Re: [sage-devel] On backdooring open source projects
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. What does game theory say about this non-cooperative "game", will there be Nash equilibrium? Will competing attackers reach equilibrium? Will everything be compromised? "Will they'll drop the bomb" (Pink Floyd)? In the past bugs has killed people by overdosing some medical stuff and water supplies has be compromised, giving the ability to overdose water "ingredients". My threat model includes a prodigy (kid) which breaks real world stuff like the electricity network (possibly while drunk). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9nc1hCGWXKFPEbhn6bVLJ0FCbA8gbEzzPJhRo4hb-OvQ%40mail.gmail.com.
[sage-devel] OT Efficient probabilistic factorization of F(x,y)=g(x,y) f(x,y) modulo composite integers n assuming the solution is unique
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 is at [1] and the code is at [2] Sage session: sage: %runfile factor_groebner2.sage sage: set_random_seed(1);p1=random_prime(2**1000);p2=random_prime(p1);n=p1*p2 sage: Kxy.=Integers(n)[] sage: D2,D3=2,3 sage: g2=Kxy.random_element(degree=D2);f2=Kxy.random_element(degree=D3);F2=g2*f2 : sage: time gg=factorgroebner2(F2,D2,D3) CPU times: user 232 ms, sys: 12.8 ms, total: 245 ms Wall time: 2.68 s sage: gg[0]*gg[1]==F2 True sage: gg[0].degree(),gg[1].degree() (2, 3) [1] https://www.researchgate.net/publication/380720202_Efficient_probabilistic_algorithm_for_factoring_bivariate_polynomials_modulo_composite_integers_with_unknown_factorization_assuming_the_solution_Fxygxy_fxy_is_unique [2] https://www.guninski.com/factor_groebner2.sage -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9xxLe5vkmFp40hesFbNrdnOz_rh2gpsWMEMDZsLm51uA%40mail.gmail.com.
[sage-devel] On a efficient algorithm for factoring bivariate polynomials modulo composite modulus assuming the solution is unique
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 $F=f g$ assuming $f,g$ are unique up to a constant factor
(by constant factor we mean if $f,g$ is solution then another
solution is $g_1=C g,f_1=C^{-1} f$).
The algorithm was tested on 2000 bits integers by generating
random $f,g$ and then tried to recover them given $F$.
Probably the algorithm may fail on some cases.
>Q1 Is this result known?
>Q2 Is it of interest?
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Re: [sage-devel] Re: SEGV Crash in `numerator(f(t)/g(t)-const)`
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9AHV%3Dmd3bW_DPVh_f4Utm__pe%2B3GMHiGbDBK%2Bv6q%3DV9Q%40mail.gmail.com.
[sage-devel] SEGV Crash in `numerator(f(t)/g(t)-const)`
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^4 + 5*t^2 + 1))
f1=numerator(c5+99/101);f2=numerator(s5-20/101)
print("Done",f1,f2)
```
Unhandled SIGSEGV: A segmentation fault occurred
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Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
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 computations, especially those that can't be verified numerically. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_MWht0_wBwXXsH-c%3DpKGSXUCgNBEbKq4PyLRc3g5k%3D_Q%40mail.gmail.com.
Re: [sage-devel] On backdooring open source projects
I think you raise very important concerns. The only sage change I see after the xz drama is @Dima occasionally PGP signing his mails. The more packages you "own", the more developers you own. The more developers you own, the more packages you own. On Thu, Apr 18, 2024 at 5:09 PM Lorenz Panny wrote: > > > This also seems like a good time to reiterate an old comment of mine: > https://groups.google.com/g/sage-devel/c/Dq83PiiCAsU/m/RKSpD9_rDQAJ > ...pasted below for your convenience. > > On Tue, 21 Dec 2021 04:04:31 +0100, Lorenz Panny wrote: > > On Mon, 20 Dec 2021 14:41:27 +0100, Michael Orlitzky > > wrote: > > > We already have 214 standard packages. That's 214 pieces of software > > > copy & pasted into the sage releases... and 214 SPKGs that the sage > > > developers need to keep updating, and 214 distro packages that every > > > distro maintainer needs to keep track of as dependencies of the sage > > > package. > > > > It's also 214 software packages which might, for all we know, at any > > time be hijacked by The Bad Guys to run arbitrarily malicious code on > > every Sage user's machine. > > > > This is terrifying. > > > > (For examples where the modern "import * from internet" mentality has > > led to security disasters, just search for terms like "malicious npm". > > Luckily it seems less bad with pip packages for now, but not for any > > real reason. Every single piece of code we import adds huge security > > questions, because updates to the dependency may be published at any > > time totally invisible to Sage developers and the review process used > > 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 > wrote: > > 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 range of popular projects > > Tue 16 Apr 2024 // 14:07 UTC > > > > Open source groups are warning the community about a wave of ongoing > > attacks targeting project maintainers similar to those that led to the > > recent attempted backdooring of a core Linux library. > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-devel" group. To unsubscribe from this group and stop receiving emails > > from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view > > this discussion on the web visit > > https://groups.google.com/d/msgid/sage-devel/CAGUWgD82%3DoROFFxZwrKZG6eB0Kd5GEKW8wrPw_Q4gm8WJjioCA%40mail.gmail.com. > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/20240418160443.79b10a15%40l4. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8tEi3SdoPABMnVgHbSVKRDSJYN12qbdCQ8YKbCZKYPqw%40mail.gmail.com.
[sage-devel] On backdooring open source projects
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 range of popular projects Tue 16 Apr 2024 // 14:07 UTC Open source groups are warning the community about a wave of ongoing attacks targeting project maintainers similar to those that led to the recent attempted backdooring of a core Linux library. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD82%3DoROFFxZwrKZG6eB0Kd5GEKW8wrPw_Q4gm8WJjioCA%40mail.gmail.com.
