Re: [sage-devel] Re: Jupyter notebook broken in 9.2.beta4

[Dima Pasechnik]

On Sun, Jul 12, 2020 at 11:06 PM Paul Masson  wrote:
>
> Confirmed that `sage -b` allows notebooks to run. There are still some 
> console error messages about not finding `preact-compat` and `preact`. Those 
> were both removed from the notebook last summer, so probably time to upgrade 
> the notebook...

the problem is tracked on https://trac.sagemath.org/ticket/30123

>
> On Saturday, July 11, 2020 at 10:58:32 PM UTC-7, Jonathan Kliem wrote:
>>
>> I posted this on sage-release, because I figured, it's due to a recent 
>> ticket. But I was mistaken because of the following:
>>
>> What worked for me is running
>>
>> sage -b
>>
>> But running
>>
>> make build
>>
>> breaks it again. I hope that works for you for now. But it is of course not 
>> acceptable.
>>
>> Am Sonntag, 12. Juli 2020 02:26:02 UTC+2 schrieb Paul Masson:
>>>
>>> Just built a ticket based on 9.2.beta3 and the same problem occurs.
>>>
>>> On Saturday, July 11, 2020 at 4:09:56 PM UTC-7, Paul Masson wrote:

 After a successful incremental build from 9.2.beta2, trying to start a new 
 notebook results in the browser console error "Failed to load resource: 
 the server responded with a status of 404 (Not Found)" when trying to 
 fetch Mathjax from http://localhost:/nbextensions/mathjax/MathJax.js. 
 Has anyone other than Dima seen this also?

 This appears to be a serious server configuration error. I don't see any 
 ticket in either this beta or the previous one that would cause this. Am I 
 missing some new configuration step? Sage built and runs just fine.
>
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Re: [sage-devel] Re: Transpiling from Mathematica syntax to sage backends

[rjf]

the problem I see here is the recipe

requiring "user choice"  and somehow specifying "inf in Mma"

Most users will not want to specify, but probably would go along with
"the mathematically consistent choice according to experts who have
studied the matter."

Certainly saying, as one choice, "inf in Mma" is inadequate since
the user, other people, other CAS, cannot make use of this with
any certainty.  Even "inf in Mma version 12.1" while specific,
is not so useful outside of Mma version 12.1.  There is no
axiomatic specification for "inf in Mma". Also the code
supporting it is secret.

Being approximately right in mathematics is different from
providing an answer which is right within some defined
level of approximation  (e.g.  numerical precision,  number
of terms in a series, approximation by polynomial, ...)

If you consider a robotic automated vehicle, being
approximately right might means it will only rarely crash
into a tree.  Being right approximately means that it
will (always) drive to its destination, give-or-take a short displacement.

RJF




On Friday, July 10, 2020 at 6:51:15 PM UTC-7, Rocky Bernstein wrote:
>
>
>
>
> User choice by option: If you want loose compatibility, then Inf in Mma. 
> If you want strict compatibility there is a strict compatibility library 
> and you can define SageInf in Mma.
>  
>
>>
>> I rarely use Google Translate.  I often use voice recognition (Alexa) 
which is remarkable but
prone to errors in recognition as well as information retrieval. Maybe you 
should build your
system for math voice parsing?  Alexa responds to
"Alexa, how much is 2+3?"
with "2+3 is 5".

You can see some background on this here:
https://people.eecs.berkeley.edu/~fateman/papers/speakmath.pdf

Maybe you should consider reviving "how to speak mathematics"
using newer technology.   (vs. 2003 or so.)

 

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Re: [sage-devel] Re: Transpiling from Mathematica syntax to sage backends

[Rocky Bernstein]

I think we've beat this to death. So let's agree to disagree.

This kind of thing is not intended for someone like you, but rather,
someone like me who is just getting started in Sage and CAS and wants to go
through a number of *simple* Mma tutorials and see *roughly* corresponding
results translated to another system. If that works out, I am happy, and
may try more ambitious things.

The specific examples showing how the various systems are hopelessly
incompatible or where there are subtleties and vagueness are interesting.
However I suspect none of this is going to matter. At least not in the
short term, if ever. This is for casual, non-mission-critical, and
educational use.  After I have something that isn't vaporware (if I get to
that stage), you can pop up again and warn people of the dangers. I hear
you, and you have some valid points. Now please go away.

