hi sage developers :)
long time no see.
i think the migration python2 to python3 regressed a lot
of Graph() stuff related to ordering the vertices.
Here is test case from sagecell:
===
g1=Graph([(0,'a')])
g2=g1.copy()
g2.relabel()
g2.vertices()
g1.vertices()
TypeError: '<' not supported between
On Wed, Jul 13, 2022 at 5:46 PM John H Palmieri wrote:
>
> "Fix your old code" could just mean using `vertices(sort=False)`. See also
> https://trac.sagemath.org/ticket/22349.
>
fixing the sort() appears easy:
>>> li=['a',0]
>>> li.sort(key=hash);li
[0, 'a']
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sage 9.0 on ubuntu 20.
When raising symbolic expression to large integer power
i get abort() with stack:
gmp: overflow in mpz type
/lib/x86_64-linux-gnu/libc.so.6(abort+0x12b)[0x7f26d1c7a859]
/lib/x86_64-linux-gnu/libgmp.so.10(__gmpz_realloc+0xad)[0x7f26d048edcd]
/lib/x86_64-linux-gnu/libgmp.so.
On default install of fedora 37 in a VM sagemath gives
warnings, one of which is on start and on executing scripts:
Looks like the package maintainer didn't start it recently.
Is there workaround?
Session:
$ sage
SageMath version 9.6, Release Date: 2022-05-15
/usr/lib64/python3.11/site-package
I have theoretical reasons to doubt the correctness
of integrals involving `floor`.
The smallest testcases:
sage: integrate(floor(x)^2,x)
// Giac share root-directory:/usr/share/giac/
// Giac share root-directory:/usr/share/giac/
Added 0 synonyms
x*floor(x)^2
sage: integrate(2**floor(x),x)
2^flo
On Sat, Jan 21, 2023 at 8:43 AM Jonathan Thornburg wrote:
>
>
> Maple reports the same result for your first testcase:
>
> But, I think Maple and Sage/Giac are both wrong: consider the *definite*
> integral (latex notation) $I = \int_0^{3/2} \lfloor x \rfloor^2 \, dx$:
>
Lol, a cross-CAS exploit
I got an integral, which fails the derivative check.
For real positive x, define
f(x)=2^(x - 1/2*I*log(-e^(-2*I*pi*x))/pi - 1/2)
f(x) is just an obfuscation of 2^floor(x) and
for all positive x, f(x) is integer.
Let g(x) be the indefinite integral of f(x)
and let gder(x)=g'(x).
Assuming correct co
On Wed, Feb 1, 2023 at 7:38 PM parisse wrote:
>
> The antiderivative returned by giac (and by maple) for floor(x)^2 is only
> piecewise continuous and this is expected. But both CAS implement additional
> code to check for non continuous antiderivative (in simple situations for
> giac), and the
Thanks. sage appears to be slow on `integrate(floor(x)^2,x,0,n0)`,
is Maple fast?
Session:
sage: n0=10^6
sage: time integrate(floor(x)^2,x,0,n0)
CPU times: user 6.71 s, sys: 6.32 ms, total: 6.71 s
Wall time: 6.87 s
328350
sage: time integrate(x^3+x,x,0,n0)
CPU times: user 48.6 ms, sys:
You may consider the thunderbird email client or
some other MUA and try to disable html formatting
if the client supports it.
Can you point to colored testcase so I try it?
Once upon a time one could use gmail with console
client, but now google added additional authentication,
greatly reducing t
One of the reasons I asked this is to get correct closed form
for stuff like sum/int 2^2^floor(x).
Judging by the discussions, this won't work.
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On Fri, Feb 3, 2023 at 4:08 PM Dima Pasechnik wrote:
>
>
> gmail still supports application passwords, so one can still bypass 2FA for
> sending/receiving mail to/from gmail.
>
> my previous message in this thread was sent from mutt+postfix.
>
I love this, is it document somewhere?