Re: [sage-devel] SEGV caused by CTL-C in C/C++ code probably related to signals
My results differ. If you want more systematic approach for QA and security (the recent paranoia induced by the xz backdoor) you will need moderate budget possibly with zero trust to me. Have a nice weekend. On Fri, Apr 12, 2024 at 3:52 PM Dima Pasechnik wrote: > > > > On 12 April 2024 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, since it depends on the time of pressing > >CTL-C. > > Well, in all my tries the crash happened in the same place, the place that > now is no longer reachable. > > And the reason for the crash was, AFAIU, due to calling a plain Python code > (where Ctrl-C was caught) from a "noexcept" Cython code. That is, it's a > crash due to inability to properly process Ctrl-C. > > How many more similar places are left there in Cython code in Sage, I don't > know. > > Dima > > > >Also, lack a crash may be silent memory corruption. > > > >It is weird that the crash is not always. > > > >Do you fix the attached new testcase (no interaction required, may > >need changing some constants)? > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/C701D76E-A116-4D83-B427-24C305F51201%40gmail.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_ObgEtxC3Ok7%2BtHE174HS8kiUzbTC0y8%3D5Wdp%2B1QjNQw%40mail.gmail.com.
Re: [sage-devel] SEGV caused by CTL-C in C/C++ code probably related to signals
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, since it depends on the time of pressing CTL-C.
Also, lack a crash may be silent memory corruption.
It is weird that the crash is not always.
Do you fix the attached new testcase (no interaction required, may
need changing some constants)?
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"""
sage SEGV in solve_mod() + alarm() possibly related to signal
Author: Georgi Guninski
Fri Apr 12 09:49:15 AM UTC 2024
"""
def modcrash1(lim=100,seed=0):
#Author: Georgi Guninski
if seed != 0: set_random_seed(seed)
U=2000
L=U//2
x,y=var('x,y')
n=10**6
for i in range(lim):
S=randint(L,U)
print(i,S)
alarm(1.0*S/U)
try:
while True:
so=solve_mod(x*y-1,n)
cancel_alarm()
break
except: pass
cancel_alarm()
modcrash1()
Re: [sage-devel] SEGV caused by CTL-C in C/C++ code probably related to signals
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-WWBUq7dyA-SWYrm761fKcQBe%3DRNkR_GL%3DxqZF%2BNveLA%40mail.gmail.com.
Re: [sage-devel] SEGV caused by CTL-C in C/C++ code probably related to signals
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 1/3
```
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1056 return self.__order
KeyboardInterrupt:
Exception ignored in: 'sage.libs.singular.singular.sa2si_ZZmod'
Traceback (most recent call last):
File
"/usr/lib64/python3.11/site-packages/sage/rings/finite_rings/integer_mod_ring.py",
line 1045, in characteristic
def characteristic(self):
KeyboardInterrupt:
/usr/lib64/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0x8329)[0x7f7109fa1329]
/usr/lib64/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0x85f9)[0x7f7109fa15f9]
/usr/lib64/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0xae3e)[0x7f7109fa3e3e]
/lib64/libc.so.6(+0x3dbb0)[0x7f7117c5fbb0]
/lib64/libgmp.so.10(__gmpz_cmp_ui+0x4)[0x7f7109572f74]
/usr/lib64/sagemath/local/lib/libpolys-4.3.1.so(+0xdb672)[0x7f70b2f9c672]
/usr/lib64/python3.11/site-packages/sage/libs/singular/polynomial.cpython-311-x86_64-linux-gnu.so(+0x791f)[0x7f70b299191f]
/usr/lib64/python3.11/site-packages/sage/rings/polynomial/multi_polynomial_libsingular.cpython-311-x86_64-linux-gnu.so(+0x35103)[0x7f70b341e103]
/usr/lib64/python3.11/site-packages/sage/rings/polynomial/multi_polynomial_libsingular.cpython-311-x86_64-linux-gnu.so(+0x356fa)[0x7f70b341e6fa]
/lib64/libpython3.11.so.1.0(+0x1cf151)[0x7f7117fcf151]
/usr/lib64/python3.11/site-packages/sage/rings/polynomial/polynomial_element.cpython-311-x86_64-linux-gnu.so(+0x14dfeb)[0x7f70c1488feb]
/usr/lib64/python3.11/site-packages/sage/rings/polynomial/polynomial_element.cpython-311-x86_64-linux-gnu.so(+0x14e566)[0x7f70c1489566]
/usr/lib64/python3.11/site-packages/sage/categories/map.cpython-311-x86_64-linux-gnu.so(+0x1cb1e)[0x7f7108fc5b1e]
/usr/lib64/python3.11/site-packages/sage/structure/parent.cpython-311-x86_64-linux-gnu.so(+0x19108)[0x7f7109002108]
/usr/lib64/python3.11/site-packages/sage/rings/polynomial/multi_polynomial_libsingular.cpython-311-x86_64-linux-gnu.so(+0x376d8)[0x7f70b34206d8]
/lib64/libpython3.11.so.1.0(_PyObject_Call+0x79)[0x7f7117fe06b9]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x4c1a)[0x7f7117fbf7ba]
/lib64/libpython3.11.so.1.0(+0x1eed6a)[0x7f7117feed6a]
/lib64/libpython3.11.so.1.0(+0x1fb026)[0x7f7117ffb026]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0xbc5)[0x7f7117fbb765]
/lib64/libpython3.11.so.1.0(+0x1eed6a)[0x7f7117feed6a]
/lib64/libpython3.11.so.1.0(+0x1eebf8)[0x7f7117feebf8]
/lib64/libpython3.11.so.1.0(+0x1ed8d5)[0x7f7117fed8d5]
/lib64/libpython3.11.so.1.0(+0x20bcb1)[0x7f711800bcb1]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x2cce)[0x7f7117fbd86e]
/lib64/libpython3.11.so.1.0(+0x1b753a)[0x7f7117fb753a]
