You can replace any function with any other using `subs`, so just replace
them with a function that has the name you want (and you can make up the
name and even include punctuation):
[image: Snag_5ac96126.png]
Note that in the last case *SymPy* will not be able to evaluate the
expression but if you pass the string version to a function that knows how
to interpret `np.exp` as numpy's version of `exp` then it will evaluate.
/c
On Thursday, September 1, 2022 at 9:54:27 PM UTC-5 z.kari...@gmail.com
wrote:
> Jonothon,
> thank you for answering
> Chris,
> Thanks, your point sounds cool. But if I make the object in a symbolic way
> and then change them to string, there are some sympy.exp and sympy.log that
> make problems. What is your suggestion on this problem?
> Regards
>
>
> Zohreh Karimzadeh
> Skype Name 49a52224a8b6b38b
> Twitter Account @zohrehkarimzad1
> +989102116325 <+98%20910%20211%206325>
>
> ((((((((((((((((Value Water)))))))))))))))
>
> On Fri, Sep 2, 2022 at 1:55 AM Chris Smith <smi...@gmail.com> wrote:
>
>> This is somewhat painful to read because none of the code snippets are
>> formatted as Python code. If possible, please post working code snippets.
>>
>> As to using string or SymPy (and then converting to string): I prefer the
>> latter because you get automatic syntax checking and a good visual of the
>> object you are building. So I would do something like:
>>
>> anion = {'Cl': 1}
>> cation = {'Na': 1, 'Mg': 2}
>>
>> def ionic(*ions):
>> I = 0
>> for itype in ions:
>> for k1 in itype:
>> I += 0.5 * (Symbol('X{0}'.format(str(k1))) * (itype[k1] ** 2))
>> return I
>>
>> str(ionic(anion, cation)) -> '0.5*XCl + 2.0*XMg + 0.5*XNa'
>>
>> /c
>> On Thursday, September 1, 2022 at 8:54:41 AM UTC-5 gu...@uwosh.edu wrote:
>>
>>> You are mixing numerical and string expressions. You must make
>>> everything a string expression.
>>> Example
>>> Ionic = 0
>>> Ionic += 0.5 * (('X'+str(k1)) * (ionic_dic[k1] ** 2))
>>> Should be
>>> Ionic = ""
>>> Ionic += "+0.5 * ((X"+str(k1)+") * ("+str(ionic_dic[k1])+'"** 2))"
>>> On Thursday, September 1, 2022 at 7:11:34 AM UTC-5 z.kari...@gmail.com
>>> wrote:
>>>
>>>> Dear Jhonoton
>>>> If my best choice is the first then I have will have difficulty to pass
>>>> some stuff in my string, as an example:
>>>>
>>>> cation = {'Na': 1,'Cl':2}
>>>> anion = {'Cl': 1}
>>>>
>>>>
>>>> ionic_dic = dict()
>>>> for d in (cation, anion):
>>>> ionic_dic.update(d)
>>>> def ionicstr():
>>>> Ionic = 0
>>>> sqrt_I = 0
>>>> for k1 in ionic_dic:
>>>>
>>>> Ionic += 0.5 * (('X'+str(k1)) * (ionic_dic[k1] ** 2))
>>>> sqrt_I += (Ionic) ** 0.5
>>>>
>>>> print(Ionic, sqrt_I)
>>>> return Ionic, sqrt_I
>>>>
>>>> def term():
>>>> for i in cation:
>>>> A ='X' + str(i) + str(ionicstr()[0])
>>>> print(A)
>>>> return A
>>>> term()
>>>>
>>>> Is there any way to pass computed ionicstr()[0] to string??
>>>> Zohreh Karimzadeh
>>>> Skype Name 49a52224a8b6b38b
>>>> Twitter Account @zohrehkarimzad1
>>>> +989102116325 <+98%20910%20211%206325>
>>>>
>>>> ((((((((((((((((Value Water)))))))))))))))
>>>>
>>>>
>>>> On Thu, Sep 1, 2022 at 12:43 AM gu...@uwosh.edu <gu...@uwosh.edu>
>>>> wrote:
>>>>
>>>>> Zohreh,
>>>>>
>>>>> I cannot tell you what is your best choice until you tell me what you
>>>>> are doing after you build the expression. Is it 1 or 2, as I asked before?