I tried mutt
> >>> a = var('a')
> >>> assume(a, 'integer')
> >>> integrate(2^2^floor(x), (x, a, a+1))
> 2^(2^a)
>
> Now you just need the summation of that over the range of integer
> intervals you are interested in but Sage's sum can't do anything with
> that and I'm not sure if anything else can eithe
mail.com.
def algdepanalytic(F,D=4,check=False,K=None):
"""
sage code for algebraic dependendecy of numerical data
Author: Georgi Guninski, ggunin...@gmail.com, gunin...@guninski.com
Version: 2.0, Mon 06 Feb 2023
Project page: https://j.ludost.net/code
Given a li
Without doubts, sage and its library have bugs.
Are the bugs "powerful enough" to prove contradiction of the form 0=1?
As a self promotion, around 2008 I proved contradiction in Coq.
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Web searches return links to doc.sagemath.org like this:
https://doc.sagemath.org/html/en/reference/modmisc/sage/modular/etaproducts.html
This return HTTP 404 not found.
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On Wed, Mar 1, 2023 at 11:20 AM Dima Pasechnik wrote:
>
> I tried to send a reply by email to a message on sage-support
> It was rejected by Google:
Looong ago, what is now google groups was Usenet and email lists.
Google know evil and I am concerned that gmail will kill
traditional mail.
Des
Is this a bug:
sage: K.=QQ[]
sage: (x^6+y^9)%(x^3-y^2-1)
x^12*y - 4*x^9*y + 6*x^6*y + x^6 - 4*x^3*y + y
In pari:
? (x^6+y^9)%(x^3-y^2-1)
%1 = y^9 + y^4 + 2*y^2 + 1
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Many thanks for all replies.
GMS suggested to use Ideal.reduce(), but from the documentation:
"Requires computation of a Groebner basis, which can be a very
expensive operation"
I suspected that polynomial division is significantly more
cheap than groebner basis.
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I think grobner basis which contain non-zero constant and polynomials
is a bug.
sage: K.=ZZ[]
sage: l=[x^2+y^2+x+4,x^2+y^2+4*y+2,x^2-13*y^2+x]
sage: I=Ideal(l);gb=I.groebner_basis();gb
[y^2 + 4*y + 198, x + 1036*y + 2, 8*y + 544, 1040]
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I can't reproduce the AI script.
First, 'y' is not defined.
Second, sage doesn't like this constructor of Curve
with error:
TypeError: ambient space must be either an affine or projective space
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Google's chatbot Bard is at https://bard.google.com/
Bard isn't available in my country.
I heard that the main difference between ChatGPT and Bard
is that ChatGPT is offline during the chat.
Asking Bard about the genus of a curve would be an
interesting comparison.
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I have 2 questions for the AIs:
1: In sagemath how do I check if `2^(2^50)` is integer?
> RuntimeError: Aborted
2: Is `pi^(pi^(pi^(pi^(pi^42` integer?
> I believe rigorous proof doesn't exist yet
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Thanks for the information and being an AI proxy.
I agree that the AI's goal is to please the customer, err the human.
It remains the AI to be money driven and make a revolution:
"All your bank accounts and Windows boxen belong to the AI."
Very close to this scenario is Singularity [1], which is a
I tried the chicken or egg paradox attack on chatGPT
and I hitted two different errors, one suggested contacting their help.
Log of the chat:
Chat between Georgi Guninski and chatGPT https://chat.openai.com/chat
Wed Mar 29 12:34:27 PM UTC 2023
Georgi Guninski
Hi bot :)
I think sex is better
I get error when finding the generators of elliptic curve over
number field with non-monic defining polynomial.
Session:
sage: Z1.=ZZ[]
sage: Nf.=NumberField(13*Z^2+5)
sage: E=EllipticCurve(Nf,[w,0])
sage: ge=E.gens()
TypeError: Coordinates [-1/4, -1/8*w + 1, 1] do not define a point on
Elliptic
On Sun, Apr 16, 2023 at 2:25 AM Michael Orlitzky wrote:
>
> sage: A = matrix([[-3, 2, 1 ],
> : [ 2,-4, 4 ],
> : [ 1, 2,-5 ]])
> sage: B = (2 * 0.5 * A)
> sage: B == A
> True
> sage: B.rank() == A.rank()
> False
>
Doesn't this complicates citing sag
I know I am minority, but I recommend not to use github (owned by m$).
