[sage-support] Re: Wrong NumberField.composite_field when embeddings are complex-conjugate roots of the same polynomial

This is now . > Hello, > >> The NumberField containing both embeddings should be larger. The >> morphisms also clearly show that something is going wrong: >> >> sage: nf = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 + >> 458*x^3 + 1875*x^2 + 4293*x +

[sage-support] Re: Wrong NumberField.composite_field when embeddings are complex-conjugate roots of the same polynomial

Hello, > The NumberField containing both embeddings should be larger. The > morphisms also clearly show that something is going wrong: > > sage: nf = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 + > 458*x^3 + 1875*x^2 + 4293*x + 3099, 'z', embedding=-1.18126721294295 + > 3.02858651117832j)

[sage-support] Re: What is right multiplication of vector spaces by matrices?

Hello, >> The bug is caused by FreeModule_generic._mul_(): > > Cool! You got the bug. Did you opened a ticket? If you do so, please cc'me. This is now http://trac.sagemath.org/ticket/17705 Pete -- You received this message because you are subscribed to the Google Groups "sage-support" group.

[sage-support] Re: What is right multiplication of vector spaces by matrices?

Hello, The bug is caused by FreeModule_generic._mul_(): def _mul_(self, other, switch_sides=False): if switch_sides: return self.span([v * other for v in self.basis()]) return self.span([other * v for v in self.basis()]) It looks like the effect of the switch_sides flag is exactl

Re: [sage-support] Failed to compute canonical height

It seems to be a precision issue; the error disappears when increasing the precision. >From within Sage: sage: point.height(precision=200) 242.47010035195076100129810400142304776375572634483556206582 Or directly in PARI: gp > \p 100 realprecision = 115 significant digits (100 digits display

Re: [sage-support] Failed to compute canonical height

I reported this bug to the PARI developers. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, sen

[sage-support] Re: Failed to compute canonical height

Hello, In the latest version of sage 6.4.1 the following code failed. > I didn't have any problem with 6.2 version of sage. > > [...] > > Sage failed to compute the canonical height. > any ideas? > This computation is actually done by PARI; this was upgraded between versions 6.2 and 6.4.1. The

[sage-support] Re: simple 'solve' error, possibly related to ecl and maxima installation

Op vrijdag 21 november 2014 04:34:44 UTC+1 schreef Nils Bruin: > > On Thursday, November 20, 2014 7:10:15 PM UTC-8, Bozh wrote: >> >> Are these warnings signs that maxima is still compiling itself every time >> I started? >> > It looks like Peter correctly identified the problem. According to his

[sage-support] Re: simple 'solve' error, possibly related to ecl and maxima installation

Op donderdag 20 november 2014 21:07:55 UTC+1 schreef Nils Bruin: > > On Thursday, November 20, 2014 4:36:52 AM UTC-8, Peter Bruin wrote: >> >> It could be caused by the following lines in the Maxima source code (in >> src/commac.lisp): >> >> (defparameter t

[sage-support] Re: simple 'solve' error, possibly related to ecl and maxima installation

Op dinsdag 18 november 2014 04:07:56 UTC+1 schreef Nils Bruin: > > On Monday, November 17, 2014 5:49:14 PM UTC-8, Bozh wrote: >> >> ;;; (RUN-PROGRAM "gcc" ("-I." "-I/Applications/sage/local/lib/ecl/" >> "-I/Users/buildslave-sage/slave/sage_git/build/local/include" >> "-I/Users/buildslave-sage/sla

[sage-support] Re: Bug in symbolic integral

Hello, This appears to be a bug in the evaluation of the incomplete Gamma function in the older PARI version(s) used by Sage up to and including 6.3. The computation is correct in the newly released Sage 6.4, which uses the recent stable PARI release 2.7.1. (See also http://trac.sagemath.org/

[sage-support] Re: simplifying an expression involving complex domain

Hello, > Somebody just complained about this on gitter >> > (https://gitter.im/sagemath/cloud): >> > >> > The simplify command is completely ignoring that the variable is >> > supposed to be complex: >> > ``` >> > t = var('t', domain='complex') >> > (conjugate(t)*t).simplify() >> > ``` >>

[sage-support] Re: var() definition in finite fields

Hello, I want to do some symbolic operations (matrix/vector) in the GF(2). > Here is an alternative approach (assuming all your expressions are polynomials in m1, m2, m3 and m4): sage: R. = PolynomialRing(GF(2)) sage: q = Matrix(R, [[m1, m2], [m3, m4]]) sage: q [m1 m2] [m3 m4] sage: q*q [ m1^2

[sage-support] Re: apparent numerical integration bug in sage

Hello Robert, Hmm, what method does PARI/GP use? The documentation for intnum > doesn't seem to mention any algorithms. ... I just looked at the > source code (intnum.c) and I can't tell what's going on. There is > some code for Romberg's method (intnumromb) but it's not called from > intnum