>>>>>
>>>>> 1) You ultimately pass a string expression to lmfit or some other
>>>>> fitting package that is parsed into a numpy expression for fitting or
>>>>> something similar.
>>>>>
>>>>> 2)You are making your own model function that returns a number every
>>>>> time it is called by some other package (fitting?).
>>>>>
>>>>> Please explain exactly how you wish to use the expression you are
>>>>> developing and, if you are using it with another tool, which one?
>>>>>
>>>>> Regards,
>>>>> Jonathan
>>>>> On Friday, August 26, 2022 at 9:24:32 PM UTC-5 z.kari...@gmail.com
>>>>> wrote:
>>>>>
>>>>>> Dear Jonathan
>>>>>> Thank you for your reply.
>>>>>> About using strings instead of sympy good idea, It is necessary to
>>>>>> know that there are bunch of functions that are inserted in the main
>>>>>> model as one of them :
>>>>>>
>>>>>> anion = {'Cl': 1}
>>>>>> cation = {'Na': 1}
>>>>>> ionic_dic = dict()
>>>>>> for d in (cation, anion):
>>>>>> ionic_dic.update(d)
>>>>>> def ionicstr():
>>>>>> Ionic = 0
>>>>>> sqrt_I = 0
>>>>>> for k1 in ionic_dic:
>>>>>> Ionic += 0.5 * (sp.symbols('X{0}'.format(str(k1))) *
>>>>>> (ionic_dic[k1] ** 2))
>>>>>> sqrt_I += sp.sqrt(Ionic)
>>>>>> print(Ionic, sqrt_I)
>>>>>> return Ionic, sqrt_I
>>>>>> AS can be seen while all of these kinds of functions must be
>>>>>> evaluated
>>>>>> or substituted in the main model.
>>>>>> Is it still possible to use strings instead of sympy??
>>>>>> Regards,
>>>>>> Zohreh
>>>>>>
>>>>>> On Fri, Aug 26, 2022 at 6:04 PM gu...@uwosh.edu <gu...@uwosh.edu>
>>>>>> wrote:
>>>>>> >
>>>>>> > Zohreh,
>>>>>> >
>>>>>> > It is still unclear what you are actually doing. I can think of two
>>>>>> possibilities (are either of them correct?):
>>>>>> >
>>>>>> > 1) You ultimately pass a string expression to lmfit or some other
>>>>>> fitting package that is parsed into a numpy expression for fitting or
>>>>>> something similar. So I am suggesting that you remove the intermediate
>>>>>> step
>>>>>> of creating a sympy expression to make things more efficient. You can
>>>>>> generate the string expression dynamically in essentially the same way
>>>>>> you
>>>>>> are currently generating the sympy expression, but avoid having the
>>>>>> intermediate step of using sympy to generate the expression and then
>>>>>> using
>>>>>> it to generate a string expression that is parsed again.
>>>>>> >
>>>>>> > 2) Alternatively, you may be making your own model function (I
>>>>>> believe for lmfit). In that case you need to generate a function that
>>>>>> does
>>>>>> a calculation. I see no reason it has to have human readable names for
>>>>>> the
>>>>>> parameters in the actual calculation. However, you could connect them
>>>>>> with
>>>>>> human readable names through a dictionary or something like that.
>>>>>> >
>>>>>> > If you want a string, your code is almost there. As long as the
>>>>>> elements of cation and anion are strings. Just replace things like
>>>>>> sp.symbols('X{0}'.format(str(i))) with 'X_'+str(i). But maybe that is
>>>>>> not
>>>>>> what you are doing.