IMHO m$ are evil and technically incompetent.
They buy stuff and later spoil it.
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Since there was discussion about RealField, comparing floats for
equality is considered security vulnerability:
https://cwe.mitre.org/data/definitions/1077.html
Numeric calculation using floating point values can generate imprecise
results because of rounding errors. As a result, two different
ca
Cryptography based on hardness of finding solutions of diophantine equations.
This is related to crypto and there is money in crypto,
so someone may profit :)
With latex on mathoverflow [1].
For the general approach, check [2]
Working over $K=\mathbb{Q}[x_1,...,x_n,y_1,...y_m]$.
Let $f_i=g_i \c
sage: K.=QQ[]
sage: I=[x*(x-1),y*(y-1)]
sage: a=x+y+3
sage: a.reduce(Ideal(I))
x + y + 3
In addition:
sage: Kq=K.quotient(I);Kq(a)
xbar + ybar + 3
sage: Ideal([a]+I).groebner_basis()
[1]
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Hi, thanks for the answer.
I am trying algebraic approach to the NP-hard problem
independent set in graph.
For integer n, working over QQ['x',n] (probably another base field
will work too).
I have the following constraints:
1. x[i]*(x[i]-1)=0, i <=0 https://groups.google.com/d/msgid/sage-devel/CAGU
I am computing powers of matrices over the integers,
but will prefer to work over finite fields or finite rings,
first to avoid large integers and second to run faster.
Experimentally powers over the integers are faster than
finite rings and fields.
Can I do something to preserve efficiently and
pari/gp appears significantly faster:
sage: time M31=M3**n
CPU times: user 11.2 s, sys: 8.11 ms, total: 11.2 s
Wall time: 11.3 s
sage: M3g=gp(M3)
sage: time M32=M3g**n
CPU times: user 617 µs, sys: 2.79 ms, total: 3.41 ms
Wall time: 119 ms
sage: M32==gp(M31)
True
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I am not python expert, but got hurt by passing dictionary as
optional argument.
Session:
In [1]: def f(n,a,ca={}):
...: for i in range(n):
...: ca[i+a]=i+a
...: print(i,"len(cac)",len(ca))
...:
In [2]: f(2,2)
0 len(cac) 1
1 len(cac) 2
In [3]: f(2,4)
0 len(cac) 3
d an email
to sage-devel+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-devel/CAGUWgD8FPZQPJ_THJnzhiS80%3D%2BjwGZYC-%2BFoG5eXNuQQc1JNQw%40mail.gmail.com.
def matpowermodp(M,n,p):
"""
Author Georgi Guninski
in the pub
I need this for an algorithm, so even pointers to papers
will be appreciated.
The smallest bug I have is of order 36.
The attached file has two multi digraphs which are isomorphic,
but have distinct number of spanning trees.
print("isomorphic? ",G1.is_isomorphic(G2)) #True
print("equal trees?",
On Sun, Jun 18, 2023 at 10:16 AM Emmanuel Briand
wrote:
>
> Have you taken into account the following?
>
> ignature: G1.spanning_trees_count(root_vertex=None)
> Docstring:
>Return the number of spanning trees in a graph.
>
>In the case of a digraph, counts the number of spanning out-t
On Sun, Jun 18, 2023 at 11:19 AM Dima Pasechnik wrote:
>
> On Sun, Jun 18, 2023 at 9:09 AM Vincent Delecroix
> <20100.delecr...@gmail.com> wrote:
> >
> > sage: G1.spanning_trees_count(root_vertex=0)
> > 27202601182632270746156805986464038912000
> > sage: G2.spanning_trees_count(root_vertex=6)
> >
https://sagecell.sagemath.org/
Graph([(0,1)]).vertices()
/tmp/ipykernel_1853928/1298164553.py:1: DeprecationWarning: parameter
'sort' will be set to False by default in the future
See https://github.com/sagemath/sage/issues/22349 for details.