There were the hacks one used to do with calculators where you'd divide a
number of times by a number and then multiply it back and get something
slightly off. Using that, Homer Simpson was able to disprove Fermat's
Theorem by finding a solution to the equation  a**12 + b**12 = c**12 in TI
calculator math. Somehow though, calculators and mathematics were both able
to survive this ordeal.

On Mon, Jul 13, 2020 at 4:25 PM rjf  wrote:

> the problem I see here is the recipe
>
> requiring "user choice"  and somehow specifying "inf in Mma"
>
> Most users will not want to specify, but probably would go along with
> "the mathematically consistent choice according to experts who have
> studied the matter."
>
> Certainly saying, as one choice, "inf in Mma" is inadequate since
> the user, other people, other CAS, cannot make use of this with
> any certainty.  Even "inf in Mma version 12.1" while specific,
> is not so useful outside of Mma version 12.1.  There is no
> axiomatic specification for "inf in Mma". Also the code
> supporting it is secret.
>
> Being approximately right in mathematics is different from
> providing an answer which is right within some defined
> level of approximation  (e.g.  numerical precision,  number
> of terms in a series, approximation by polynomial, ...)
>
> If you consider a robotic automated vehicle, being
> approximately right might means it will only rarely crash
> into a tree.  Being right approximately means that it
> will (always) drive to its destination, give-or-take a short displacement.
>
> RJF
>
>
>
>
> On Friday, July 10, 2020 at 6:51:15 PM UTC-7, Rocky Bernstein wrote:
>>
>>
>>
>>
>> User choice by option: If you want loose compatibility, then Inf in Mma.
>> If you want strict compatibility there is a strict compatibility library
>> and you can define SageInf in Mma.
>>
>>
>>>
>>> I rarely use Google Translate.  I often use voice recognition (Alexa)
> which is remarkable but
> prone to errors in recognition as well as information retrieval. Maybe you
> should build your
> system for math voice parsing?  Alexa responds to
> "Alexa, how much is 2+3?"
> with "2+3 is 5".
>
> You can see some background on this here:
> https://people.eecs.berkeley.edu/~fateman/papers/speakmath.pdf
>
> Maybe you should consider reviving "how to speak mathematics"
> using newer technology.   (vs. 2003 or so.)
>
>
>
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> .
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Re: [sage-devel] Making Sagemath available to Raspberry Pi

[Dima Pasechnik]

There is an official Rasbrian package for Sage, sagemath, it gives you Sage 8.6.

I suppose it's the result of semi-automatic import of Debian Buster
into Rasbrian.

I did

pi@raspberrypi:~ $ sudo apt install sagemath

and after a long download, I could do

pi@raspberrypi:~ $ sage
┌┐
│ SageMath version 8.6, Release Date: 2019-01-15 │
│ Using Python 2.7.16. Type "help()" for help.   │
└┘
Setting permissions of DOT_SAGE directory so only you can read and write it.
sage:
Exiting Sage (CPU time 0m0.12s, Wall time 0m9.49s).


Naturally one wants newer versions, but still this is a start.