/lib64/libpython3.11.so.1.0(PyEval_EvalCode+0xac)[0x7f711803d99c]
/lib64/libpython3.11.so.1.0(+0x253cc2)[0x7f7118053cc2]
/lib64/libpython3.11.so.1.0(+0x1c875a)[0x7f7117fc875a]
/lib64/libpython3.11.so.1.0(PyObject_Vectorcall+0x37)[0x7f7117fc86c7]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x72d)[0x7f7117fbb2cd]
/lib64/libpython3.11.so.1.0(+0x1eed6a)[0x7f7117feed6a]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x358a)[0x7f7117fbe12a]
/lib64/libpython3.11.so.1.0(+0x1eed6a)[0x7f7117feed6a]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x358a)[0x7f7117fbe12a]
/lib64/libpython3.11.so.1.0(+0x1eed6a)[0x7f7117feed6a]
/lib64/libpython3.11.so.1.0(+0x251c57)[0x7f7118051c57]
/lib64/libpython3.11.so.1.0(+0x1df934)[0x7f7117fdf934]
/lib64/libpython3.11.so.1.0(PyObject_Vectorcall+0x37)[0x7f7117fc86c7]
/lib64/libpython3.11.so.1.0(_PyEval_EvalFrameDefault+0x72d)[0x7f7117fbb2cd]
/lib64/libpython3.11.so.1.0(+0x1b753a)[0x7f7117fb753a]
/lib64/libpython3.11.so.1.0(PyEval_EvalCode+0xac)[0x7f711803d99c]
/lib64/libpython3.11.so.1.0(+0x25aa63)[0x7f711805aa63]
/lib64/libpython3.11.so.1.0(+0x256efa)[0x7f7118056efa]
/lib64/libpython3.11.so.1.0(+0x26c342)[0x7f711806c342]
/lib64/libpython3.11.so.1.0(_PyRun_SimpleFileObject+0x1b8)[0x7f711806bb28]
/lib64/libpython3.11.so.1.0(_PyRun_AnyFileObject+0x48)[0x7f711806b7e8]
/lib64/libpython3.11.so.1.0(Py_RunMain+0x358)[0x7f71180660a8]
/lib64/libpython3.11.so.1.0(Py_BytesMain+0x3b)[0x7f711802dc0b]
/lib64/libc.so.6(+0x27b8a)[0x7f7117c49b8a]
/lib64/libc.so.6(__libc_start_main+0x8b)[0x7f7117c49c4b]
/usr/bin/python3(_start+0x25)[0x560df1abc095]
[sage-devel] SEGV caused by CTL-C in C/C++ code probably related to signals
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() or similar in signal handler and this was documented in the literature. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_7t9OTNdo6Ovrt%3DJdNqmGJLPGsZHVoJK0mNPQhuz1CKQ%40mail.gmail.com.
Re: [sage-devel] xz/liblzma has been compromised
The Register journo analysis of the SNAFU: https://www.theregister.com/2024/04/01/xz_backdoor_open_source/ -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD95yB%2BAUqnTPFQS0rC6_HQ5Fhxr%3DKF%3DyRTEHxYfrY-JAQ%40mail.gmail.com.
[sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
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,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
sage: CC(su4)
1.17227289255719 - 7.88860905221012e-31*I
sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
sage: su5=sum(1/factorial(i**2) for i in range(1,100))
sage: CC(su5)
1.04166942239864
sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
mpf('1.0416694223986369')
[1]:
https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
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Re: [sage-devel] Re: Problem extracting base B fractional digits of a number
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, this code was written by chatgpt and I have seen it on other places. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_S2N9YxGsjun1_VPmBCA6HjtC%2BSUHDkQY-o99S04UcZA%40mail.gmail.com.
[sage-devel] Re: Problem extracting base B fractional digits of a number
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(digit) >fractional_part = fractional_part * B - digit >if prot: print(fractional_part) > return digits > ``` > > I am not sure the program must terminate. > Just for the record, this this digit extraction algorithm doesn't terminate for A=0.5 and B=3 in sage and pari/gp. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9Oz1N%2BwQCVcucyMJCUeH6n6bjDFCCydR7qeqrMFkwVgQ%40mail.gmail.com.
[sage-devel] Problem extracting base B fractional digits of a number
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): digits=[] fractional_part = A - int(A) while fractional_part != 0: digit = int(fractional_part * B) digits.append(digit) fractional_part = fractional_part * B - digit if prot: print(fractional_part) return digits ``` tt=base_B_digits(SR(1/3).numerical_approx(digits=10),10,1) The fractional part starts: 0.33 0.31 0.14 0.333139 0.331393 ... 0.781250 0.812500 0.125000 0.25 0.50 0.00 I am not sure the program must terminate. For A=1/4, the base 10 digits are computed correctly. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9HpSwbwyWqc5BWkr4tnOhMfg5avhrRKUZJ7W24DCuATA%40mail.gmail.com.
Re: [sage-devel] Re: Exception in floor(tanh(91))
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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[sage-devel] Exception in floor(tanh(91))
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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[sage-devel] Exception in sum((4*n+1)/factorial(n),n,1,oo)
hi,
var('n')
sum((4*n+1)/factorial(n),n,1,oo)
TypeError: 'NoneType' object is not callable
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Re: [sage-devel] Efficiency of Groebner basis for constraints of the form $(a_i x_i+b_i)(a_j x_j+b_j)=0$
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-groebner-basis-for-constraints-of-the-form-a-i-x-ib-ia-j-x-j -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_LN2xQUZv4fKm_zT8rCpQbi%3DTZwHWQq6t8y7OZwYkGaw%40mail.gmail.com.