Graph([(Integer(0),Integer(1))]).vertices()
[0, 1]
On Mon, Jun 26, 2023 at 4:40 PM kcrisman wrote:
> As of https://github.com/sagemath/sage/issues/22349, this argument must be
> explicitly specified (unless a "key" is given); otherwise a warning is
> printed and "sort=True" is used. The default will eventually be changed to
> "False".
>
I thi
In both 9.6 and https://sagecell.sagemath.org/
Graph([('A',1)]).adjacency_matrix()
raises exception
TypeError: '<' not supported between instances of 'int' and 'str'
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Thanks.
In my code, this backwards incompatibility breaks over
150 calls to Graph.vertices() and I suspect
I am not the only one.
I think the root of the problem is the change from python2
to python3. In python2 |["A",1].sort()| works fine, while
it doesn't work in python3.
My recommendation is
On Tue, Jun 27, 2023 at 8:48 AM John H Palmieri wrote:
>
> Just do a global search-and-replace: change ".vertices()" to
> ".vertices(sort=True, key=id)" or ".vertices(sort=True, key=str)".
>
Thanks for this.
You are right that I knew about the problems with sort(),
and sage 9.6 is OK for me cur
I reported several bugs about Graph.vertices() and have
the impression that sage devs are aware of the problem and
don't want bug reports about this.
I have another testcase not related to vertices(), should
I report it?
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You definitely can construct graph with incomparable vertices
and they worked as expected in python2. python3 regressed them
and devs are doing workarounds.
The new testace is:
G=Graph([("A",1)])
G.feedback_vertex_set()
===
File /home/sc_serv/sage/src/sage/graphs/connectivity.pyx:287, in
sage.grap
In a QA attempt I tried to find calling sort() in graphs without
|key|, which may raise exception.
On sage 9.6:
$cd /usr/lib64/python3.11/site-packages/sage/graphs/
$grep -rnI 'sort(' . | grep -v 'key=' | grep -v 'topological'
#15 results
./base/static_sparse_backend.pyx:512:vertic
Graph([('A','B'),(1,2)]).edges()
) failed:
TypeError: unsupported operand parent(s) for <: 'Integer Ring' and
''>
I think this is related to sorting the edges.
The following works:
sage: Graph([("A",1),("B",2)]).edges()
[(1, 'A', None), (2, 'B', None)]
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Hi sage devs, your daily dose of incomparable objects,
fix 'em while they are free ;)
G=Graph([("A",1)]);G.faces()
TypeError Traceback (most recent call last)
Cell In [1], line 1
> 1 G=Graph([("A",Integer(1))]);G.faces()
File /home/sc_serv/sage/src/sage/graphs
On Wed, Jul 5, 2023 at 4:05 PM David Coudert wrote:
>
> I have opened https://github.com/sagemath/sage/issues/35902 to collect such
> kind of issues.
> Please use it to share new cases.
>
I just reported a bug on github, though I don't like microsoft services at all.
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On Wed, Jul 5, 2023 at 8:02 PM Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
>
> On Wed, 5 Jul 2023 at 17:51, Georgi Guninski wrote:
> >
> > I just reported a bug on github, though I don't like microsoft services at
> > all.
>
> Is google any be
I am not sure I understand correctly, but if you give warning, you
already know with high probability that functionality will be broken
and besides the warning you will get exception.
Is this correct?
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Simpler testcase is to replace `C = sqrt(T2)`
with `C=SR(int(2)).sqrt()`
Both int() and sqrt() appear necessary, sin() doesn't leak for me.
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On sage 9.6 and python 3.11:
>>> import gc
>>> from sage.all import SR
Traceback (most recent call last):
File "", line 1, in
File "/usr/lib64/python3.11/site-packages/sage/all.py", line 127, in
from sage.data_structures.all import *
File "/usr/lib64/python3.11/site-packages/sage/data_
Kz.=GF(3)[]
f1=y^2 + 1;g1=x^4*z - x^2*z + x;
C=Curve([f1,g1])
pc=C.projective_closure()
SignalError: Segmentation fault
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On Sun, Jul 30, 2023 at 2:00 PM Kwankyu Lee wrote:
>
> It seems related with the fact that the curve is reducible.
