Re: [sage-devel] Re: Failed tests for accuracy reasons

Hello, What if we introduce a "# numeric 1e-10" doctest flag (like #optional, etc.) that does just that---reads in the doctest answer, gets the output of the function, and does an abs(actual-expected)< epsilon (where epsilon can be specified in the flag, or it has a default). sage: some_numerica

Re: [sage-devel] Re: Inverse of permutation group elements

Hello, I have some questions about semantics and typographics convention in : 1/ Permutation 2/ PermutationGroupElement 3/ permutations (with lower p) 4/ Permutations Suppose I don't know Sage. How can I imagine the design of each function ? What is the first (question or) answer I must get ? I

Re: [sage-devel] Series expansion.

Dox ask : I'd like to know if there is a way of finding the series expansion of a given function around zero and infinity. Around 0 : sage: taylor (2*x/sinh(2*x), x, 0, 10) -292/13365*x^10 + 254/4725*x^8 - 124/945*x^6 + 14/45*x^4 - 2/3*x^2 + 1 I see that the serie is right, even if partial com

Re: [sage-devel] Coercion between polynomial rings

mmarco a écrit : Dealing with polynomial ringsi found something that seems incorrect sage: R=QQ['x','y'] sage: S=QQ['x']['y'] Shouldn't there be natural coercions from rings like QQ[x,y][z] or QQ[x][y][z] to QQ[x,y,z] and vice-versa? One easy way to coerce is Domain("the-expression")

[sage-devel] fuzzy (-1)^(1/3)

Andrzej Chrzeszczyk finds this numerical error in this equation : sage: s=solve(3*x^3-9*x+10,x,solution_dict=True) sage: ns=[n(s[k][x]) for k in range(3)] sage: ns [1.06780542232902 - 1.84949324407141*I, 0.0277635108030695 + 1.24902476648341*I, -1.09556893313209 + 0.600468477588001*I]

[sage-devel] a maxima? bug in sum.

Hello, I test sage: var ('n,k') sage: sum (binomial(n,k)*k^2, k, 0, n) # seems right sage: sum (binomial(n,k)*k^2, k, 1, n) # seems right n(n+1)2^(n-2) sage: sum (binomial(n,k)*k^2, k, 2, n) # is false : I get 0 Is it a maxima bug ? Do I push a Sage ticket for it ? F. -- To post to this gr

Re: [sage-devel] Transforming exponentials to hyperbolic functions.

Dox a écrit : Hi guys! I have an easy question... got an expression with exponentials, say exp(x)+exp(-x), How can I get the result in terms of hyperbolic functions 1/ First you can use the expr.subs method : y=exp(x)+exp(-x) y.subs(exp(x)==sinh(x)+cosh(x)).subs(exp(-x)=cosh(x)-sinh(x)) [You

Re: [sage-devel] desired behavior on #optional with ellipses

Dear kcrisman, While reviewing #7981, I discoverd something a little interesting. sage: animate([plot(sin(x + float(k)), (0, 2*pi), ymin=-5, ymax=5) ...for k in srange(0,2*pi,0.3)]).show() # optional You'd think this would be optional. Nope - it creates a file in doctesting. I

[sage-devel] Tests of improvements in timeit

Hello, I plot and analyse "timeit (a-calculus(n))" in a log-log scale from n=1..to..10..100..10^5...even...10^6 and I find some curious features in timesit, so I post these remarks and questions : /1/ I get the timeit result by timeit.eval("string_2+2").stats but timeit("string_2+2") displa

Re: [sage-devel] Simplification of symbolic sums and Maxima simpsum option

Hello Jean-Pierre, It would be nice to add an option to set Maxima simpsum option when calling Sage symbolic_sum function, or to enable it by default. Indeed, without it Maxima (and so Sage) does not evaluate symbolic sums of sums, i.e. something as sage: var('n') n sage: sum(2^x+2^-x,x,0,n) sum(

Re: [sage-devel] simplify_full on matrices.