[sage-support] Re: Question About Finite Field propertie in polynomial ring

Hello, Let be the field > q = 2 > K. = GF(q^n) > and the Polynomial Ring > PR = PolynomialRing(K,"X") > Let be a random monomial of PR for example > P = t*X^(q^a). > Is there any method in sage to reduce X degree of polynomial P, such that > equivalent polynomial is t*X^(q^b) where b = mod(P.degr

[sage-support] Re: PARI Group Notation

Hi Steve, The documentation of PARI's group labelling/naming conventions is here (there are an "old" and a "new" convention, and Sage uses the new one): http://pari.math.u-bordeaux.fr/dochtml/html.stable/Functions_related_to_general_number_fields.html#polgalois I don't see 2^n S_n mentioned her

[sage-support] Re: Quotient ring over Finite Field 2^n

Hello, It seems like quotient_ring doesn't have '__call__'. Does it a bug or a > feature? > > sage: K = GF(2^8,'a') > sage: P = PolynomialRing(K,'x') > sage: Q = P.quotient_ring(P("x^256+x"),'y') > sage: f = Q.random_element() > sage: f.subs(y=K.random_element()) # random > (a^7 + a^6 + a^3 + a)*

[sage-support] Re: Overflow creating finite field element

Hello, I seem to have run across a potential bug on Sage: > > p = previous_prime(2^64) >> F. = GF(p^2) >> x * 2**63 >> >> > throws a "overflow in t_INT-->long assignment" exception creating the > element x * 2**63. > This is indeed a bug. Sage calls the wrong PARI function for this conversion:

[sage-support] Re: ECL says: In function GCD, the value of the second argument is not of the expected type INTEGER

Hello, This kind of problem has been reported before; see . You could try the workaround sage: sage.calculus.calculus.maxima('keepfloat: false') although this seems to be very slow (but maybe you expect it to be). Peter > Hi, > I'm having problem

[sage-support] Re: incomplete gamma function: evaluation and taylor series

Correction: it is not exactly the same bug, but the two are certainly related. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegr

[sage-support] Re: incomplete gamma function: evaluation and taylor series

This is in fact a long-standing bug, reported here: http://trac.sagemath.org/ticket/7099 (serious incomplete gamma function precision bugs) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emai

[sage-support] Re: incomplete gamma function: evaluation and taylor series

Hello, > However, I seem to be having trouble with the incomplete gamma function. > > Here are two difficulties. First, in trying to evaluate the incomplete > > gamma function at a point where the result should be very small, I just > get > > zero even if I increase the precision arbitrarily.

Re: [sage-support] Re: How to define a homomorphism between two algebras

s fields, though both A1.is_field() and > A2.is_field() return True. It might work to construct GF(p^12) > separately and define isomorphims from both A1 and A2 to it. > > Unfortunately you are discovering that the ability of Sage to work > with relative extensions of finite fields is not as good a

Re: [sage-support] Re: Computational geometry in the plane: in Sage?

A certain amount of work on adding functionality for hyperbolic geometry to Sage has been done in recent years, see here: http://trac.sagemath.org/ticket/9439 There seem to be several different implementations by different authors; I am not sure about the status of all this work and how much of

[sage-support] Re: How to define a homomorphism between two algebras

Can you post a complete example? The following (simple) example works for me (at least in 6.2.beta8): sage: F=GF(5).extension(2) sage: A1.=F.extension(x^2+3) sage: A2.=F.extension(x^2+3) sage: A1.hom([z],A2) Ring morphism: From: Univariate Quotient Polynomial Ring in y over Finite Field in a o

Re: [sage-support] Change the field where a polynomial is considered

This works for me in Sage 5.13 (I don't have an older version installed), after replacing the definition of FFps by FFps.=PolynomialRing(Fps) # the . was missing However, without the . the error I got was different from yours (TypeError: You must specify the names of the variables.) Op donde

[sage-support] Re: Change the field where a polynomial is considered

Hello, I want to define a polynomial that I know lies in GF(p^2,'b')[x], > p=371. The problem is that I have to define it as a product > E=(X-a_1)*(X-a_2)*(X-a_3)*(X-a_4)*(X-a_5)*(X-a_6), where every a_j is in > GF(p^13,'a')[X]. > I tried to do GF(p^2,'b')[x](E), but then Sage just changes

[sage-support] Re: Writing a particular Elliptic Curve

Dear Bhavin, Thank you very much for your answer. It helps but still I do not know how > to see the answer to my exact problem. > My exact problem is the see the graph of y^2=x(x+1)(2*x+1)/6. > If you have constructed an elliptic curve (after scaling the variables), say E, then you can do sag

[sage-support] Re: Writing a particular Elliptic Curve

Hello, Sage only supports equations where the coefficients of y^2 and x^3 are 1; you first need to multiply the equation by A^2 and then put A*y = Y and A*x = X, so the equation becomes Y^2 = X^3 + B*X^2 + A*C*X + A^2*D You can construct this (assuming A, B, C, D are set to suitable values) u

[sage-support] Re: Some GIT help

Hello, I'm also a git beginner, so the experts should correct me if there is a better way, but what I normally do in such situations is $ git stash $ git pull git://trac.sagemath.org/sage.git develop $ git stash pop Since you say your change is just one line, this is probably the least-effort

[sage-support] Re: int() on real numbers broken?

