L and K are independent variables that will be passed to minimize. Zohreh Karimzadeh *https://www.researchgate.net/profile/Zohreh-Karimzadeh* <https://www.researchgate.net/profile/Zohreh-Karimzadeh> Skype Name 49a52224a8b6b38b Twitter Account @zohrehkarimzad1 [email protected] +989102116325 ((((((((((((((((Value Water)))))))))))))))
On Thu, Aug 18, 2022 at 4:08 PM Peter Stahlecker <[email protected]> wrote: > I just have no idea what > > np.sum((np.log(AV) + Vlam_est)**2) > > could possibly mean. np.log(VA) is an array of floats, that is an array > of *numbers*. > Vlam_est is a *function*. How you can add numbers and a function I do not > know.. > Vlam_est will become an array of numbers, once you give it the arguments. > > NB: > it seems, that Vi_est uses the arguments alpha,.., eta, L, K > When you lambdify it, you skipped the arguments L and K. > Any reason for this? > > On Thu 18. Aug 2022 at 18:18 Zohreh Karimzadeh <[email protected]> > wrote: > >> It seems always an expression of parameters and independent variables is >> needed to be passed to fit and find parameters. >> Zohreh Karimzadeh >> *https://www.researchgate.net/profile/Zohreh-Karimzadeh* >> <https://www.researchgate.net/profile/Zohreh-Karimzadeh> >> Skype Name 49a52224a8b6b38b >> Twitter Account @zohrehkarimzad1 >> [email protected] >> +989102116325 >> ((((((((((((((((Value Water))))))))))))))) >> >> >> On Thu, Aug 18, 2022 at 3:28 PM Peter Stahlecker < >> [email protected]> wrote: >> >>> In your first return statement, where it works, you seem to return a >>> number. >>> In your second return, your a ‚mixture‘ of numbers and functions: >>> Vlam_est is a *function*, which requires four arguments as per its >>> definition. Would you not have to return Vlam_est(alpha, beta, gamma, eta) ? >>> >>> On Thu 18. Aug 2022 at 17:35 Zohreh Karimzadeh <[email protected]> >>> wrote: >>> >>>> the following code is ok when expression is passed as : >>>> >>>> import numpy as np >>>> from scipy.optimize import minimize, curve_fit >>>> from lmfit import Model, Parameters >>>> >>>> L = np.array([0.299, 0.295, 0.290, 0.284, 0.279, 0.273, 0.268, 0.262, >>>> 0.256, 0.250]) >>>> K = np.array([2.954, 3.056, 3.119, 3.163, 3.215, 3.274, 3.351, 3.410, >>>> 3.446, 3.416]) >>>> VA = np.array([0.919, 0.727, 0.928, 0.629, 0.656, 0.854, 0.955, 0.981, >>>> 0.908, 0.794]) >>>> >>>> >>>> def f(param): >>>> gamma = param[0] >>>> alpha = param[1] >>>> beta = param[2] >>>> eta = param[3] >>>> VA_est = gamma - (1 / eta) * np.log(alpha * L ** -eta + beta * K ** >>>> -eta) >>>> >>>> return np.sum((np.log(VA) - VA_est) ** 2) >>>> >>>> >>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>> x0 = (1, 0.01, 0.98, 1) >>>> result = minimize(f, x0, bounds=bnds) >>>> print(result.message) >>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>> >>>> but when the expression is passed as the following way: >>>> >>>> import numpy as np >>>> import sympy as sp >>>> from scipy.optimize import minimize, curve_fit >>>> from lmfit import Model, Parameters >>>> >>>> L = np.array([0.299, 0.295, 0.290, 0.284, 0.279, 0.273, 0.268, 0.262, >>>> 0.256, 0.250]) >>>> K = np.array([2.954, 3.056, 3.119, 3.163, 3.215, 3.274, 3.351, 3.410, >>>> 3.446, 3.416]) >>>> VA = np.array([0.919, 0.727, 0.928, 0.629, 0.656, 0.854, 0.955, 0.981, >>>> 0.908, 0.794]) >>>> >>>> >>>> def f(param): >>>> gamma, alpha, beta, eta = sp.symbols('gamma, alpha, beta, eta') >>>> gamma = param[0] >>>> alpha = param[1] >>>> beta = param[2] >>>> eta = param[3] >>>> Vi_est = gamma - (1 / eta) * sp.log(alpha * L ** -eta + beta * K ** >>>> -eta) >>>> Vlam_est = sp.lambdify((gamma, alpha, beta, eta), Vi_est) >>>> >>>> return np.sum((np.log(VA) - Vlam_est) ** 2) >>>> >>>> >>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>> x0 = (1, 0.01, 0.98, 1) >>>> >>>> result = minimize(f, x0, bounds=bnds) >>>> >>>> print(result.message) >>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>> >>>> >>>> I face difficulty: >>>> ********************************************* >>>> Traceback (most recent call last): >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>> line 70, in wrapper >>>> retval = cfunc(*args, **kwargs) >>>> TypeError: unhashable type: 'numpy.ndarray' >>>> >>>> During handling of the above exception, another exception occurred: >>>> >>>> Traceback (most recent call last): >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>> line 70, in wrapper >>>> retval = cfunc(*args, **kwargs) >>>> TypeError: unhashable type: 'numpy.ndarray' >>>> >>>> During handling of the above exception, another exception occurred: >>>> >>>> Traceback (most recent call last): >>>> File >>>> "F:\Zohreh\MainZohreh\postdoc-field\CSU\pythonProject\fit_test_2.py", line >>>> 26, in <module> >>>> result = minimize(f, x0, bounds=bnds) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_minimize.py", >>>> line 692, in minimize >>>> res = _minimize_lbfgsb(fun, x0, args, jac, bounds, >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_lbfgsb_py.py", >>>> line 308, in _minimize_lbfgsb >>>> sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, >>>> epsilon=eps, >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_optimize.py", >>>> line 263, in _prepare_scalar_function >>>> sf = ScalarFunction(fun, x0, args, grad, hess, >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>> line 158, in __init__ >>>> self._update_fun() >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>> line 251, in _update_fun >>>> self._update_fun_impl() >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>> line 155, in update_fun >>>> self.f = fun_wrapped(self.x) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>> line 137, in fun_wrapped >>>> fx = fun(np.copy(x), *args) >>>> File >>>> "F:\Zohreh\MainZohreh\postdoc-field\CSU\pythonProject\fit_test_2.py", line >>>> 17, in f >>>> Vi_est = gamma - (1 / eta) * sp.log(alpha * L ** -eta + beta * K ** >>>> -eta) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>> line 74, in wrapper >>>> retval = func(*args, **kwargs) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\function.py", >>>> line 476, in __new__ >>>> result = super().__new__(cls, *args, **options) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>> line 74, in wrapper >>>> retval = func(*args, **kwargs) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\function.py", >>>> line 288, in __new__ >>>> evaluated = cls.eval(*args) >>>> File >>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\functions\elementary\exponential.py", >>>> line 718, in eval >>>> coeff = arg.as_coefficient(I) >>>> AttributeError: 'ImmutableDenseNDimArray' object has no attribute >>>> 'as_coefficient' >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> Zohreh Karimzadeh >>>> https://www.researchgate.net/profile/Zohreh-Karimzadeh >>>> Skype Name 49a52224a8b6b38b >>>> Twitter Account @zohrehkarimzad1 >>>> [email protected] >>>> +989102116325 >>>> ((((((((((((((((Value Water))))))))))))))) >>>> >>>> Zohreh Karimzadeh >>>> *https://www.researchgate.net/profile/Zohreh-Karimzadeh* >>>> <https://www.researchgate.net/profile/Zohreh-Karimzadeh> >>>> Skype