domain, where I was
only thinking of the real numbers.
Can I not do something to the effect of assume(x, 'real') ?
On Saturday, December 28, 2013 10:07:41 AM UTC-8, JamesHDavenport wrote:
erf, as a function C-C, is not 1:1 (see 7.13(i) of DLMF), so this
simplification would be incorrect
erf, as a function C-C, is not 1:1 (see 7.13(i) of DLMF), so this
simplification would be incorrect.
I do not know how to tell Sage that you want real-valued
functions/variables, when of course it would be correct to do the
simplification.
On Friday, 27 December 2013 22:40:40 UTC, Buck
Furthermore, DLMF 7.17 only defines the inverse error function on the real
line (in fact (-1,1))
I do not recall ever seeing a discussion of the complex inverse error
function. Strecok (1968) shows that it satisfies y''=2yy'y',
but this is nonlinear, so the methodology of the paper below doesn't
Curious. The polynomial does not seem particularly ill-conditioned, in the
sense that its discriminat is roughly what one might expect (unlike, say,
Wilkinson's). Maple gives 50 roots with |f(x)|10^{-12}, and one with f(x)=,
i.e. much larger.
On Thursday, 12 December 2013 15:35:53 UTC, AWWQUB
UTC, JamesHDavenport wrote:
Curious. The polynomial does not seem particularly ill-conditioned, in the
sense that its discriminant is roughly what one might expect (unlike, say,
Wilkinson's). Maple gives 50 roots with |f(x)|10^{-12}, and one with f(x)=,
i.e. much larger.
On Thursday, 12
Although not SAGE-specific, some of the issues are discussed in our
Davenport,J.H. Trager,B.M.,
Scratchpad's View of Algebra I: Basic Commutative Algebra.
Proc. DISCO '90 (Springer Lecture Notes in Computer Science Vol.
429, ed. A. Miola) pp. 40-54.
http://opus.bath.ac.uk/32336/.
Davenport,J.H.,
You may be right - my University Maple 16 gets the right answer, but my
17beta does not. I've reported this as a Maple beta bug.
On Tuesday, 27 August 2013 06:34:07 UTC+1, Georgi Guninski wrote:
Thank you for the note.
You claim: For \int_{1/3}^1 fra(1/x) dx Maple returns ln 3 - 1/3.
I
Well, the derivative of the fractional part is indeed 1 where it is
defined, as
lim((fra(x+eps)-fra(x))/eps)=lim(eps/eps)=1 unless adding eps crosses a
boundary,
which it won't do for eps small enough.
Maxima (5.29) returns (4 pi log 2 + i log(-1) +pi)/(4 pi).
Depending on the value of log(-1),
Maxima, from memory supplemented with an experiment with 5.27, has
a) infinity, which is the infinity of the (one-point compactification of
the) complex plane
b) inf, which is the positive one of the two-point compactification of the
reals (plus infinity)
c) minf, which is the negative one of
, 2013 1:40:29 PM UTC-4, JamesHDavenport wrote:
On Tuesday, 30 July 2013 15:29:43 UTC+1, rickhg12hs wrote:
sage: var('a b')
(a, b)
sage: assume(a, 'real')
sage: assume(b, 'real')
sage: bool( sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2) )
True
sage:bool( (sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2
On Tuesday, 30 July 2013 15:29:43 UTC+1, rickhg12hs wrote:
sage: var('a b')
(a, b)
sage: assume(a, 'real')
sage: assume(b, 'real')
sage: bool( sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2) )
True
sage:bool( (sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2)).subs(a=1,b=-1) )
False
sage:
Why the
On Wednesday, 12 December 2012 02:28:19 UTC, kcrisman wrote:
On Tuesday, December 11, 2012 6:52:53 PM UTC-5, JamesHDavenport wrote:
Pedantic Note. Jacques Carette's paper: Understanding Expression
Simplification.
Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79
On Tuesday, 11 December 2012 13:15:09 UTC, kcrisman wrote:
I wouldn't worry about it, since in general there is no way to define
simpler expression that is fully useful at all times, and for more
complicated expressions more detail work would be needed anyway.
Pedantic Note. Jacques
I have no idea whether SAGE supports this, but basically what you need is
fraction-free Gaussian elimination: See section 3.2.3 of
http:/staff.bath.ac.uk/masjhd/JHD-CA.pdf
On Wednesday, 22 August 2012 13:04:08 UTC+1, Erik Aas wrote:
I'm trying to solve a system of linear equations over the
But this is a rather fragile concept: see
http://whww.sagenb.org/home/pub/4840 http://www.sagenb.org/home/pub/4840
If you can't, expand f below as x^2-2*x+1 then try perturbing the +1 term,
e.g. +1+10^(-20).
What you really need in the approximate square-free decomposition of f:
see, e.g.
