You mean I can use the numpyprint of sympy and then pass it to fit?
Zohreh Karimzadeh
Contact me on
+989102116325
and at
z.karimza...@gmail.com
🌧️🌍🌱
On Fri, 2 Sep 2022, 16:31 Chris Smith, <smi...@gmail.com> wrote:
> 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>
>>> .
>>>
>> --
> You received this message because you are subscribed to a topic in the
> Google Groups "sympy" group.
> To unsubscribe from this topic, visit
> https://groups.google.com/d/topic/sympy/CAGn_agpz6M/unsubscribe.
> To unsubscribe from this group and all its topics, send an email to
> sympy+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sympy/a9bd0c6b-75f7-4711-9e02-19c06648c86dn%40googlegroups.com
> <https://groups.google.com/d/msgid/sympy/a9bd0c6b-75f7-4711-9e02-19c06648c86dn%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+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/CA%2B1XYLO5%2BESOevA_ujZGDpnuaaM_MMaKWb%3DtH1nZei9L5WooFg%40mail.gmail.com.