Name 49a52224a8b6b38b >>>> Twitter Account @zohrehkarimzad1 >>>> [email protected] >>>> +989102116325 >>>> ((((((((((((((((Value Water))))))))))))))) >>>> >>>> >>>> On Thu, Aug 18, 2022 at 10:42 AM Peter Stahlecker < >>>> [email protected]> wrote: >>>> >>>>> I use lambdify quite a bit, on rather large expressions. >>>>> Basically, it always works like this for me: >>>>> >>>>> import sympy as sm >>>>> x1, x2, …, xn = sm.symbols(‚x1, x2, ….., xn‘) >>>>> …. >>>>> … >>>>> expr = some expression of generally with me: sm.sin, sm.cos, sm.exp, >>>>> sm.sqrt, >>>>> sm.Heaviside, etc.. >>>>> This expression may have 50,000 terms, may be an (axb) matrix, >>>>> whatever. >>>>> >>>>> expr_lam = sm.lambdify([x1, x2, …,xn], expr) >>>>> >>>>> Now I can evaluate expr_lam(…) like I would evaluate any numpy >>>>> function. >>>>> >>>>> I have no idea, what expr_lam looks like, I would not know how to look >>>>> at it. >>>>> I assume, it converts sm.sin(..) to np.sin(…), etc >>>>> >>>>> This is how it works for me. >>>>> As I do not really understand your points, like ‚dynamically created‘, >>>>> ‚parse and subs‘, this may be of not help at all for you. >>>>> >>>>> Peter >>>>> >>>>> >>>>> On Thu 18. Aug 2022 at 09:21 Zohreh Karimzadeh <[email protected]> >>>>> wrote: >>>>> >>>>>> Before run I import sp.sqrt or sp.exp but after run they get >>>>>> disappeared. My expression is big and dynamically created and not >>>>>> possible to parse and subs np.exp or sp.exp. >>>>>> >>>>>> Zohreh Karimzadeh >>>>>> >>>>>> Contact me on >>>>>> +989102116325 >>>>>> and at >>>>>> [email protected] >>>>>> 🌧️🌍🌱 >>>>>> >>>>>> >>>>>> On Thu, 18 Aug 2022, 01:17 Aaron Meurer, <[email protected]> wrote: >>>>>> >>>>>>> Your expression uses "sqrt" but you haven't imported it from >>>>>>> anywhere, since you only did "import sympy as sp". You need to use >>>>>>> sp.sqrt. >>>>>>> >>>>>>> Aaron Meurer >>>>>>> >>>>>>> On Wed, Aug 17, 2022 at 11:02 AM Zohreh Karimzadeh < >>>>>>> [email protected]> wrote: >>>>>>> >>>>>>>> Here is my code: >>>>>>>> >>>>>>>> import matplotlib.pyplot as plt >>>>>>>> import numpy as np >>>>>>>> import sympy as sp >>>>>>>> import pandas as pd >>>>>>>> #exp_NaCl path: F:\Zohreh\MainZohreh\postdoc-field\CSU\Duplicat_Pure >>>>>>>> df = >>>>>>>> pd.read_excel(r'F:\Zohreh\MainZohreh\postdoc-field\CSU\Duplicat_Pure\data.xlsx', >>>>>>>> sheet_name='NaCl_exp') >>>>>>>> XNa = df['XNa'] >>>>>>>> XCl = df['XCl'] >>>>>>>> Xwater = df['Xwater'] >>>>>>>> Y = df['gama_x'] >>>>>>>> L=['WwaterNaCl', 'UwaterNaCl', 'VwaterNaCl', 'XCl', 'XNa', 'Xwater', >>>>>>>> 'BNaCl'] >>>>>>>> for j in range(len(L)): >>>>>>>> locals()[L[j]] = sp.symbols(L[j]) >>>>>>>> expr = >>>>>>>> -0.0118343195266272*BNaCl*XCl*XNa*(-2*(9.19238815542512*sqrt(XNa) + >>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1)*exp(-9.19238815542512*sqrt(XNa) >>>>>>>> - 9.19238815542512*sqrt(XCl + XNa)) + 2)/((XCl + XNa)*(sqrt(XNa) + >>>>>>>> sqrt(XCl + XNa))**2) + >>>>>>>> 0.00591715976331361*BNaCl*XCl*(-2*(9.19238815542512*sqrt(XNa) + >>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1)*exp(-9.19238815542512*sqrt(XNa) >>>>>>>> - 9.19238815542512*sqrt(XCl + XNa)) + 2)/(sqrt(XNa) + sqrt(XCl + >>>>>>>> XNa))**2 + >>>>>>>> 0.00591715976331361*BNaCl*XNa*(-2*(9.19238815542512*sqrt(XNa) + >>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1)*exp(-9.19238815542512*sqrt(XNa) >>>>>>>> - 9.19238815542512*sqrt(XCl + XNa)) + 2)/(sqrt(XNa) + sqrt(XCl + >>>>>>>> XNa))**2 - 1.0*Cl*WwaterNaCl*Xwater*(0.5*XCl + 