Re: [sage-devel] Efficiency of Groebner basis for constraints of the form $(a_i x_i+b_i)(a_j x_j+b_j)=0$
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, choose it as you want. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9AtK43yGeasyiDkyBOvQ_%3DV1Yx930N3%3DPHZ7g723o42g%40mail.gmail.com.
[sage-devel] Efficiency of Groebner basis for constraints of the form $(a_i x_i+b_i)(a_j x_j+b_j)=0$
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 "efficiently" we mean polynomial in the number of variables and
wall clock time of seconds for say 100 variables and if we a add
single constraint of other form the running time degrades.
For $K=\mathbb{F}_2$ this is equivalent to 2-SAT, which is
efficiently solvable.
We believe that adding one more linear factor, $(a_k x_k+b_k)$
will be NP-complete.
>Q2 Why adding the factor brings hardness?
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Re: [sage-devel] Re: crash with coredump in `crt` for polynomials over finite rings
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/364267/12481 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9u4SrSWfTAWApJtFa86CXOQCEr%3DnDrK9A8Us7cRNstNg%40mail.gmail.com.
[sage-devel] crash with coredump in `crt` for polynomials over finite rings
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)
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[sage-devel] PolynomialRing().random_element() returns 0 rather often.
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_eXb%2BJi_CVBCC5_Q%3DiYhg0A%3DKnvZZCAbG9Fv-NKYSL7A%40mail.gmail.com.
[sage-devel] maxima-to-sr exception in `sum(1/(5*n)-1/(5*n+1),n,2,oo)`
```
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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[sage-devel] Memory leak in `try: a=ZZ(10)**(2**61)`
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` -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9-%2BqN-Ri%2Bbz8fkeOGzDTzxUdgryC75C_bT_sDAGrdSdA%40mail.gmail.com.
[sage-devel] Re: Memory leaks in `while SR(float(0.5))` and in `a=gp('bnfinit(x^2+1)')`
``` while 1: a=bool(SR(float(0.5))) ``` leaks much. The stack and the global vars appear ugly to me. -- guninski https://www.guninski.com/me.html -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-wfE_M9A%2BHB84J%3DVm97dEW7pBKSykGBqVD8mOuOfSSHA%40mail.gmail.com.
[sage-devel] Memory leaks in `while SR(float(0.5))` and in `a=gp('bnfinit(x^2+1)')`
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 following does NOT leak, can someone confirm?
```
while 1: a=SR(float(0.5))
```
Another leak in gp:
```
while 1: a=gp('bnfinit(x^2+1)') #leaks
```
The leak is about few megabytes per seconds in the `gp` separate process
(note that `gp` leaks, not sage).
--
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https://www.guninski.com/me.html
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Re: [sage-devel] Overflow error in `set_random_seed(1);a=(Integers(13)(2))**randint(2,2**4000-1)`
btw, why this code works? sage: a=Integers(13)(2);X=2**14000-19;a**X==a**(X%12) True -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8UUVh1%2BsJLXt62HufSq4ZqyqRNKE7YyYhr05-1Qk_fPQ%40mail.gmail.com.
Re: [sage-devel] Overflow error in `set_random_seed(1);a=(Integers(13)(2))**randint(2,2**4000-1)`
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8MtndQyeO36fpLeEeNbUkNrLYAkDAyjfK2FfHoM%2BN88g%40mail.gmail.com.
[sage-devel] Overflow error in `set_random_seed(1);a=(Integers(13)(2))**randint(2,2**4000-1)`
``` 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 result should be computed correctly in time O(4000) via fast doubling without knowledge of the factorization. pari/gp computes it fast. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_nLYg8Ey0LZpfZjFLD4iXLQaz55CsX%3DbLpF0g362_TqQ%40mail.gmail.com.
Re: [sage-devel] Re: Caught SEGV in Curve().projective_closure()
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 of Affine Space of dimension 3 over Finite Field of size 3 defined by: z + 1, x + y, Closed subscheme of Affine Space of dimension 3 over Finite Field of size 3 defined by: z - 1, x + y - 1 ] sage: C.projective_closure() Projective Curve over Finite Field of size 3 defined by -x0^2 + x3^2, x0 + x1 + x2 + x3 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_1xcnKmSaurpzt6zmbSt2O%3DOvd3FG3d0e8cdEwabm8AA%40mail.gmail.com.
[sage-devel] Caught SEGV in Curve().projective_closure()
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD85fCHW7Dx%2B9oBVT9ck_Br2MthfC_bhMTV_w0SVERk_mg%40mail.gmail.com.
[sage-devel] import gc; from sage.all import SR; fails on python 3.11 and sage 9.6
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_structures/all.py", line 2, in from .bitset import Bitset, FrozenBitset File "sage/data_structures/bitset.pyx", line 1, in init sage.data_structures.bitset ModuleNotFoundError: No module named 'memory_allocator' This doesn't raise exception in sage shell. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-z_VKPpgZYk64%2BgUECeRjzs4J4rTDDWDOpsU4-nW%3DSuw%40mail.gmail.com.
Re: [sage-devel] Memory leak (quite bad)
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-Zbqzu2RzCZ7DYbtzPDDD9i1SX3zh%3DexL2xwNOcYcL2A%40mail.gmail.com.
Re: [sage-devel] Graph([('A','B'),(1,2)]).edges() raises weird traceback
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? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_q07qJagHLd2OnssTBCNHkdpY8afgMGg8JrJXeamyKYg%40mail.gmail.com.
Re: [sage-devel] Re: Exception in `G=Graph([("A",1)]);G.faces()`
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 better? > That is an open problem for me. I don't like them too, they collect a lot of info. At least google are technically skilled IMHO. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-CNTbtw7DUhkp_XaPwW2_whLBGWPtGQzr7MBberRuAiQ%40mail.gmail.com.