>>>>>> >
>>>>>> > Jonathan
>>>>>> >
>>>>>> > On Friday, August 26, 2022 at 5:03:00 AM UTC-5 z.kari...@gmail.com
>>>>>> wrote:
>>>>>> >>
>>>>>> >> Jonathan has recommended to use string instead of sympy approche
>>>>>> to
>>>>>> >> derive your model and -parameters.
>>>>>> >> But I stated that my model is driven dynamically. It means, as an
>>>>>> >> example for one term in model I have:
>>>>>> >>
>>>>>> >> term_unca = 0
>>>>>> >> for k in anion:
>>>>>> >> for j in cation:
>>>>>> >> for i in neutral:
>>>>>> >> term_unca += term_uncX - 2 *
>>>>>> >> sp.symbols('X{0}'.format(str(i))) * sp.symbols(f'X{str(j)}') * \
>>>>>> >> sp.symbols(f'X{str(k)}') * ((cation[j] +
>>>>>> >> anion[k]) ** 2 / (cation[j] * anion[k])) \
>>>>>> >> * sp.symbols(f'U{str(i)}{str(j)}{str(k)}')
>>>>>> >> This way all the parameters should be created for each run of
>>>>>> fitting.
>>>>>> >>
>>>>>> >>
>>>>>> >> Zohreh Karimzadeh
>>>>>> >> https://www.researchgate.net/profile/Zohreh-Karimzadeh
>>>>>> >> Skype Name 49a52224a8b6b38b
>>>>>> >> Twitter Account @zohrehkarimzad1
>>>>>> >> z.kari...@gmail.com
>>>>>> >> +989102116325 <+98%20910%20211%206325>
>>>>>> >> ((((((((((((((((Value Water)))))))))))))))
>>>>>> >>
>>>>>> >> Zohreh Karimzadeh
>>>>>> >> https://www.researchgate.net/profile/Zohreh-Karimzadeh
>>>>>> >> Skype Name 49a52224a8b6b38b
>>>>>> >> Twitter Account @zohrehkarimzad1
>>>>>> >> z.kari...@gmail.com
>>>>>> >> +989102116325 <+98%20910%20211%206325>
>>>>>> >> ((((((((((((((((Value Water)))))))))))))))
>>>>>> >>
>>>>>> >>
>>>>>> >> On Fri, Aug 26, 2022 at 7:58 AM Peter Stahlecker
>>>>>> >> <peter.st...@gmail.com> wrote:
>>>>>> >> >
>>>>>> >> > Dear Zohreh,
>>>>>> >> >
>>>>>> >> > I think, you should describe precisely what you want, rather
>>>>>> than referring to previous correspondence.
>>>>>> >> > Someone out there (likely not me) might have a solution to what
>>>>>> you need - but cannot be bothered to read through you previous
>>>>>> correspondence.
>>>>>> >> >
>>>>>> >> > 1.
>>>>>> >> > Parameter names should be made in a dynamic way.
>>>>>> >> > what exactly do you mean by this?
>>>>>> >> > Better give an example of what you would like to do.
>>>>>> >> >
>>>>>> >> > 2.
>>>>>> >> > how using for loop in string can be simultaneously handled.
>>>>>> >> > I have no idea, what your question is - and I am afraid, not
>>>>>> many people understand.
>>>>>> >> > Better give an example of what you want to do.
>>>>>> >> >
>>>>>> >> > Peter
>>>>>> >> >
>>>>>> >> > On Fri 26. Aug 2022 at 04:42 Zohreh Karimzadeh <
>>>>>> z.kari...@gmail.com> wrote:
>>>>>> >> >>
>>>>>> >> >> As can be seen in the former script, parameter names should be
>>>>>> made in a dynamic way.
>>>>>> >> >> I am wondering how using for loop in string can be
>>>>>> simultaneously handled.