0.5*XNa + 0.5)/XCl - >>>>>>>> 0.5*Cl*WwaterNaCl/XCl - 4.0*UwaterNaCl*XCl*XNa*Xwater + >>>>>>>> 2.0*UwaterNaCl*XCl*Xwater + 2.0*UwaterNaCl*XNa*Xwater - >>>>>>>> 4.0*UwaterNaCl*XNa - 6.0*VwaterNaCl*XCl*XNa*Xwater**2 - >>>>>>>> 4.0*VwaterNaCl*XCl*Xwater**2 + 2.0*VwaterNaCl*XNa*Xwater**2 - >>>>>>>> 1.0*WwaterNaCl*Xwater*(0.5*XCl + 0.5*XNa + 0.5) + >>>>>>>> 2.0*WwaterNaCl*Xwater - 0.5*WwaterNaCl - >>>>>>>> 1.45739430799067*(0.707106781186548*sqrt(XNa) + >>>>>>>> 0.707106781186548*sqrt(XCl + XNa))*(-XCl - XNa + >>>>>>>> 1)/(9.19238815542512*sqrt(XNa) + 9.19238815542512*sqrt(XCl + XNa) + 1) >>>>>>>> - 1.45739430799067*(0.707106781186548*sqrt(XNa) + >>>>>>>> 0.707106781186548*sqrt(XCl + XNa))*(-1.4142135623731*sqrt(XNa) - >>>>>>>> 1.4142135623731*sqrt(XCl + XNa) + 1)/(9.19238815542512*sqrt(XNa) + >>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1) - >>>>>>>> 0.448429017843282*log(9.19238815542512*sqrt(XNa) + >>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1) >>>>>>>> model_func = sp.lambdify(L, expr ) >>>>>>>> >>>>>>>> def f(param): >>>>>>>> BNaCl = param[0] >>>>>>>> UwaterNaCl = param[1] >>>>>>>> VwaterNaCl = param[2] >>>>>>>> WwaterNaCl = param[3] >>>>>>>> Y_est = model_func >>>>>>>> return np.sum((np.log(Y) - Y_est)**2) >>>>>>>> >>>>>>>> >>>>>>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>>>>>> x0 = (1, 0.01, 0.98, 1) >>>>>>>> con = {"type": "eq", "fun": c} >>>>>>>> >>>>>>>> result = minimize(f, x0, bounds=bnds) >>>>>>>> >>>>>>>> print(result.fun) >>>>>>>> print(result.message) >>>>>>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>>>>>> >>>>>>>> while I got : >>>>>>>> NameError: name 'sqrt' is not defined >>>>>>>> >>>>>>>> Zohreh Karimzadeh >>>>>>>> *https://www.researchgate.net/profile/Zohreh-Karimzadeh* >>>>>>>> <https://www.researchgate.net/profile/Zohreh-Karimzadeh> >>>>>>>> Skype Name 49a52224a8b6b38b >>>>>>>> Twitter Account @zohrehkarimzad1 >>>>>>>> [email protected] >>>>>>>> +989102116325 >>>>>>>> >>>>>>>> ((((((((((((((((Value Water))))))))))))))) >>>>>>>> >>>>>>>> >>>>>>>> On Wed, Aug 17, 2022 at 7:46 PM Peter Stahlecker < >>>>>>>> [email protected]> wrote: >>>>>>>> >>>>>>>>> I use lambdify(....) a lot, but always like this: >>>>>>>>> >>>>>>>>> x = sympy.symbols('x') >>>>>>>>> expr = symy.S(10.) * sympy.sqrt(x) >>>>>>>>> expr_lam = sympy.lambdify([x], expr) >>>>>>>>> >>>>>>>>> a = expr_lam(10.) >>>>>>>>> >>>>>>>>> This seems to work for me. >>>>>>>>> >>>>>>>>> On Wed 17. Aug 2022 at 20:38, Zohreh Karimzadeh < >>>>>>>>> [email protected]> wrote: >>>>>>>>> >>>>>>>>>> Dear sympy group >>>>>>>>>> Thanks for your sympy. >>>>>>>>>> >>>>>>>>>> I am working on a code, after creating my big expression using >>>>>>>>>> sympy it includes sqrt. >>>>>>>>>> >>>>>>>>>> I need to lambdify my expression to make it consistent with numpy >>>>>>>>>> and other suffs. >>>>>>>>>> >>>>>>>>>> expr =10 * sp.sqrt(sp.symbols('x')) >>>>>>>>>> >>>>>>>>>> model_func = sp.lambdify('x', expr) >>>>>>>>>> >>>>>>>>>> But I found my expression after lambdifying becomes somethings >>>>>>>>>> like this: >>>>>>>>>> >>>>>>>>>> 10*sqrt(x) >>>>>>>>>> >>>>>>>>>> while I need : >>>>>>>>>> >>>>>>>>>> 10*numpy.sqrt(x) >>>>>>>>>> >>>>>>>>>> Could possibly let me know how get sqrt to work with numpy? >>>>>>>>>> >>>>>>>>>> Regards, >>>>>>>>>> >>>>>>>>>> Zohreh >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> -- >>>>>>>>>> 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 [email protected]. >>>>>>>>>> To view this discussion on the web visit >>>>>>>>>> https://groups.google.com/d/msgid/sympy/1f0b313f-31c5-402e-991e-142a556016f4n%40googlegroups.com >>>>>>>>>> <https://groups.google.com/d/msgid/sympy/1f0b313f-31c5-402e-991e-142a556016f4n%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>>>>>> . >>>>>>>>>> >>>>>>>>> -- >>>>>>>>> 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 [email protected]. >>>>>>>>> To view this discussion on the web visit >>>>>>>>> https://groups.google.com/d/msgid/sympy/CABKqA0ZoGwsadsk4SWCbJVMbCDwXcO_gNGumJH00GAeEFod7Cw%40mail.gmail.com >>>>>>>>> <https://groups.google.com/d/msgid/sympy/CABKqA0ZoGwsadsk4SWCbJVMbCDwXcO_gNGumJH00GAeEFod7Cw%40mail.gmail.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 [email protected]. >>>>>>>> To view this discussion on the web visit >>>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLPRvXZ6jiJbUS_xpWNKqMuUH7Kt5evue%2BwKEwDMvGekBQ%40mail.gmail.com >>>>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLPRvXZ6jiJbUS_xpWNKqMuUH7Kt5evue%2BwKEwDMvGekBQ%40mail.gmail.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 [email protected]. >>>>>>> To view this discussion on the web visit >>>>>>> https://groups.google.com/d/msgid/sympy/CAKgW%3D6JfUmU7Uu%2BSrcA1STxVvWWm7bGWE%3Dit8CTchksTC0Qk7g%40mail.gmail.com >>>>>>> <https://groups.google.com/d/msgid/sympy/CAKgW%3D6JfUmU7Uu%2BSrcA1STxVvWWm7bGWE%3Dit8CTchksTC0Qk7g%40mail.gmail.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 [email protected]. >>>>>> To view this discussion on the web visit >>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLPiCR%3DS2Fac3FZtjMpspqB7BRKtYEi45BVWPjkizVbNvw%40mail.gmail.com >>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLPiCR%3DS2Fac3FZtjMpspqB7BRKtYEi45BVWPjkizVbNvw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>> . >>>>>> >>>>> -- >>>>> 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 [email protected]. >>>>> >>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/sympy/CABKqA0b%3DF0akMH4oyg5%2By9dGvgrf_vvVJTnVhVduMP1f%2Bp1pFw%40mail.gmail.com >>>>> <https://groups.google.com/d/msgid/sympy/CABKqA0b%3DF0akMH4oyg5%2By9dGvgrf_vvVJTnVhVduMP1f%2Bp1pFw%40mail.gmail.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 [email protected]. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLMK-fgpxc71GYzue5gJvd%3Dfj2sV6Dvhj8zrmVpPhiVk%2Bw%40mail.gmail.com >>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLMK-fgpxc71GYzue5gJvd%3Dfj2sV6Dvhj8zrmVpPhiVk%2Bw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> -- >>> 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 [email protected]. >>> >> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sympy/CABKqA0aBsD2WhpTuQqzZGUK1pfkUyH4q3Om9DdBQOpoaaO4rqQ%40mail.gmail.com >>> <https://groups.google.com/d/msgid/sympy/CABKqA0aBsD2WhpTuQqzZGUK1pfkUyH4q3Om9DdBQOpoaaO4rqQ%40mail.gmail.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 [email protected]. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/CA%2B1XYLNiQNVa_hg25e-_f8xs%2B2w88p7JC4ntneBrqO4YFajTgA%40mail.gmail.com >> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLNiQNVa_hg25e-_f8xs%2B2w88p7JC4ntneBrqO4YFajTgA%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> > -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CABKqA0YedBPPLH73J6ScxkgNWN9_NCR-YvOcd7vpGX4SsGZj0g%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CABKqA0YedBPPLH73J6ScxkgNWN9_NCR-YvOcd7vpGX4SsGZj0g%40mail.gmail.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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CA%2B1XYLOkAu3fHK8Fm1eRoO8CQxkN70mnO%3DM7iNqeRg3bt44yZQ%40mail.gmail.com.