Re: [sage-devel] Re: Exception in `G=Graph([("A",1)]);G.faces()`
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD98uLfnfNqccXP8WGA3NuvFn6yCZuTERkacMsW1ByM-hQ%40mail.gmail.com.
[sage-devel] Exception in `G=Graph([("A",1)]);G.faces()`
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/generic_graph.py:6385, in
GenericGraph.faces(self, embedding)
6383 # Storage for face paths
6384 faces = []
-> 6385 minedge = min(edgeset)
6386 path = [minedge]
6387 edgeset.discard(minedge)
TypeError: '<' not supported between instances of 'int' and 'str'
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[sage-devel] Graph([('A','B'),(1,2)]).edges() raises weird traceback
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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[sage-devel] grep-ing for sort() in graphs
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:vertices.sort()
./base/static_sparse_graph.pxd:10:void qsort(void *base, int
nmemb, int size,
./base/static_sparse_graph.pyx:293:qsort(g.neighbors[i],
g.neighbors[i+1] - g.neighbors[i], sizeof(int), compare_uint32_p)
./graph_decompositions/vertex_separation.pyx:1841:delta.sort()
./connectivity.pyx:287:c.sort()
./generic_graph.py:3413:multi_edges.sort()
./generic_graph.py:12124:output.sort()
./generic_graph.py:21508:sage: lap.sort(reverse=True)
./generic_graph.py:21521:evals.sort(reverse=True)
./graph.py:2715:e.sort()
./graph_database.py:75:degree_sequence.sort()
./schnyder.py:278:l.sort()
./schnyder.py:427:ones.sort()
./schnyder.py:428:twos.sort()
./schnyder.py:429:threes.sort()
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Re: [sage-devel] Should I report codepaths leading to comparing incomparable objects?
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.graphs.connectivity.connected_component_containing_vertex()
285
286 if sort:
--> 287 c.sort()
288 return c
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[sage-devel] Should I report codepaths leading to comparing incomparable objects?
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? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9Ynqi2ddLrd%3Ds9JtUGV34DG%2BGyfLmp5sa-L-dHMDKMJw%40mail.gmail.com.
Re: [sage-devel] Re: DeprecationWarning on sagecell in Graph([(0,1)]).vertices()
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 currently. I noticed the warning when I shared permanent link to sagecell and it gave several warnings to the audience. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_6avqD4idK6Hn48R_y%2BTNo6fTC%3Dk2j5O%3DwLv4NcqYEzg%40mail.gmail.com.
Re: [sage-devel] Re: DeprecationWarning on sagecell in Graph([(0,1)]).vertices()
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 to reverse engineer python2.sort() and use it as a custom function for sorting heterogeneous vertices. In this scenario, the code won't be more broken than it was in python2. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-gDCQtwXywyx1C011Ak1zcBtJ4t7RV6JwqhFnKh%3D6p_g%40mail.gmail.com.
[sage-devel] Graph([('A',1)]).adjacency_matrix() raises exception
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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Re: [sage-devel] Re: DeprecationWarning on sagecell in Graph([(0,1)]).vertices()
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 think this sucks. Don't see any warning on version 9.6. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9SNgTKkTh4fwekkJnuhFG92Qg0uppfkHEGkarBuN1zJg%40mail.gmail.com.
[sage-devel] DeprecationWarning on sagecell in Graph([(0,1)]).vertices()
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] -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_K%3DY45Pb3sWOVvASBR2J1UMCfJcG07ZUqsXf1qmdDeMw%40mail.gmail.com.
Re: [sage-devel] Isomorphic multi digraphs have distinct number of spanning trees, bug?
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) > > 27202601182632270746156805986464038912000 > > indeed, and for all other vertices I get > 40803901773948406119235208979696058368000 > Many thanks to all :) Just to clarify: 1. If I don't equality for all V(G2) then G1,G2 are non-isomorphic multi digraphs, right? 2. If I get equality for a single vertex (0 -> 6 in the example) then then all isomorphisms map 0 to 6 (in this case G1.automorphism_group().order() == 96)? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9DqNNy7TKExXz%2BaRkj7xni-STpaE%2BBO8tR3ouOLQzHsw%40mail.gmail.com.
Re: [sage-devel] Isomorphic multi digraphs have distinct number of spanning trees, bug?
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-trees >rooted in "root_vertex". Default is to set first vertex as root. > > Thanks, I should have RTFM. This still doesn't work for me: sage: G1.spanning_trees_count(root_vertex=None),G2.spanning_trees_count(root_ver : tex=None) (27202601182632270746156805986464038912000, 40803901773948406119235208979696058368000) Is it rigorous to set c1=G1.spanning_trees_count() and then do: sage: c1=G1.spanning_trees_count() sage: for i in range(G1.order()): : c2=G2.spanning_trees_count(i) : if c2==c1: print(i) : 6 I expect for isomorphic multi digraphs the loop to find equal c1,c2? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_Zkf7g2py2PxWkYA4PqBOW6Ws%2BW31JtsQF2nmO6JE9tg%40mail.gmail.com.
[sage-devel] Isomorphic multi digraphs have distinct number of spanning trees, bug?
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?",G1.spanning_trees_count()==G2.spanning_trees_count())
#False
iso,map=G1.is_isomorphic(G2,certificate=True)
G3=G1.copy()
G3.relabel(lambda x: map[x])
print("verify iso",G3==G2) #True
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Re: [sage-devel] Re: Why matrix powers are slower over Integers(p) than in ZZ?