Dima

On Fri, Jul 10, 2020 at 12:01 PM Jaap Spies  wrote:
>
> In a previous post I wrote:
>
> \begin quote
> Saying Raspberry Pi is saying education. There are zillion Raspberry Pi's out 
> there.
> Almost all of them are running Raspbian, now called Raspberry Pi OS.
> On every raspbian system there is an implementation of Mathematica.
> Wolfram was clever when he decided to make Matematica available to the
> people of Raspberries.
>
> I did some experimentation out of an old book Mathematica Second Edition.
> You can really do some math on a Raspberry Pi 4.
> [snipped]
>
> I think it is of major importance to have at least a binary for Raspberry Pi 
> OS!
>
> I'm old and have no time and no energy to pursue this to the end, but I plea
> someone would take this serious.
>
> Jaap
>
> early adapter of sage
> \end quote
>
> I wanted to start a discussion on the need to be present on the Raspberry Pi 
> platform.
> But my intentions were buried under a lot of technicalities.
>
> SAGE was intended to by an opensource alternative for the big M's, among them 
> Mathematica.
> What we see on the rasbian distribution:
> du:
> 32000 Wolfram/WolframEngine/12.0/AddOns/Applications
> 36244 Wolfram/WolframEngine/12.0/AddOns
> 1097480 Wolfram/WolframEngine/12.0
> 1097484 Wolfram/WolframEngine
> 1101392 Wolfram/
> root@rasp4g:/opt#
>
> You see Wolfram was very clever in getting Mathematica in raspbian: 1.1 GB of 
> disk space
>
> We will never get that space in the official distro, but I plea to make 
> Sagemath
> more available and known on the Raspberry Pi platform.
>
> There are a lot of computer labs in schools and colleges all running rasbian.
> And users easily link Math and Mathematics to Mathematica.
> Try Google Search: math Raspberry Pi of raspberry math
> and you will be overwhelmed by Wolfram's Mathematica
>
> Do a Google Search: raspberry pi sagemath
> and you see some pages from the year 2013 and a page of my website.
>
> The only thing we can do is to try getting Sagemath more visible.
> In documentation, on the website and make a binary available.
> (William are you here?)
>
> Jaap Spies
>
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[sage-devel] Re: cryptominisat does not buld on Ubuntu 20.04

[Matthias Koeppe]

Please also send the top-level config.log 

Lots of optional and experimental packages are broken. See 
https://trac.sagemath.org/ticket/29900 - which needs help.

On Monday, July 13, 2020 at 1:16:44 PM UTC-7, Andrey Novoseltsev wrote:
>
> Hello,
>
> While switching SageMathCell to Ubuntu 20.04 I am having problems with 
> cryptominisat installation into Sage-9.1. Any ideas what is going on?
>
> Thank you!
> Andrey
>
> Tail of the log, full one attached:
>
> ...
> /usr/bin/ld: 
> CMakeFiles/cryptominisat5-bin.dir/main.cpp.o:(.data.rel.ro._ZTVN5boost16exception_detail10clone_implINS0_19error_info_injectorINS_15program_options20invalid_option_valueE[_ZTVN5boost16exception_detail10clone_implINS0_19error_info_injectorINS_15program_options20invalid_option_valueE]+0x28):
>  
> undefined reference to 
> `boost::program_options::error_with_option_name::what() const'
> /usr/bin/ld: 
> CMakeFiles/cryptominisat5-bin.dir/main.cpp.o:(.data.rel.ro._ZTVN5boost16exception_detail10clone_implINS0_19error_info_injectorINS_15program_options20invalid_option_valueE[_ZTVN5boost16exception_detail10clone_implINS0_19error_info_injectorINS_15program_options20invalid_option_valueE]+0x38):
>  
> undefined reference to 
> `boost::program_options::error_with_option_name::substitute_placeholders(std::__cxx11::basic_string  
> std::char_traits, std::allocator > const&) const'
> /usr/bin/ld: CMakeFiles/cryptominisat5-bin.dir/main_exe.cpp.o: in function 
> `boost::program_options::variables_map::~variables_map()':
> /usr/include/boost/program_options/variables_map.hpp:146: undefined 
> reference to `vtable for boost::program_options::variables_map'
> collect2: error: ld returned 1 exit status
> make[4]: *** [cmsat5-src/CMakeFiles/cryptominisat5-bin.dir/build.make:117: 
> cryptominisat5] Error 1
> make[4]: Leaving directory 
> '/home/sc_serv/sage/local/var/tmp/sage/build/cryptominisat-5.6.8/src'
> make[3]: *** [CMakeFiles/Makefile2:161: 
> cmsat5-src/CMakeFiles/cryptominisat5-bin.dir/all] Error 2
> make[3]: Leaving directory 
> '/home/sc_serv/sage/local/var/tmp/sage/build/cryptominisat-5.6.8/src'
> make[2]: *** [Makefile:130: all] Error 2
> make[2]: Leaving directory 
> '/home/sc_serv/sage/local/var/tmp/sage/build/cryptominisat-5.6.8/src'
>
> 
> Error building cryptominisat-5.6.8
>
> 
>
>

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[sage-devel] Re: cryptominisat does not buld on Ubuntu 20.04

[Zachary Scherr]

I was able to successfully build cryptominisat using an Ubuntu 20.04 docker 
image.  Some weird things I noticed from your log files:

config log says you have boost lib >= 1.66 yet your cryptominisat log file 
says "Boost 1.46 found".  On the next line it says:

"-- Found Boost components: program_options"

which seems to be related to all of the errors.