>>>>>> >> >> Regards,
>>>>>> >> >> Zohreh Karimzadeh
>>>>>> >> >> https://www.researchgate.net/profile/Zohreh-Karimzadeh
>>>>>> >> >> Skype Name 49a52224a8b6b38b
>>>>>> >> >> Twitter Account @zohrehkarimzad1
>>>>>> >> >> z.kari...@gmail.com
>>>>>> >> >> +989102116325 <+98%20910%20211%206325>
>>>>>> >> >> ((((((((((((((((Value Water)))))))))))))))
>>>>>> >> >>
>>>>>> >> >>
>>>>>> >> >> On Wed, Aug 24, 2022 at 9:32 PM gu...@uwosh.edu <
>>>>>> gu...@uwosh.edu> wrote:
>>>>>> >> >>>
>>>>>> >> >>> Zohreh,
>>>>>> >> >>>
>>>>>> >> >>> The code snippets you have provided do not suggest you are
>>>>>> doing anything that requires sympy. So, I am confused. It looks like you
>>>>>> need a function that generates a string of the summations in your
>>>>>> expression, when passed species. I think there is a fixed number of
>>>>>> parameters for each species. You are probably better off building the
>>>>>> string for your expressions without involving sympy. I am thinking
>>>>>> something like this to define part of your fit function:
>>>>>> >> >>>
>>>>>> >> >>>
>>>>>> >> >>> def term(species_name):
>>>>>> >> >>>
>>>>>> return(species_name+'_param1*conc_'+species_name+'+'+species_name+'_param2*np.sqrt(conc_'+species_name+')')
>>>>>>
>>>>>>
>>>>>> >> >>> Then
>>>>>> >> >>> term('Cl')
>>>>>> >> >>> returns
>>>>>> >> >>> 'Cl_param1*conc_Cl+Cl_param2*np.sqrt(conc_Cl)'
>>>>>> >> >>>
>>>>>> >> >>> Then build your overall expression from these pieces. Then do
>>>>>> a fit with initial guesses for all the parameters.
>>>>>> >> >>>
>>>>>> >> >>> That's how I would do it unless I am manipulating the
>>>>>> expressions using sympy first.
>>>>>> >> >>>
>>>>>> >> >>> Jonathan
>>>>>> >> >>> On Wednesday, August 24, 2022 at 11:11:58 AM UTC-5
>>>>>> z.kari...@gmail.com wrote:
>>>>>> >> >>>>
>>>>>> >> >>>> I should extract the required model for each system of
>>>>>> chemicals and do a least squre for derived model and parameters to find
>>>>>> the
>>>>>> parameters for each chemical systems.
>>>>>> >> >>>>
>>>>>> >> >>>>
>>>>>> >> >>>> Zohreh Karimzadeh
>>>>>> >> >>>>
>>>>>> >> >>>> Contact me on
>>>>>> >> >>>> +989102116325 <+98%20910%20211%206325>
>>>>>> >> >>>> and at
>>>>>> >> >>>> z.kari...@gmail.com
>>>>>> >> >>>> 🌧️🌍🌱
>>>>>> >> >>>>
>>>>>> >> >>>> On Wed, 24 Aug 2022, 19:33 gu...@uwosh.edu, <gu...@uwosh.edu>
>>>>>> wrote:
>>>>>> >> >>>>>
>>>>>> >> >>>>> Zohreh,
>>>>>> >> >>>>>
>>>>>> >> >>>>> I pulled the paper. I see no reason you need to use SymPy to
>>>>>> do the numerical fitting. I would approach this by inputting the species
>>>>>> in
>>>>>> a dictionary or list and then use that to call functions that generate
>>>>>> the
>>>>>> computed value for each term/sum. Are you trying to keep track of the
>>>>>> complete symbolic expression or do a numerical calculation?
>>>>>> >> >>>>>
>>>>>> >> >>>>> If you are using chemical symbols or reactions, are you
>>>>>> taking advantage of ChemPy?