On Wed, Jun 14, 2023 at 8:15 PM David Roe wrote: > > Another possibility would be to change the __pow__ method for integer > matrices to not ignore the modulus argument. As a workaround you can either > use pari (as you discovered), or use an integer matrix and occasionally > reduce the coefficients. I implemented something very close to efficiently reduction modulo integers when working over ZZ and probably it can implemented in __pow__(). check the attached file. sage: time M1f=matpowermodp(M,n,p) CPU times: user 528 ms, sys: 2.98 ms, total: 531 ms Wall time: 362 ms sage: time M1s=M1p**n CPU times: user 21.3 s, sys: 4.01 ms, total: 21.3 s Wall time: 21.4 s sage: M1s==M1f True -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send 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 public domain M**n mod p M: matrix over the integers p=next_prime(2**100) n=200;l=list(range(n**2)) M=Matrix(ZZ,n,n,l) M1p=Matrix(Integers(p),n,n,l) M1f=matpowermodp(M,n,p) M1s=M1p**n M1s==M1f sage: time M1f=matpowermodp(M,n,p) CPU times: user 528 ms, sys: 2.98 ms, total: 531 ms Wall time: 362 ms sage: time M1s=M1p**n CPU times: user 21.3 s, sys: 4.01 ms, total: 21.3 s Wall time: 21.4 s sage: M1s==M1f True """ assert n>0,"n>0" R=M n=n-1 x=M N=M.nrows() while n: if n%2==1: R *= x x=x**2 n=n//2 for i in range(N): for j in range(N): R[i,j]=R[i,j]%p x[i,j]=x[i,j]%p return R
[sage-devel] Passing dictionary as an optional argument?
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
1 len(cac) 4
What is the scientific way to avoid `0 len(cac) 3`?
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[sage-devel] Re: Why matrix powers are slower over Integers(p) than in ZZ?
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD829%2BHC5D-YpvdR6hab7gHAfc9cGQTN%2BGft-DsW8T526A%40mail.gmail.com.
[sage-devel] Why matrix powers are slower over Integers(p) than in ZZ?
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 avoid large integers? session: sage: n=200;l=list(range(n**2)) sage: p=next_prime(2**30) sage: M1=Matrix(ZZ,n,n,l) sage: M2=Matrix(Integers(p),n,n,l) sage: M3=Matrix(GF(p),n,n,l) sage: time a=M1**n CPU times: user 1.97 s, sys: 36.3 ms, total: 2.01 s Wall time: 2.09 s sage: time a=M2**n CPU times: user 11 s, sys: 12 ms, total: 11 s Wall time: 11.2 s sage: time a=M3**n CPU times: user 11.1 s, sys: 5.96 ms, total: 11.1 s Wall time: 11.3 s -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9syfnCd2SKw%3DyZ-wydxutQwYSbVvuFF%3DvyS_bmiwFmLw%40mail.gmail.com.
Re: [sage-devel] Re: Is this feature: (x+y+3).reduce(Ideal([x*(x-1),y*(y-1)])) == x+y+3
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/CAGUWgD9sQSSWiGnEmQtYnHxO1FwW_VxCaddGaj01eMi0eDZEeg%40mail.gmail.com.
[sage-devel] Is this feature: (x+y+3).reduce(Ideal([x*(x-1),y*(y-1)])) == x+y+3
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] -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-OvonwOD9wM_35Sbutn13M%2Bdr4gJd7Gsd%3Dg0qdDLujeA%40mail.gmail.com.
[sage-devel] Complexity of finding solutions of trapdoored polynomial?
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 $f_i=g_i \cdot (h_i(y_i)+l_i(x_i))$ where $l_i$ is linear
and depends on only $x$ variables and $h_i$ depends on only $y$
variables.
There are no restrictions on $g_i$.
Let $F=\sum_{i=1}^k f_i$ be given as sum of monomials.
If we know the set of $f_i$ (the secret trapdoor) and we are given $y_i$
, for sufficiently general $l_i$, we can find the solutions
of $F=0$ as the solutions of the linear in $x_i$ system
of linear equations $(h_i(y_i)+l_i(x_i))=0$
>Q1 Can we find $f_i$ such that solving $F=0$ is hard
without knowing the trapdoor?
>Q2 Assume an oracle gives many solutions to $F=0$,
can we still get hardness results for new solutions?
[1] Complexity of finding solutions of trapdoored polynomial
https://mathoverflow.net/questions/445899/complexity-of-finding-solutions-of-trapdoored-polynomial
[2] Cryptography signature scheme based on hardness of finding points
on varieties?
https://mathoverflow.net/questions/445898/cryptography-signature-scheme-based-on-hardness-of-finding-points-on-varieties
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[sage-devel] Security weakness CWE-1077: Floating Point Comparison with Incorrect Operator
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 calculations might generate numbers that are mathematically equal, but have slightly different bit representations that do not translate to the same mathematically-equal values. As a result, an equality test or other comparison might produce unexpected results. This issue can prevent the product from running reliably. If the relevant code is reachable by an attacker, then this reliability problem might introduce a vulnerability. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8qR%2BA-P711-x8Mf9UQV5Oa-o64Q9GBQhU7y9puYCj8Fg%40mail.gmail.com.
Re: Re: [sage-devel] ChatGPT is an expert in SageMath too
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8j71OEw7LdzhWUDjy7B8-A2ENHZQeTxT7E88nKJnVGjw%40mail.gmail.com.
Re: [sage-devel] RealField isn't doing it right
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 sagemath in papers?
e.g. Proof: according \cite{sage} we have A != B, QED.
The testcases appear plausible to me.