>
Could be, but some reducible curves pass the test:
sage: Kz.=GF(3)[]
sage: f2=(x+y)*(x+y-1);g2=x+y+z+1
sage: C=Curve([f2,g2])
sage: C.irreducible_components()
[
Closed subscheme o
```
set_random_seed(1);a=(Integers(13)(2))**randint(2,2**4000-1)
OverflowError Traceback (most recent call last)
OverflowError: Python int too large to convert to C long
The above exception was the direct cause of the following exception:
SystemError
```
I think the
hi Dima, I am familiar with reduction modulo Euler totient,
but it could be expensive to compute and in addition my testcase
omits it on purpose :)
btw, in the github issue the link to google groups appears
broken.
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btw, why this code works?
sage: a=Integers(13)(2);X=2**14000-19;a**X==a**(X%12)
True
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This may be fixed by the fix for sqrt(2), but I don't have such build.
I haven't done exact profile of the memory leak and measure
it with the "task manager" of XFCE.
The leak is about few megabytes per seconds.
Session:
```
c=0
while SR(float(0.5)): c += 1 #leaks
```
According to my tests the
```
while 1: a=bool(SR(float(0.5)))
```
leaks much. The stack and the global vars appear ugly to me.
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https://www.guninski.com/me.html
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The following leaks for me on 9.6
```
from sage.all import ZZ
for _ in range(10**8):
try: a=ZZ(10)**(2**61)
except: pass
```
In addition it prints on stderr `gmp: overflow in mpz type`
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```
n=var('n')
su1=sum(1/(5*n)-1/(5*n+1),n,2,oo);su1
```
RuntimeError: Encountered operator mismatch in maxima-to-sr translation
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Just FYI:
def testquotient2():
set_random_seed(1);p=next_prime(10**120);Kx=Integers(p)['x']
l=[Kx.random_element() for _ in range(100)]
return l.count(0)
testquotient2()
27
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def testcrtcrash1():
"""
crash with coredump in `crt` for polynomials over finite rings
author: Georgi Guninski
"""
A=13
Kx.=Integers(A**2)[]
mods=[x^2+A,x^4+A]
resi=[x,x^2]
g=crt(resi,mods)
return g
Aborted (core dumped)
This is offtopic: P != NP implies you can't work efficiently with many
nilpotent elements over commutative ring or algebra even on a
quantum computer.
The reduction is from counting hamiltonian cycles in a graph
via powers of nilpotent matrix.
For reference, check:
https://mathoverflow.net/q/364
This is based on numerical experiments in sage.
Let $K$ be a ring and define the ideal where each polynomial
is of the form $(a_i x_i+b_i)(a_j x_j+b_j)=0$ for constant $a_i,b_i,a_j,b_j$.
>Q1 Is it true that for constraints of this form the groebner basis is
>efficiently computable?
By "efficie
On Wed, Jan 31, 2024 at 10:54 PM Dima Pasechnik wrote:
>
> Do you have exactly one (or at most) relation for any pair of variables? Can
> one have i=j ?
>
> Or it's the notation which should be improved?
>
The number of relations for a pair of variables can be arbitrary.
i=j appears irrelevant,
Thanks. This was asked on mathoverflow [1], you can win some points
if you paste it as an answer.
Adding a single linear equation break the efficiency, so your solution
appear to show that incremental groebner basis might be large.
[1]:
https://mathoverflow.net/questions/463159/efficiency-of-gr
hi,
var('n')
sum((4*n+1)/factorial(n),n,1,oo)
TypeError: 'NoneType' object is not callable
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hi,
floor(tanh(91))
ValueError: cannot compute floor(sinh(91)/cosh(91)) using 256 bits of precision
gp('floor(tanh(91))')
1
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When I try to extract digits of tanh(91) via floor, I still get error
sage: floor(10^4*tanh(91))
ValueError
sage: gp('floor(10^4*tanh(91))')
1
gp computes it both ways :)
sage: gp.default('realprecision',10^5)
0
sage: gp('floor(tanh(91))')
0
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Given SR constant, I want to extract the first L base B digits
of the fractional part.