>>>>>> >> >>>>>
>>>>>> >> >>>>> Jonathan
>>>>>> >> >>>>> On Tuesday, August 23, 2022 at 12:01:02 AM UTC-5
>>>>>> z.kari...@gmail.com wrote:
>>>>>> >> >>>>>>
>>>>>> >> >>>>>> As following, I should generate each parameters dynamically
>>>>>> (for 20-30 terms):
>>>>>> >> >>>>>>
>>>>>> >> >>>>>> term_vnca = 0
>>>>>> >> >>>>>> for k in anion:
>>>>>> >> >>>>>> for j in cation:
>>>>>> >> >>>>>> for i in neutral:
>>>>>> >> >>>>>> term_vnca += term_vncX - 4 * 3 * sp.symbols(f'X{str(k)}') *
>>>>>> sp.symbols('X{0}'.format(str(i))) \
>>>>>> >> >>>>>> ** 2 * sp.symbols(f'V{str(i)}{str(j)}{str(k)}')
>>>>>> >> >>>>>> lnfXs = term_wnca + term_unca + term_vnca +
>>>>>> termx_w_solvent1 + termx_w_solvent2
>>>>>> >> >>>>>>
>>>>>> >> >>>>>> Zohreh Karimzadeh
>>>>>> >> >>>>>> https://www.researchgate.net/profile/Zohreh-Karimzadeh
>>>>>> >> >>>>>> Skype Name 49a52224a8b6b38b
>>>>>> >> >>>>>> Twitter Account @zohrehkarimzad1
>>>>>> >> >>>>>> z.kari...@gmail.com
>>>>>> >> >>>>>> +989102116325 <+98%20910%20211%206325>
>>>>>> >> >>>>>> ((((((((((((((((Value Water)))))))))))))))
>>>>>> >> >>>>>>
>>>>>> >> >>>>>>
>>>>>> >> >>>>>> On Tue, Aug 23, 2022 at 9:26 AM Zohreh Karimzadeh <
>>>>>> z.kari...@gmail.com> wrote:
>>>>>> >> >>>>>>>
>>>>>> >> >>>>>>> Not these model and parameters, My model is very
>>>>>> complicated wit large number of parameters:
>>>>>> >> >>>>>>>
>>>>>> >> >>>>>>> As a very simple example I raise this question.
>>>>>> >> >>>>>>> Zohreh Karimzadeh
>>>>>> >> >>>>>>>
>>>>>> >> >>>>>>> Contact me on
>>>>>> >> >>>>>>> +989102116325 <+98%20910%20211%206325>
>>>>>> >> >>>>>>> and at
>>>>>> >> >>>>>>> z.kari...@gmail.com
>>>>>> >> >>>>>>> 🌧️🌍🌱
>>>>>> >> >>>>>>>
>>>>>> >> >>>>>>>
>>>>>> >> >>>>>>> On Tue, 23 Aug 2022, 05:16 Peter Stahlecker, <
>>>>>> peter.st...@gmail.com> wrote:
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> Dear Zohreh,
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> Just for my understanding:
>>>>>> >> >>>>>>>> 1.
>>>>>> >> >>>>>>>> You params are alpha, betta ,gamma, eta (?)
>>>>>> >> >>>>>>>> 2.
>>>>>> >> >>>>>>>> What do you mean by generating them dynamically?
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> Peter
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> On Tue 23. Aug 2022 at 02:44 Zohreh Karimzadeh <
>>>>>> z.kari...@gmail.com> wrote:
>>>>>> >> >>>>>>>>>
>>>>>> >> >>>>>>>>> Dear Oscar
>>>>>> >> >>>>>>>>> BIG help !
>>>>>> >> >>>>>>>>> Here I seriously need to use sympy to generate my params
>>>>>> dynamically.