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[sage-devel] Exception in elliptic curve over number field with non-monic defining polynomial
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 Curve defined by y^2 = x^3 + w*x over Number Field in w with defining polynomial 13*Z^2 + 5 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-ROP%3DQVhPPtqjy7PsY2%3DZb-8tOc%2BuO29PGWzz1KQ10Jg%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
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 than logic, but can't prove it. Can you prove or disprove it? Bot: I'm sorry, but as an AI language model, I cannot provide a subjective opinion on whether sex is better than logic or vice versa. Both sex and logic serve different purposes and are not necessarily comparable in terms of value or importance. However, I can provide information about the benefits and importance of both sex and logic. Sex is ..SNIPPED... GG: I am writing a paper about chickens and eggs and I need your help. Lemma 1: Chickens come from eggs. Is Lemma 1 correct? Bot: !Error in body stream There was an error generating a response REGENERATE: Yes, Lemma 1 is generally considered to be correct. Chickens, like all birds, hatch from eggs laid by their parents. The eggs contain the genetic material necessary for the development of a chicken embryo, which eventually grows and hatches into a chick. Therefore, it can be concluded that chickens come from eggs. Georgi Guninski Lemma 2: Eggs come from chickens. Is Lemma 2 correct? Yes, Lemma 2 is also generally considered to be correct. Eggs that are laid by chickens are fertilized or unfertilized reproductive cells that contain the genetic material necessary for the development of a chick embryo if fertilized. Therefore, it can be concluded that eggs come from chickens. Georgi Guninski Which came first: egg or chicken? Bot: ! Something went wrong. If this issue persists please contact us through our help center at help.openai.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_RWeAwQQPW8Q%3DL09X%2BBBFqXqR7M9UieP0QNEM1kBznFQ%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
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 serious theory, not crank theory. I read that significant ratio of geniuses are mentally ill and if the AI reaches certain level of creativity, the AI shows symptoms of mental disorder (can't find reference ATM). I am very impressed by chatGPT answers and to less impressed by Bard. I think Bard cheated in the `2^2^50` question. [1] https://en.wikipedia.org/wiki/Technological_singularity -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_vYtHFOumWYaKVZzPuy-hnZh%2BX9qGLf7_JFgoox_JYPg%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9H7GAFp%3D-JPfm0zaP45RUaMibYCZuneP6KeF-pGJA%2BNA%40mail.gmail.com.
[sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD__9APP5iTQwxYdNpCSOuJ%2B66EH_X4xghSQVxLoUxeK7A%40mail.gmail.com.
Re: [sage-devel] ChatGPT is an expert in SageMath too
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_0PdfBvdjcM5iy-Jsq4ph_zmfoQKAe5obS6gjBHRE_%3DA%40mail.gmail.com.
[sage-devel] Possibly incorrect result in groebner basis over the integers
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] -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-Cp%2BcYuQFqM84jAdMySjSw_Sc9NPeDdpjzQxqujSWawQ%40mail.gmail.com.
Re: [sage-devel] (x^6+y^9)%(x^3-y^2-1) == x^12*y - 4*x^9*y + ...
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9p-Jd7vUacWddbatMNDB9aQRvYC%3DyQDKGA0mFwXhHExQ%40mail.gmail.com.
[sage-devel] (x^6+y^9)%(x^3-y^2-1) == x^12*y - 4*x^9*y + ...
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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8y6MxLfERAoP2D4xyX4sHy%2B8_L_Mn92FnXzw3Ha40_Fg%40mail.gmail.com.
Re: [sage-devel] I am being (almost) banned from posting on sage-* groups
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. Despite @Dima's suggestion to use console Mutt with gmail, last month I couldn't find other MUA except Thunderbird for gmail. For Mutt found unofficial path for 2FA. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8WsaKdnTYk_LKK5fo2CA-kZJkdTL8Y-SfKj-qXLCNCCw%40mail.gmail.com.
[sage-devel] doc.sagemath.org appears broken
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-oWHKSbv3%2BtnOdGna-1k9PUObE7NmpU_x20vh%2BpOynWw%40mail.gmail.com.
[sage-devel] Can I easily prove a contradiction of the form 0=1 in sage?
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8OgXNZ1ZmT5aCeMfs0tUMeYi73UMxT1cP%2BaR9RUYGPDw%40mail.gmail.com.
[sage-devel] Suggested contribution: algebraic dependendecy of numerical data
Hi sage devs,
I am proposing contribution to sage.
Attaching https://j.ludost.net/code/algdep_numeric.py.txt
>From the comments:
Given a list F of numeric lists F_{i,1},F_{i,2},...F_{i,k}
Finds a list of polynomials G_i, such that G_i(F_j)=0
Examples:
F=[ [ZZ(fibonacci(2*i)),fibonacci(2*i+1)] for i in range(2,50)]
ag=algdepanalytic(F,D=2,check=1);ag
[x0^2 + x0*x1 - x1^2 + 1]
The X coordinate of an Elliptic Curve over finite field:
F=[ X(n*P),X((n+1)*P)]
p=next_prime(10**3);K=GF(p)
E=EllipticCurve(GF(p),[0,2]);P=E.gens()[0]
def X_n(P,n): return (n*P).xy()[0]
F=[ [X_n(P,2*i),X_n(P,2*i+1)] for i in range(2,47)]
ag=algdepanalytic(F,D=4,check=1);ag
[126*x0^2*x1^2 - 97*x0^2*x1 - 97*x0*x1^2 + 353*x0^2 + 303*x0*x1 +
353*x1^2 + x0 + x1 - 388]
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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 list F of numeric lists F_{i,1},F_{i,2},...F_{i,k}
Finds a list of polynomials G_i, such that G_i(F_j)=0
Examples:
FI=[fibonacci(2*i),fibonacci(2*i+1)]
def FI(n): return fibonacci(n)
F=[ [ZZ(fibonacci(2*i)),fibonacci(2*i+1)] for i in range(2,50)]
ag=algdepanalytic(F,D=2,check=1);ag
[x0^2 + x0*x1 - x1^2 + 1]
The X coordinate of an Elliptic Curve over finite field:
F=[ X(n*P),X((n+1)*P)]
p=next_prime(10**3);K=GF(p)
E=EllipticCurve(GF(p),[0,2]);P=E.gens()[0]
def X_n(P,n): return (n*P).xy()[0]
F=[ [X_n(P,2*i),X_n(P,2*i+1)] for i in range(2,47)]
ag=algdepanalytic(F,D=4,check=1);ag
[126*x0^2*x1^2 - 97*x0^2*x1 - 97*x0*x1^2 + 353*x0^2 + 303*x0*x1 + 353*x1^2 + x0 + x1 - 388]
"""
n=len(F[0])
if K is None: K=F[0][0].base_ring()
Kx=PolynomialRing(K,x,n)
ge=Kx.gens()
mo=prod(ge)**D
mo=Kx.monomial_all_divisors(mo)
mo=[i for i in mo if i.degree()<=D]
mo += [Kx(1)]
if len(F)
Re: [sage-devel] Re: Doubts about correctness of `integrate(floor(x)^2,x)`
> >>> 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 either.
