instead of sage foo.sa
Nils Bruin wrote:
> If a field embeds into QQbar, then there should be an implied coercion
> into CC, though: QQbar as implemented in sage is a subfield of the
> field of complex numbers (as you can see from how the elements print).
Let me add that there are long-standing tickets (#5355, #12715) f
Simon King wrote:
> Wouldn't it be better to [...] or change the
> arithmetic operations by *avoiding* a call to __init__()?
That's what the branch I pointed to tries to do, to some extent at
least. But the structure of generic polynomial classes (with many
operations implemented in an abstract
Nils Bruin wrote:
> polynomial aritmetic over ZZ and QQ is so much more optimized than
> over number fields,
Yes, polynomial arithmetic over number fields is painfully slow. The
branch trac:u/mmezzarobba/speed_up_generic_polynomials (not fully tested
yet) may help a little.
Another trick you ca
als must predate the introduction of
Groebner bases in Sage...
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Jeroen Demeyer wrote:
> Is there any reason that quo_rem is not consistent with .mod()? That
> is no longer arbitrary and would also extend the Euclidean division of
> univariate polynomials.
Not quite: you'd have to return a tuple of quotients.
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for exact divisions or
divisions by monomials...)
> Is multivariate division in the sense of
> https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Reduction implemented
> somewhere in Sage?
Yes: p.mod(ideal) or ideal.reduce(p).
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Nico Van Cleemput wrote:
> Looking at the implementation of the
> float conversion, the problem seems to come from the following:
>
> sage: AA(ge)
So apparently Sage is trying to prove that the imaginary part of the
algebraic result is exactly zero.
> Is there another way to get a good float ap
Hi Dror,
dror fidler wrote:
> i recently used is_distance_regular() in the graph package.
> however the definition of the function in the documentation page does
> not fit the definition of distance regular graphs. i would be very
> interested to find the source of the information the author used
Dima Pasechnik wrote:
> sage: r0=QQ['a1,a2']
> sage: a1,a2=r0.gens()
> sage: r=r0['x1,x2']
[...]
> I am using such a ring as I want to treat ai as parameters, i.e. I
> would like monomial expansions in xi alone.
> Perhaps there is a better way to accomplish this?
The best I can think of is
p.map_
fficients() functions. I think I'm not doing a good job with
> difference between symbolic expressions, functions, and polynomials.
I think what you want is to replace the first line by
R. = PolynomialRing(SR, 2)
Then the elements of R will be allowed to contain symbolic variabl
for polynomials, not power series:
sage: x = polygen(GF(17))
sage: (1-x+x^2-x^3).rational_reconstruct(x^4, 1, 1)
(1, x + 1)
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I am sending you a more detailed reply in French (this is much easier for
me) off-list.
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