Hello, Any chance that we can add simplify_full on matrices? So that each element is simplified if possible? /1/ I suppose you know the map function that operate over each term of a list. map (lambda x: 3*x, [1,2,3]) # computes [3,6,9] # you can replace 3*x by the function simplify_what_y

Re: [sage-devel] Re: Riemann sums , trapezoid mode

Hello, (and copy to Sage-edu) Currently, both riemann_sum and riemann_sum_integral_approximation does not support trapezoid mode. But instead there are separate function which computes these for trapezoid mode . I am added this mode to both riemann_sum and riemann_sum_integral_approximati

Re: [sage-devel] translating, transforming graphics objects?

Hi, I would like something like this to work: L = line([ some 2d points ]) L.translate(1, -1) I don't find how to transform a line to a list of points. But L[0] seens almost right (when L is a line) You apply the function lambda (x,y):(x+1,y+1) to each point. So map (lambda(x,y):(x+1,y

Re: [sage-devel] Re: emacs, prompt and readline

d its md5sum. All others questions are welcome ! Francois Maltey (in France) I use ; "GNU Emacs 22.2.1 (i486-pc-linux-gnu, GTK+ Version 2.16.1) of 2010-03-26 on palmer, modified by Ubuntu" The sage part in my .emacs file : (add-to-list 'load-path (expand-file-name "/usr/l

[sage-devel] emacs, prompt and readline

Hi, I use Sage in emacs in the shell buffer named *Sage-main*, in Inferior Sage Mode. I get an error when I type this input bellow with indent spaces. But the input is right without any indent space. In a xterm Sage adds theses spaces after the prompt, so I type the indented code without any

Re: [sage-devel] Re: Renaming the debugging function trace() to trace_execution()

Dear all, Students discover Sage for mathematical computations, and the functions are the most usual way to write mathematics. So I prefer a light interface with the matrix function "trace(...)". The determinant is a function and a method... but trace is only a method. And .methods() aren't ful

Re: [sage-devel] sqrt() returns wrong result for large inputs

David Roe wrote : I posted a patch there that should fix it; I have to work on other stuff, but if someone else wants to take over and write some doctests, make sure it works in lots of cases... David On Mon, Oct 25, 2010 at 17:14, Burcin Erocal > wrote: On Mon,

Re: [sage-devel] sqrt() returns wrong result for large inputs

Georg wrote : while calculating the integer part of square roots I realized that sqrt() returns wrong results for large inputs (although the sqrt() command itself accepts "bignum" values). example: int(sqrt(2^94533)) int isn't a "mathematical" Sage type, but Integer is a Sage type. And Integ

Re: [sage-devel] Re: log(1) returns int, not Integer

Hi Karl-Dieter and Burcin, You wrote (I cut a lot) Yup, I see what you are talking about - e.g. if (x.is_equal(_ex1)) // log(1) -> 0 return _ex0; Although it might be nice to stay relatively close to Ginac and fix such things on the Sage level if that's

Re: [sage-devel] Re: Test the "log" function in an expression for a rewrite function.

Hi Burcin and Karl-Dieter, // 1 // And what do you think about log ? Look at these test : exp(x).operator() == exp # is True, and all(?) trigonometric functions are fine log(x).operator() == ln # is True, yes the alias ln is better than the log name log(x).operator() == log # is False (this

Re: [sage-devel] Re: Test the "binomial" function in an expression

dagss wrote : op = y.operator # so op == cos if op == cos : ... # this test is fine, not the next one Now I want to test an expression with the binomial function call. y = binomial (3*x, x)# is fine op = y.operator() # is also fine Why is there a () here, but not in the previou

[sage-devel] Test the "binomial" function in an expression

Hello, I play with expressions, and transform sin(x) to (exp(i*x)-exp(-i*x))/2. So I use a lot of test as var ('x') y = cos(x) # or any other expression" op = y.operator # so op == cos if op == cos : ... # this test is fine, not the next one else : ... Now I want to test an expression

[sage-devel] 1==0 with "eval", sqrt and imag.