It may be branch cut strangeness, but if so it is very strange. The
integrand is clearly well-behaved, and the integral,
while in terms of the incomplete gamma function, seems to be off the usual
branch cut (negative real axis).
On Monday, 14 May 2012 15:35:01 UTC+1, Robert Dodier wrote:
On
I would doubt it very much. I imagine the same techniques as Fr\ohlich,A.
Shepherdson,J.C., Effective Procedures in Field Theory. Phil, Trans. Roy.
Soc. Ser. A 248(1955-6) pp. 407-432, can be used to construct a ring which
has nontrivial idempotents iss we can determine membership in a
.
James
On Feb 22, 5:18 pm, Mark Rahner rah...@alum.mit.edu wrote:
On Feb 22, 2:37 am, JamesHDavenport j.h.davenp...@bath.ac.uk wrote:
Canonical form and simplify aren't the same thing (necessarily).
See Carette,J., Understanding Expression Simplification. Proc. ISSAC
2004 (ed. J. Gutierrez), ACM
On Feb 21, 9:36 pm, Mark Rahner rah...@alum.mit.edu wrote:
So once it comes back to Sage, its internal representation goes back to the
Ginac one.
My initial problem was the severe obfuscation that resulted when extra
factors added by the canonical form refused to cancel and then
replicated
...@orlitzky.com wrote:
On 01/13/2012 07:38 PM, JamesHDavenport wrote:
Unfortunately, full_simplify has its own problems, notably with branch
cuts.
sage: f = (1/2)*log(2*t) + (1/2)*log(-t)
sage: f.full_simplify()
1/2*log(2)
In my session, I had the difference of two logarithms. In yours above
Unfortunately, full_simplify has its own problems, notably with branch
cuts.
sage: f = (1/2)*log(2*t) + (1/2)*log(-t)
sage: f.full_simplify()
1/2*log(2)
Unfortunately, when t=-1, we have the sum of the logarithms of two
negative numbers, and therefore the imaginary part is 2i pi, not 0
On Jan 12,
As I said previously, you are only going to reconstruct RATIONALs with
num,den less than sqrt((1/2)*p^k), i.e. 92 in this case. It is true
that the integers are a subset of the rationals, but the convert to
integer problem is not a sub-problem of the convert to rational
problem.
On Jun 16, 3:22
I know very little about SAGE, but surely the point is that this is
not well-defined:
what rational were you expecting? You can only guarantee to get a
number with (num,den)
sqrt(p^k/2), and there isn't one, as 1 itself doesn't work.
Did you wnat to convert to integer?
On May 26, 1:53 am, Mel
The fact that the number of singularities quoted is precisely 2^32-1
makes me suspect a faulty return fo -1 from somewhere.
On Nov 21, 5:22 am, VictorMiller victorsmil...@gmail.com wrote:
sage: T.t1,t2,u1,u2 = QQ[]
sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1-
u2)^2 -1])
Disclaimer: I do not know the SAGE code here, just general theory.
As BFJ pointed out, there is no 'canonical' form for such expressions,
where 'canonical' means (see 2.3.1, p.79 of Davenport, Siret
Tournier) that there is a unique representation for every expression.
But there may well be a
My maxima (5.19.2) also generates an error here.
On Nov 8, 8:24 am, pong wypon...@gmail.com wrote:
I have encountered a problem in using integral
integral(x * sqrt((-2*cos(x))^2 + (2*sin(x))^2), x, 0, pi)
correctly gives pi^2
but
integral(sin(x) * sqrt((-2*cos(x))^2 + (2*sin(x))^2), x,
On Sep 3, 6:56 pm, Jason Bandlow jband...@gmail.com wrote:
For polynomial equations, the following should work in general.
sage: R.x,y = CC['x','y']
sage: f = x-y
sage: g = x^2 - y^2
sage: I = R.ideal([f]).radical()
sage: g in I
True
In general, to see if the equation g == 0 is implied
On Jul 16, 11:14 pm, Daniel Friedan dfrie...@gmail.com wrote:
an update:
minimize() is much improved using Harald Schilly's suggestion to
provide an explicit gradient function defined with fast_float().
succeeded:
minimizing a quartic polynomial in 100 variables containing
1,100,411
On May 5, 10:09 am, Mike Hansen mhan...@gmail.com wrote:
Hello,
On Wed, May 5, 2010 at 5:03 AM, Matt Bainbridge
bainbridge.m...@gmail.com wrote:
I wrote a sage program which does a lot of arithmetic in the field of
rational functions Frac(Q[x,y,z]). The problem is that sage doesn't
I am a co-organizer of Programming Languages for Mechanized
Mathematics Systems (PLMMS 2010): have you considered mounting a
demonstration of SAGE at the conference, which is part of CICM 2010 in
Paris in early July? There may well be sme SAGE peple at CICM, but I
can't
find out easily. The
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