>>>>>> >> >>>>>>>>> All Bests
>>>>>> >> >>>>>>>>> Zohreh Karimzadeh
>>>>>> >> >>>>>>>>> https://www.researchgate.net/profile/Zohreh-Karimzadeh
>>>>>> >> >>>>>>>>> Skype Name 49a52224a8b6b38b
>>>>>> >> >>>>>>>>> Twitter Account @zohrehkarimzad1
>>>>>> >> >>>>>>>>> z.kari...@gmail.com
>>>>>> >> >>>>>>>>> +989102116325 <+98%20910%20211%206325>
>>>>>> >> >>>>>>>>> ((((((((((((((((Value Water)))))))))))))))
>>>>>> >> >>>>>>>>>
>>>>>> >> >>>>>>>>>
>>>>>> >> >>>>>>>>> On Mon, Aug 22, 2022 at 7:42 PM Oscar Benjamin <
>>>>>> oscar.j....@gmail.com> wrote:
>>>>>> >> >>>>>>>>>>
>>>>>> >> >>>>>>>>>> On Mon, 22 Aug 2022 at 15:36, Peter Stahlecker
>>>>>> >> >>>>>>>>>> <peter.st...@gmail.com> wrote:
>>>>>> >> >>>>>>>>>> >
>>>>>> >> >>>>>>>>>> > Dear Oscar,
>>>>>> >> >>>>>>>>>> >
>>>>>> >> >>>>>>>>>> > Thanks for your hint about these parameters!.
>>>>>> >> >>>>>>>>>> > Probably dumb question of mine:
>>>>>> >> >>>>>>>>>> > Could one not define f_Vi_est directly as
>>>>>> >> >>>>>>>>>> >
>>>>>> >> >>>>>>>>>> > def_Vi_est(gamma, alfa, beta, eta, L, K, VA):
>>>>>> >> >>>>>>>>>> > Vi_est = gamma - (1 / eta)…..
>>>>>> >> >>>>>>>>>> > return np.sum(…..)
>>>>>> >> >>>>>>>>>> >
>>>>>> >> >>>>>>>>>> > without any ‚lambdification‘?
>>>>>> >> >>>>>>>>>>
>>>>>> >> >>>>>>>>>> Yes. In an earlier post the OP showed that they had
>>>>>> working code like
>>>>>> >> >>>>>>>>>> that but wanted to know how to do it using SymPy and
>>>>>> lambdify. I
>>>>>> >> >>>>>>>>>> presume there is a reason for wanting to use SymPy
>>>>>> there (perhaps to
>>>>>> >> >>>>>>>>>> accomplish something slightly different from the exact
>>>>>> code shown).
>>>>>> >> >>>>>>>>>> It's also possible that there isn't any actual reason
>>>>>> to use SymPy for
>>>>>> >> >>>>>>>>>> this at all though.
>>>>>> >> >>>>>>>>>>
>>>>>> >> >>>>>>>>>> --
>>>>>> >> >>>>>>>>>> Oscar
>>>>>> >> >>>>>>>>>>
>>>>>> >> >>>>>>>>>> --
>>>>>> >> >>>>>>>>>> You received this message because you are subscribed to
>>>>>> the Google Groups "sympy" group.
>>>>>> >> >>>>>>>>>> To unsubscribe from this group and stop receiving
>>>>>> emails from it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >>>>>>>>>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CAHVvXxQJUuZ4tVnECPyWE%3DLd03hhhUB5mqv1bjHcjSNf9WP22Q%40mail.gmail.com.
>>>>>>
>>>>>>
>>>>>> >> >>>>>>>>>
>>>>>> >> >>>>>>>>> --
>>>>>> >> >>>>>>>>> You received this message because you are subscribed to
>>>>>> the Google Groups "sympy" group.
>>>>>> >> >>>>>>>>> To unsubscribe from this group and stop receiving emails
>>>>>> from it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >>>>>>>>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLOMV_i3VJXwwVN7JWnuJ9Wo6ZPhULmC1SOubAfFLt-DBQ%40mail.gmail.com.
>>>>>>
>>>>>>
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> --
>>>>>> >> >>>>>>>> Best regards,
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> Peter Stahlecker
>>>>>> >> >>>>>>>>
>>>>>> >> >>>>>>>> --
>>>>>> >> >>>>>>>> You received this message because you are subscribed to
>>>>>> the Google Groups "sympy" group.