Hello, Maybe I'm wrong, but I don't understand the last 0. Test : var('m') ; y=sqrt(m^2-1) y(m=0) # =I, is right imag(y)# = feels right, arctan2(0,-1)=pi when m=0 imag(y(m=0)) # =1, is right (imag(y))(m=0) # is 0 and I don't understand why ! Francois in France. -- To pos

[sage-devel] A curious result with len : an int is not an Integer.

Hello, I play with random in order to approximate Pi by Monte-Carlo method. sage: n=10^5 ; len(filter(lambda t:t, [random()^2+random^2() < 1 for k in [1..n]])) / len([1..n]) The test looks at the point (random(), random()) and tests if it's in the quarter circle. The result may be about pi

Re: [sage-devel] Re: Bug in determinant?

Sebastian Pancratz wrote : > The problem is here: > > > http://trac.sagemath.org/sage_trac/attachment/ticket/6441/trac_6441_b_df_charpoly_412rebase.patch > new lines 1084--1089 > > When I wrote the code for computing characteristic polynomials in a > division-free way in order for it to wo

[sage-devel] Re: slightly confusing pynac simplification

Jason wrote : > The calculation below caused some concern for a few minutes with one of > my students the other day. We reasoned through it and saw that > everything was mathematically correct, but it seemed odd that Sage/pynac > would automatically pull a negative one out of (x-2t) and square

[sage-devel] Re: Adding new functions for specific tasks related (logarithm, rational functions, ....)

Many thanks for the 2 previous help ! About operator.add and expr.variables()... The (real-?) last question is a=4*x b=4/3*x c=4.0*x d=4*I*x I can get the constant by a.operands(), a.operands()[-1], but how can I test (without error) if this term is an integer, a rational, a float or a compl

[sage-devel] Re: Adding new functions for specific tasks related (logarithm, rational functions, ....)

William wrote : > But isn't it just operator()??? > > sage: var('x,y'); a = x+y > (x, y) > sage: a.operator() > > Sage also need tests over theses operators : In an expression we test op = expr.operator if op == sin : ... # is right elif op == + : ... # doesn't work (or add or _plus...) The

[sage-devel] Re: Adding new functions for specific tasks related (logarithm, rational functions, ....)

Hello, This purpose about expression has 3 differents aspects. A/ The first aspect we discover is the user interface. This interface must be coherent. This means that 1/ it's possible to describe it with "few word" 2/ The most common calculus has no option 3/ This system will be able to be re

[sage-devel] Re: Adding new functions for specific tasks related (logarithm, rational functions, ....)

quot;rewriting" > tasks through a few conceptually defined methods like rewrite(), expand > () and combine()( or contract()?). > > Francois Maltey had a proposal for a possible interface to all this. > Maybe he can comment here, or we can discuss his proposal on sage- > de

[sage-devel] Re: A plot may have several branchs

kcrisman wrote > It would also be great to see how to integrate your ideas with > #6878, which probably should still stand alone as a ticket since one > might wish to exclude points for reasons other than asymptotes or > jumps. > > Why not try to make this patch within the current plot code... I s

[sage-devel] A plot may have several branchs

Hello, I test the plot command, decode the plot.py file and also follow the patch #6878. So I understand that a plot is one line between points. The exclude option seems to cut this lines at each break point after the computation. Of corse a continuous plot is a such line. But the plot result

[sage-devel] Re: 0^0

About 0^0 > Even for discrete things like elements of GF(5)? I haven't thought > about what 0^0 is for things where the continuous limit doesn't make sense. > In any ring, integer power x^n is défined by x^0 = 1, because an empty product is the unit element. The reason is the same for 0!=1.