>
Thanks. I expected the definite integral to give solution.
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Re: [sage-devel] Colours
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 with `imap` but couldn't make it work. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_midQJ%3D2P2ZabMasyGjaeu3wotEdFOBP2ayQYVbYqR2Q%40mail.gmail.com.
Re: [sage-devel] Re: Doubts about correctness of `integrate(floor(x)^2,x)`
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. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9yqP_L7C3kvrsr0eO-7gnTjxdTrNh_mX86o%2BOeYsrU8Q%40mail.gmail.com.
Re: [sage-devel] Colours
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 the options for client. google turned Usenet to google groups and now they are on the road to takeover email. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8OqWi%3DANKHVrfXW1kta67BZXW2S5Ltd8oKfprT4Tz5LQ%40mail.gmail.com.
Re: [sage-devel] Doubts about correctness of `integrate(floor(x)^2,x)`
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: 2 µs, total: 48.6 ms Wall time: 69.8 ms 25005000 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD86XKwzeO-26DW_paueKzLTjWEFbv2k8GM9A%2BJLSY_kuQ%40mail.gmail.com.
Re: [sage-devel] Doubts about correctness of `integrate(floor(x)^2,x)`
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 they correctly evaluate integrate(floor(x)^2,x,0,3/2) to 1/2. For > definite integration without parameters, giac also checks that the exact > answer matches a numeric value using approximate algorithms. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_brf_-0GDBi4O_XV%2BVTEcNbgjx%3DqpMXLDMU7bcc%2B8ssg%40mail.gmail.com.
[sage-devel] Integral of log() and exp() failing the derivative check
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 computations, we should have gder(x)=g'(x)=f(x) (*) According to sage, gder is the constant $1$ and (*) fails. sage session: === f=2^(x - 1/2*I*log(-e^(-2*I*pi*x))/pi - 1/2) g=integrate(f,x);gder=g.derivative(x) g #1/2*sqrt(2)*(-1)^(-1/2*I*log(2)/pi)*x gder #1/2*sqrt(2)*(-1)^(-1/2*I*log(2)/pi) CC(gder) #1.00 x0=5;CC((f-gder)(x=x0)) #31.0 === Some questions: 1. What other CASes say about g(x)? 2. Why the derivative test fails? 3. Besides the jumps at integer, do branches of log() give instability? Some comments suggest discontinuous functions cause integral problems. There are built-in discontinuous functions like tan() which are widely used. 4. Why tan() integrals are used without problems (?) when this fails the derivative check? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-E3tab-kwWUPAZQkJLzWOOYOLPLRZoe4VuqMU8znqR7A%40mail.gmail.com.
Re: [sage-devel] Doubts about correctness of `integrate(floor(x)^2,x)`
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 doubt sage and maple share source code, could
they share a buggy paper?
Here is a geometric disprove of the closed form.
Plot floor(x)^2 from 1 to 3. The area of the definite
integral is 1^2+2^2=5, which agrees with
integrate(floor(x)^2,x,1,3)
but disagrees with the indefinite integral.
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[sage-devel] Doubts about correctness of `integrate(floor(x)^2,x)`
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^floor(x)*x Would someone check with another CAS or prove/disprove by hand? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8C_AeV31g3J%2BbQP-am7dKUj2gK1OzPYrqXMiPh8-y5JQ%40mail.gmail.com.
[sage-devel] Multiple warnings in sagemath on default fedora 37
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-packages/sage/rings/polynomial/pbori/gbrefs.py:3: DeprecationWarning: 'uu' is deprecated and slated for removal in Python 3.13 import uu 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 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_2OPoUqzpFqvbm%3DgNJMJcC1_9Fhx5Uqz%3DdzLsuxiDbkw%40mail.gmail.com.
[sage-devel] abort() in __gmpz_realloc of symbolic expression with `gmp: overflow in mpz type`
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.10(__gmpz_n_pow_ui+0x7e7)[0x7f26d048ba97]
/lib/x86_64-linux-gnu/libpynac.so.18(_ZNK5GiNaC7numeric5powerEl+0x114)[0x7f26683b1c14]
The non-minimal testcase
===
def binnk3u(n,k): return ( (n/k)**(k))
n1=(2*10**3);d0=29004853178239;n0=SR(log(n1));tt=binnk3u(n0+d0-1,(d0))
print("passed :(")
===
on sagecell i get no output, just an animated rotating circle.
if possible please don't regress the following, which works:
sage: log(pi)**(2**80)
log(pi)^1208925819614629174706176
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Re: [sage-devel] Graph([(0,'a')]).vertices() raises exception
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'] -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD8QGrV69nW5stapeF-NUoeyhNcweGQ%3D5Bh7FHPCsNyvpg%40mail.gmail.com.
[sage-devel] Graph([(0,'a')]).vertices() raises exception
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 instances of 'int' and 'str' === -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-KgJS9CnNCJPun0TcQjbi6Y2RBS8JLYpca%3D1oPjLpi4w%40mail.gmail.com.