>>>>>> >> >>>>>>>> To unsubscribe from this group and stop receiving emails
>>>>>> from it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >>>>>>>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CABKqA0YTOzyZkjhnQmKQKQh-Mrc_H_TcmD9FrXObaTadkfLpkQ%40mail.gmail.com.
>>>>>>
>>>>>>
>>>>>> >> >>>>>
>>>>>> >> >>>>> --
>>>>>> >> >>>>> You received this message because you are subscribed to the
>>>>>> Google Groups "sympy" group.
>>>>>> >> >>>>> To unsubscribe from this group and stop receiving emails
>>>>>> from it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >>>>>
>>>>>> >> >>>>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/17d62c5c-11d8-4b1b-9a44-ae67c8021832n%40googlegroups.com.
>>>>>>
>>>>>>
>>>>>> >> >>>>>
>>>>>> >> >>>>>
>>>>>> >> >>> --
>>>>>> >> >>> You received this message because you are subscribed to the
>>>>>> Google Groups "sympy" group.
>>>>>> >> >>> To unsubscribe from this group and stop receiving emails from
>>>>>> it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/837a3351-3aa3-4e1e-98d6-b34f3185d5b2n%40googlegroups.com.
>>>>>>
>>>>>>
>>>>>> >> >>
>>>>>> >> >> --
>>>>>> >> >> You received this message because you are subscribed to the
>>>>>> Google Groups "sympy" group.
>>>>>> >> >> To unsubscribe from this group and stop receiving emails from
>>>>>> it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> >> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLMEq2OLN0npw8RHfghS7m6vgewkrpshqw8gBBU%2BfUAnoQ%40mail.gmail.com.
>>>>>>
>>>>>>
>>>>>> >> >
>>>>>> >> > --
>>>>>> >> > Best regards,
>>>>>> >> >
>>>>>> >> > Peter Stahlecker
>>>>>> >> >
>>>>>> >> > --
>>>>>> >> > You received this message because you are subscribed to the
>>>>>> Google Groups "sympy" group.
>>>>>> >> > To unsubscribe from this group and stop receiving emails from
>>>>>> it, send an email to sympy+un...@googlegroups.com.
>>>>>> >> > To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CABKqA0b261cO3ixRjsp_YPU0Yk1ahRVgnEytcOkLrQUW-eHdwQ%40mail.gmail.com.
>>>>>>
>>>>>>
>>>>>> >
>>>>>> > --
>>>>>> > You received this message because you are subscribed to the Google
>>>>>> Groups "sympy" group.
>>>>>> > To unsubscribe from this group and stop receiving emails from it,
>>>>>> send an email to sympy+un...@googlegroups.com.
>>>>>> > To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/ec94798a-fcdc-4df8-b80e-2642f5a60ec5n%40googlegroups.com.
>>>>>>
>>>>>>
>>>>>>
>>>>> --
>>>>> You received this message because you are subscribed to the Google
>>>>> Groups "sympy" group.
>>>>> To unsubscribe from this group and stop receiving emails from it, send
>>>>> an email to sympy+un...@googlegroups.com.
>>>>>
>>>> To view this discussion on the web visit
>>>>> https://groups.google.com/d/msgid/sympy/54b70a36-3ee5-4d14-b30a-813b8fbf31fcn%40googlegroups.com
>>>>>
>>>>> <https://groups.google.com/d/msgid/sympy/54b70a36-3ee5-4d14-b30a-813b8fbf31fcn%40googlegroups.com?utm_medium=email&utm_source=footer>
>>>>> .
>>>>>
>>>> --
>> You received this message because you are subscribed to the Google Groups
>> "sympy" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to sympy+un...@googlegroups.com.
>>
> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sympy/6eae7b43-e685-4892-a943-8605ad04c2efn%40googlegroups.com
>>
>> <https://groups.google.com/d/msgid/sympy/6eae7b43-e685-4892-a943-8605ad04c2efn%40googlegroups.com?utm_medium=email&utm_source=footer>
>> .
>>
>
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