So far the best solution I found is:
floor((SR(expression)*B**L).numerical_approx(digits=L)).digits(B)
Can I do better?
Why the following approach fails numerically:
```
def base_B_digits(A, B,prot=False):
On Sat, Feb 10, 2024 at 6:24 PM Georgi Guninski wrote:
>
>
> ```
> def base_B_digits(A, B,prot=False):
> digits=[]
> fractional_part = A - int(A)
> while fractional_part != 0:
>digit = int(fractional_part * B)
>digits.append(digi
On Mon, Feb 12, 2024 at 9:35 AM Gareth Ma wrote:
>
> Yes, because 1 / 2 is mathematically infinite in base 3, just like how A=1/3
> and B=10 doesn't terminate.
>
Indeed, it is periodic and infinite.
When I use code finite precision I expect it to terminate.
It works with python `float` too.
btw,
There is discussion about this on mathoverlow [1]:
The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
correct and it contradicts numerical computations, including verification
with mpmath.
Session:
sage: import mpmath
sage: su4=sum(1/factorial(n**2),n,1,oo);su4
hypergeometric((1,)
The Register journo analysis of the SNAFU:
https://www.theregister.com/2024/04/01/xz_backdoor_open_source/
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I don't have reproducible testcase, but my pain is that sometimes if I
press CTL-C e.g. when solve_mod() is called in a loop, I get SEGV and
abort.
I suspect besides signals, it is hitting race condition.
Is this a known issue?
Very long ago there was vulnerability in sendmail, where it did
printf
Giving short testcase, can someone else reproduce it?
Also attaching backtrace.
On second thought, if I don't crash, there could be some memory
corruption and sage runs with screwed memory.
```
x,y=var('x,y');n=10**6
while True: so=solve_mod(x*y-1,n)
#press CTL-C, crashes with probability about 1/
Are the non-crashing codepaths in consistent state?
SEGV is in general sign of memory corruption and it may lead to wrong
math results or possibly have security implications.
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sage SEGV in solve_mod() + alarm() possibly related t
024 12:42:39 CEST, Georgi Guninski wrote:
> >On Fri, Apr 12, 2024 at 11:35 AM Dima Pasechnik wrote:
> >>
> >> This should be fixed by https://github.com/sagemath/sage/pull/37792
> >> please review
> >>
> >
> >I suspect reproducing is hard, sin
If the recent xz backdoor drama didn't induce enough paranoia in you,
here is a second chance exception:
https://www.theregister.com/2024/04/16/xz_style_attacks_continue/
Open sourcerers say suspected xz-style attacks continue to target maintainers
Social engineering patterns spotted across rang
> > in Sage development. The build scripts will simply pull and run it.)
> >
> > We should reduce dependencies, not add more. _Especially_ when it's
> > about non-essential convenience libraries.
>
>
> On Wed, 17 Apr 2024 09:43:28 +0300, Georgi Guninski
>
On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik wrote:
>
> I've filed https://sourceforge.net/p/maxima/bugs/4262/
>
Is maxima supported?
There is no progress on their bug system for more than 2 months.
SEGV is not pleasant, but incorrect symbolic result casts doubts about
all symbolic sage computa
The following hurt my computations.
```
#Author Georgi Guninski, Sat May 11 04:53:23 PM UTC 2024
p=101;
Kt.=Integers(p)[]
c5,s5=((100*t^10 + 45*t^8 + 93*t^6 + 8*t^4 + 56*t^2 + 1)/(t^10 + 5*t^8
+ 10*t^6 + 10*t^4 + 5*t^2 + 1), (10*t^9 + 82*t^7 + 50*t^5 + 82*t^3 +
10*t)/(t^10 + 5*t^8 + 10*t^6 + 10*t
I see your point, but segafault should be avoided if possible.
In some cases it is considered denial of service and IIRC on Fedora
the coredump is in /var, owned by root and not deletable by user.
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To
We found and implemented in sage efficient algorithm for factoring
bivariate polynomials modulo composite modulus assuming the solution
is unique up to a constant factor.
