I don't know about numpyprint. I am just noting that you can get a
well-defined mathematical expression to print as a string with certain
function having a "np." prefix (if that is what you want). And it doesn't
require any string parsing on your part. This string (if that is what you
want) can be passed to whatever needs a string.
/c
On Friday, September 2, 2022 at 8:30:52 PM UTC-5 z.kari...@gmail.com wrote:
> You mean I can use the numpyprint of sympy and then pass it to fit?
>
>
> Zohreh Karimzadeh
>
> Contact me on
> +989102116325 <+98%20910%20211%206325>
> and at
> z.kari...@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
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>> 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>
>> .
>>
>
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