I'll let a more experienced person chime in, but I imagine that if you get 
the latest version of libboost-dev and cmake from apt and let sage find it 
via ./configure then maybe cyrptominisat will build.

On Monday, July 13, 2020 at 11:26:06 PM UTC-4 Andrey Novoseltsev wrote:

> On Monday, 13 July 2020 21:11:11 UTC-6, Matthias Koeppe wrote:
>>
>> Please also send the top-level config.log 
>>
>
> Attached!
>
>
>> Lots of optional and experimental packages are broken. See 
>> https://trac.sagemath.org/ticket/29900 - which needs help.
>>
>
> Thank you for working on this! Can't commit to more help than supplying 
> logs...
>
>

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[sage-devel] Re: Newforms calculation is nondeterministic

[ethanyi...@gmail.com]

I've provided some more information to this post. Could someone please let 
me know whether this behavior is intended, or a bug?

I believe the different q-expansions are equivalent - they seem to just be 
generated by equivalent number fields with different defining polynomials. 
I confirmed this by running pari's polredabs function. I still find it 
quite odd that different polynomials would be used when run multiple times 
- is this intended? I tried poking through the library code, but couldn't 
find a cause.

*Example:*

sage: eps = kronecker_character(364)

: M = ModularForms(eps)

: S = M.cuspidal_subspace()

: New = S.newforms('a')

: 

sage: New[0]

q + (-1/7*a0^3 - 5/7*a0)*q^2 + 2*q^4 + O(q^6)

sage: New[0].hecke_eigenvalue_field()

Number Field in a0 with defining polynomial x^4 + 12*x^2 + 49

*Running in a different session:*

sage: eps = kronecker_character(364)

: M = ModularForms(eps)

: S = M.cuspidal_subspace()

: New = S.newforms('a')

: 
sage: New[0]

q + (-1/33*a0^3 + 7/33*a0)*q^2 + 2*q^4 + O(q^6)

sage: New[0].hecke_eigenvalue_field()

Number Field in a0 with defining polynomial x^4 + 4*x^2 + 121

sage: pari(New[0].hecke_eigenvalue_field().polynomial()).polredabs()

x^4 + 12*x^2 + 49




On Friday, August 30, 2019 at 10:44:11 PM UTC-7 ethanyi...@gmail.com wrote:

> Calculating newforms of a cuspidal subspace gives different answers on 
> different runs. 
>
> I did not (and don't know how to) check whether the newforms are 
> equivalent (and if they aren't, this would be a much more serious bug), 
> but, regardless, this type of calculation should definitely be 
> deterministic.
>
> *Steps to reproduce:*
>
> eps = kronecker_character(105)
>
> M2 = ModularForms(eps)
>
> S2 = M2.cuspidal_subspace()
>
> print(S2.newforms('a'))
>
>
> Running it multiple times, one gets a variety of q-expansions for the 
> newforms. Here I have listed 4 that I have received in output.
>
>
> [q + (-1/10*a0^3 + 3/10*a0^2 + 2/5*a0 - 3/5)*q^2 + (-1/10*a0^3 + 3/10*a0^2 
> - 3/5*a0 - 3/5)*q^3 + q^4 + (a0 - 1)*q^5 + O(q^6),
>
>  q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6),
>
>  q + (-1/10*a2^3 + 3/10*a2^2 + 2/5*a2 - 3/5)*q^2 + (1/10*a2^3 - 3/10*a2^2 
> + 3/5*a2 + 3/5)*q^3 + q^4 + (-a2 + 1)*q^5 + O(q^6)]
>
>
> [q + (-1/22*a0^3 - 3/11*a0^2 - 1/2*a0 - 3/11)*q^2 + (1/44*a0^3 + 3/22*a0^2 
> + 3/4*a0 + 3/22)*q^3 + q^4 + (-3/44*a0^3 - 9/22*a0^2 - 5/4*a0 - 31/22)*q^5 
> + O(q^6), 
>
> q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6), 
>
> q + (-1/22*a2^3 - 3/11*a2^2 - 1/2*a2 - 3/11)*q^2 + (-1/44*a2^3 - 3/22*a2^2 
> - 3/4*a2 - 3/22)*q^3 + q^4 + (3/44*a2^3 + 9/22*a2^2 + 5/4*a2 + 31/22)*q^5 + 
> O(q^6)]
>
>
> [q + (-1/10*a0^3 - 3/10*a0^2 + 2/5*a0 + 3/5)*q^2 + (1/10*a0^3 + 3/10*a0^2 
> + 3/5*a0 - 3/5)*q^3 + q^4 + (-1/5*a0^3 - 3/5*a0^2 - 1/5*a0 + 1/5)*q^5 + 
> O(q^6), 
>
> q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6), 
>
> q + (-1/22*a2^3 - 3/11*a2^2 - 1/2*a2 - 3/11)*q^2 + (-1/44*a2^3 - 3/22*a2^2 
> - 3/4*a2 - 3/22)*q^3 + q^4 + (3/44*a2^3 + 9/22*a2^2 + 5/4*a2 + 31/22)*q^5 + 
> O(q^6)]
>
>
> [q + (-1/22*a0^3 + 3/11*a0^2 - 1/2*a0 + 3/11)*q^2 + (-1/44*a0^3 + 
> 3/22*a0^2 - 3/4*a0 + 3/22)*q^3 + q^4 + (-1/44*a0^3 + 3/22*a0^2 + 1/4*a0 - 
> 19/22)*q^5 + O(q^6), 
>
> q - a1*q^3 - 2*q^4 + (-1/3*a1^3 - 2/3*a1)*q^5 + O(q^6), 
>
> q + (-1/10*a2^3 - 3/10*a2^2 + 2/5*a2 + 3/5)*q^2 + (-1/10*a2^3 - 3/10*a2^2 
> - 3/5*a2 + 3/5)*q^3 + q^4 + (1/5*a2^3 + 3/5*a2^2 + 1/5*a2 - 1/5)*q^5 + 
> O(q^6)]
>
>
> Version: 8.7
> OS: macOS High Sierra 10.13.6, 64 Bit
>

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Re: [sage-devel] Re: Newforms calculation is nondeterministic

[David Roe]

As Kevin suggested, the fact that different defining polynomials are chosen
is an artifact of the algorithm.  Perhaps one could add a keyword argument
to the newforms method that had it call polredabs on the field?  Polredabs
can be expensive in larger degree, so there should be an option to disable
the computation of the standard form and just use the provided one.
David

On Tue, Jul 14, 2020 at 1:39 AM ethanyi...@gmail.com <
ethanyisaper...@gmail.com> wrote:

> I've provided some more information to this post. Could someone please let
> me know whether this behavior is intended, or a bug?
>
> I believe the different q-expansions are equivalent - they seem to just be
> generated by equivalent number fields with different defining polynomials.
> I confirmed this by running pari's polredabs function. I still find it
> quite odd that different polynomials would be used when run multiple times
> - is this intended? I tried poking through the library code, but couldn't
> find a cause.
>
> *Example:*
>
> sage: eps = kronecker_character(364)
>
> : M = ModularForms(eps)
>
> : S = M.cuspidal_subspace()
>
> : New = S.newforms('a')
>
> :
>
> sage: New[0]
>
> q + (-1/7*a0^3 - 5/7*a0)*q^2 + 2*q^4 + O(q^6)
>
> sage: New[0].hecke_eigenvalue_field()
>
> Number Field in a0 with defining polynomial x^4 + 12*x^2 + 49
>
> *Running in a different session:*
>
> sage: eps = kronecker_character(364)
>
> : M = ModularForms(eps)
>
> : S = M.cuspidal_subspace()
>
> : New = S.newforms('a')
>
> :
> sage: New[0]
>
> q + (-1/33*a0^3 + 7/33*a0)*q^2 + 2*q^4 + O(q^6)
>
> sage: New[0].hecke_eigenvalue_field()
>
> Number Field in a0 with defining polynomial x^4 + 4*x^2 + 121
>
> sage: pari(New[0].hecke_eigenvalue_field().polynomial()).polredabs()
>
> x^4 + 12*x^2 + 49
>
>
>
>
> On Friday, August 30, 2019 at 10:44:11 PM UTC-7 ethanyi...@gmail.com
> wrote:
>
>> Calculating newforms of a cuspidal subspace gives different answers on
>> different runs.
>>
>> I did not (and don't know how to) check whether the newforms are
>> equivalent (and if they aren't, this would be a much more serious bug),
>> but, regardless, this type of calculation should definitely be
>> deterministic.
>>
>> *Steps to reproduce:*
>>
>> eps = kronecker_character(105)
>>
>> M2 = ModularForms(eps)
>>
>> S2 = M2.cuspidal_subspace()
>>
>> print(S2.newforms('a'))
>>
>>
>> Running it multiple times, one gets a variety of q-expansions for the
>> newforms. Here I have listed 4 that I have received in output.
>>
>>
>> [q + (-1/10*a0^3 + 3/10*a0^2 + 2/5*a0 - 3/5)*q^2 + (-1/10*a0^3 +
>> 3/10*a0^2 - 3/5*a0 - 3/5)*q^3 + q^4 + (a0 - 1)*q^5 + O(q^6),
>>
>>  q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6),
>>
>>  q + (-1/10*a2^3 + 3/10*a2^2 + 2/5*a2 - 3/5)*q^2 + (1/10*a2^3 - 3/10*a2^2
>> + 3/5*a2 + 3/5)*q^3 + q^4 + (-a2 + 1)*q^5 + O(q^6)]
>>
>>
>> [q + (-1/22*a0^3 - 3/11*a0^2 - 1/2*a0 - 3/11)*q^2 + (1/44*a0^3 +
>> 3/22*a0^2 + 3/4*a0 + 3/22)*q^3 + q^4 + (-3/44*a0^3 - 9/22*a0^2 - 5/4*a0 -
>> 31/22)*q^5 + O(q^6),
>>
>> q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6),
>>
>> q + (-1/22*a2^3 - 3/11*a2^2 - 1/2*a2 - 3/11)*q^2 + (-1/44*a2^3 -
>> 3/22*a2^2 - 3/4*a2 - 3/22)*q^3 + q^4 + (3/44*a2^3 + 9/22*a2^2 + 5/4*a2 +
>> 31/22)*q^5 + O(q^6)]
>>
>>
>> [q + (-1/10*a0^3 - 3/10*a0^2 + 2/5*a0 + 3/5)*q^2 + (1/10*a0^3 + 3/10*a0^2
>> + 3/5*a0 - 3/5)*q^3 + q^4 + (-1/5*a0^3 - 3/5*a0^2 - 1/5*a0 + 1/5)*q^5 +
>> O(q^6),
>>
>> q - 1/2*a1*q^3 - 2*q^4 + (-1/24*a1^3 - 1/3*a1)*q^5 + O(q^6),
>>
>> q + (-1/22*a2^3 - 3/11*a2^2 - 1/2*a2 - 3/11)*q^2 + (-1/44*a2^3 -
>> 3/22*a2^2 - 3/4*a2 - 3/22)*q^3 + q^4 + (3/44*a2^3 + 9/22*a2^2 + 5/4*a2 +
>> 31/22)*q^5 + O(q^6)]
>>
>>
>> [q + (-1/22*a0^3 + 3/11*a0^2 - 1/2*a0 + 3/11)*q^2 + (-1/44*a0^3 +
>> 3/22*a0^2 - 3/4*a0 + 3/22)*q^3 + q^4 + (-1/44*a0^3 + 3/22*a0^2 + 1/4*a0 -
>> 19/22)*q^5 + O(q^6),
>>
>> q - a1*q^3 - 2*q^4 + (-1/3*a1^3 - 2/3*a1)*q^5 + O(q^6),
>>
>> q + (-1/10*a2^3 - 3/10*a2^2 + 2/5*a2 + 3/5)*q^2 + (-1/10*a2^3 - 3/10*a2^2
>> - 3/5*a2 + 3/5)*q^3 + q^4 + (1/5*a2^3 + 3/5*a2^2 + 1/5*a2 - 1/5)*q^5 +
>> O(q^6)]
>>
>>
>> Version: 8.7
>> OS: macOS High Sierra 10.13.6, 64 Bit
>>
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