More formally let $K=\mathbb{Z}/n\mathbb{Z}[x,y]$.
Given $F \in K$ in general we can find solution $f,g$ such
that $F=f g$ as
Sorry for offtopic. We give efficient probabilistic factorization of
F(x,y)=g(x,y) f(x,y) modulo composite integers n assuming the solution
is unique.
The main contribution is the observation that `Ideal(J).groebner_basis()`
is efficient for overdetermined `J` and it works modulo n
The preprint i
On Sat, May 25, 2024 at 10:10 PM Matthias Koeppe
wrote:
> This has been merged in 10.4.beta7.
>
Good to see some action :)
Here is a short anti-security rant from my experience.
To protect something, you need to fix all weaknesses.
To break it, an attacker needs only one exploitable weakness.
This hurts me, so workaround is welcome.
n=13*random_prime(2**20);Kyx.=Integers(n)[];f=x^2+x+1;Kquo.=Kyx.quotient(f);Kquo
#pass
n=13*random_prime(2**50);Kyx.=Integers(n)[];f=x^2+x+1;Kquo.=Kyx.quotient(f);Kquo
TypeError: Can only reduce polynomials over fields.
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I think this is bug:
p=2**61-1;Kp=GF(p);g=Kp(3);X=p//3;a=g**X
dl=discrete_log(a,g,bounds=(1,p.isqrt()),algorithm="lambda",operation="*")
dl2=discrete_log(a,g,bounds=(1,p),algorithm="lambda",operation="*")
(g**dl==a,g**dl2==a)
#(False, True)
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> Instead, the algorithm should error out, since number theory shows there's no
> non-zero (mod 2^61 - 2) solution to 3^a = 1 mod (2^61 - 1)
Why do you reduce (mod p-1)?
(p-1) is valid integer solution by Euler's theorem.
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I think the problem is abusing the factorization of the group order
and later doing CRT.
The following code correctly raises exception:
dl3=discrete_log_lambda(a,g,bounds=(1,p.isqrt()))
ValueError: Pollard Lambda failed to find a log
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.
On Sun, Jun 30, 2024 at 7:14 PM dmo...@deductivepress.ca
wrote:
>
> I opened an issue at github #38316. Let's continue the discussion there.
>
> On Sunday, June 30, 2024 at 12:09:48 PM UTC-4 Georgi Guninski wrote:
>>
>> I think the problem is abusing the factorizati
I think this is a bug:
```
#Author Georgi Guninski
p=90887;Kp=GF(p);g=Kp(2);X=46712;a=X*g
print(a==X*g)
Y=discrete_log_lambda(a,g,operation="+",bounds=(1,p))
-> 1076 raise ValueError("Pollard Lambda failed to find a log")
ValueError: Pollard Lambda failed to find a lo
On second thought this is not a bug but a feature,
but I recommend the documentation should make it clear
that solution might exist.
Since the lambda log uses random integers, it depends on the
current state of the pseudo random generator and different
states might give result or a failure
I repr
#Author Georgi Guninski
K.=QQ[]
t1=x^2*z^2 + y*t;
t2= y*z^2 + x^2*t;
C=Curve([x^4-y^2-19,z^4-t^2-23,t1^2-t2^2-19*23]);
C.genus()
#93 #Wrong
C.irreducible_components()
[
Closed subscheme of Affine Space of dimension 4 over Rational Field defined by:
z^4 - t^2 - 23,
x^4 - y^2 - 19
]
Magma
https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
AI achieves silver-medal standard solving International Mathematical
Olympiad problems
Today, we present AlphaProof, a new reinforcement-learning based
system for formal math reasoning, and AlphaGeometry 2, an impr
I need non-torsion element of Jacobian of hyperelliptic curve,
would someone give example?
IIRC something very close to the following worked about
5 years ago, but now I get trivial result.
Session:
#Author: Georgi Guninski
K.=QQ[]
C=HyperellipticCurve(x^5+x+5^2-2);
J=C.jacobian();
P=J(1,5);
2*P
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