[sage-devel] Re: Decimals of Pi

Hello Nathann, > I know this is totally useless, but why shouldn't it work nevertheless > ? :-) > > sage: n(pi,digits=1000) Useless indeed... Maple often fails between 10^4 and 10^5 digits and axiom around 10^5. I don't know the reason : Ligther mathematics or bad code. It seems that numeri

[sage-devel] Numerical discont for plot ?

Hello, Functions plot is fine with singular functions as plot (sin(1/x), x, 0, 5) Plot has also a symbolic option detect_poles=True. But this option isn't designed for theses plots. There are unpleasant vertical lines. plot (floor(10*x), x, 0, 2) plot (x*floor(1/x), x, 0, 2) plot (arctan ((tan

[sage-devel] imaginary and plot - an other error after the patch 6905 in sage 4.1.2 alpha 4

Hello ! I test with success : var('m') plot (m^2,m,0,6) # for one plot plot ([m^3],m,0,6) # for one plot plot(sqrt(m^2+1),m,0,6) plot([sqrt(m^2+1)],m,0,6) plot(real (sqrt(m^2+1)),m,0,6) They are all right But this one fails : plot([real (sqrt(m^2+1))],m,0,6) Of corse I don't want to plot only

[sage-devel] Call pyginac functions in sage.

Hello, If I am right, the symbolic manipulations of Sage come from the (py)ginac librairies. In ginac documentation I find very intersting functions for my use of expressions : is_a is_a is_a There are about 30 tests for possible types. The types I can test by Expression.any_tests_I_find_iw

[sage-devel] Re: Sage 4.1.2.alpha4 released

I run upgrade from a sage-4.1.1 built at home on an ubuntu jaunty with a dual-core pentium by ./sage -upgrade http://sage.math.washington.edu/home/mvngu/release/upgrade/sage-4.1.2.alpha4 Then I get an error with an unknown function PC when I ran the updated sage. The ticket #6990 gives a new

[sage-devel] Re: Notebook feature request

Maurizio wrote : > At the beginning of the worksheet I could write in a cell something like: > > a,b = "any live data" > > So, three cells later I have: > > c = a + b; c > > And whenever I update a or b, the evaluation of that cell is repeated > and c gets updated accordingly... With students all

[sage-devel] Where can I find the inner sage code ?

Hi, I'm testing sage, the expressions and I play with expr.expand(). After test = 3*x, I find test.expand? and get the help text, and test.expand?? and the main call about expand. Then emacs goes to expression.pyx at the lines defining the interface (outer) function expand. In this code I fi

[sage-devel] Re: the Sage notebook

Hi, I'm not sure that discuss about the interface design of sage notebook inside firefox is at the right place. But let me give my advise during the first uses of sage 2 weeks ago or forget this mail. Even if I also use sage.el in emacs, the web-interface is really a very great-great-great wo

[sage-devel] Re: round(), floor() and ceil() on interval objects

Hello, > sage: a = RIF(1.5,2.3) > > I see no way to easily get 1 2 or 3 from a. > I propose, but I'm perhaps missunderstanding. a.lower().floor() a.upper().ceil() a.center().round() François --~--~-~--~~~---~--~~ To post to this group, send an email to sage-d

[sage-devel] Re: round(), floor() and ceil() on interval objects

William Stein wrote : > 2009/9/17 Jason Grout : > >> Currently, round(), floor(), and ceil() on interval objects return >> intervals. >> >> There is a patch up at #2899 that changes these functions to return >> integers (round-> "round the midpoint", floor -> largest integer below >> the bottom

[sage-devel] Re: log(x) versus ln(x)

mirko wrote : > Would it be possible to support both ln(x) and log(x), tg(x) and tan > (x) and so on via a locale setting? > If one locale is selected log, tan and so on, will be used, if another > that ln, tg, etc. > The input and the output must be the same, even in tex output and help files