Hello, > I am working on a Z80 project and I needed 72 bits of precision for 64 > elements of the form log2(1+2^-i) (so log2(3/2), log2(5/4),...). I > needed to convert these to hexadecimal, and it worked until I tried > the following for i=56: > int(256*log(1+2^-56,2)) > > This returns 1, when in

[sage-support] Re: extension de corps

Bonjour, Il est malheureusement un peu problématique de construire des tours (extensions successives) de corps. Sage sait bien vérifier que votre F6 est un corps, mais F6 est toujours représenté comme anneau quotient et non comme corps fini ; c'est pourquoi certaines opérations naturelles ne marc

Re: [sage-support] Re: Possible Bug in Matrix Nullity Method

Hello John, Surely not? For the left nullity the vectors are row vectors on the > left, but the matrix is acting on the right (unless I got out of bed > on the wrong side this norming). > Yes, I now realise that I read the phrase in a "left-associative way", interpreting "kernel of this matr

[sage-support] Re: Possible Bug in Matrix Nullity Method

Hi Dima, Is there something wrong in documentation regarding them? > Possibly: the documentation of m.nullity() says Return the (left) nullity of this matrix, which is the dimension of the (left) kernel of this matrix acting from the right on row vectors. This should probably be "acting from

[sage-support] Re: Possible Bug in Matrix Nullity Method

It is not a bug, but a consequence of a different convention. In Sage, nullity means left nullity, i.e. the dimension of the left kernel. In this example, m.nullity() + m.rank() = m.nrows(). For the more common right nullity (resp. kernel), use m.right_nullity() (resp. m.right_kernel()) inst

[sage-support] Re: Polynomial rings and homogenization

Hello Tristan, > n = 100; d=3 > load DATA+'my_functions.py' > coefficients = poly_expand(n,int(n**(1/d)),d) > R. = ZZ[] > f = 0 > for c in coefficients: > f += c*t^d > d -= 1 > g = f.homogenize('s') > > Running this returns "AttributeError: 'GlobalPolynomialRing' object has no > attribu

[sage-support] Re: confused about primality of Ideal(1)

Hello, > I'm a bit confused about Sage's answer if Ideal(1) is prime. > > R.= QQ[] > I = Ideal(R(1)) > I.is_prime() > > Sage (5.11, not only) says yes, > conflicting to the definition, > http://en.wikipedia.org/wiki/Prime_ideal > Has somebody an expanation of this behaviour? The example Singular

[sage-support] Re: hyperbolic triangles using disc model

Hello, I've been using Sage's hyperbolic_triangle function quite a lot to produce > a few pictures. I'm very happy with them, but I was also wondering whether > Sage could handle the "disc model" for hyperbolic triangles... Only the > "upper half-plane model" seems to be available, but I may be

[sage-support] Re: Calling gp.F(n) in a loop about 2^16 times raises exception

> To partially solve the above bug, we should make sure doubling of the > "sage" array works when an allocatemem() has to be done; this seems to be > broken, and I just opened a ticket for it (#15446). It is only a partial > fix because doing GP calculations still leaks memory. > I also open

[sage-support] Re: Calling gp.F(n) in a loop about 2^16 times raises exception

Op vrijdag 22 november 2013 18:48:27 UTC schreef Nils Bruin: > > On Friday, November 22, 2013 10:26:52 AM UTC-8, Peter Bruin wrote: >> >> The results of all GP command are stored in an array named 'sage' inside >> GP. If you execute too many commands, th

[sage-support] Re: Calling gp.F(n) in a loop about 2^16 times raises exception

The results of all GP command are stored in an array named 'sage' inside GP. If you execute too many commands, this array apparently isn't enlarged anymore. I suspect that this is because GP runs out of stack space and that Sage's GP interface does not notice this. I don't see a quick and eas

Re: [sage-support] Is it normal to get negative canonical height of a point on EC over NF ?

The problem is indeed fixed by applying #13951 (which still needs reviewing). Peter Op vrijdag 8 november 2013 17:35:01 UTC schreef John Cremona: > > On 8 November 2013 16:11, Georgi Guninski > > wrote: > > I am not an expert, but is it normal to get negative canonical > > height of a point o

[sage-support] Incorrect computations of Eisenstein series

271). The method __compute_general_case of the class EisensteinSeries in modular/modform/element.py reproduces this formula in the form v.append(sum([psi(n)*chi(m/n)*n**(k-1) for n in rings.divisors(m)])) Here psi should be ~psi. Thanks, Peter Bruin