Whatever they are, I believe your second return statement does not work, because you are adding ‚things‘ which cannot be added. I do not understand your program, but I do understand, that your second return statement cannot work.
On Thu 18. Aug 2022 at 18:56 Zohreh Karimzadeh <z.karimza...@gmail.com> wrote: > 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 > z.karimza...@gmail.com > +989102116325 > ((((((((((((((((Value Water))))))))))))))) > > > On Thu, Aug 18, 2022 at 4:08 PM Peter Stahlecker < > peter.stahlec...@gmail.com> 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 <z.karimza...@gmail.com> >> 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 >>> z.karimza...@gmail.com >>> +989102116325 >>> ((((((((((((((((Value Water))))))))))))))) >>> >>> >>> On Thu, Aug 18, 2022 at 3:28 PM Peter Stahlecker < >>> peter.stahlec...@gmail.com> 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 <z.karimza...@gmail.com> >>>> 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 >>>>> z.karimza...@gmail.com >>>>> +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 >>>>> z.karimza...@gmail.com >>>>> +989102116325 >>>>> ((((((((((((((((Value Water))))))))))))))) >>>>> >>>>> >>>>> On Thu, Aug 18, 2022 at 10:42 AM Peter Stahlecker < >>>>> peter.stahlec...@gmail.com> 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 < >>>>>> z.karimza...@gmail.com> 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 >>>>>>> z.karimza...@gmail.com >>>>>>> 🌧️🌍🌱 >>>>>>> >>>>>>> >>>>>>> On Thu, 18 Aug 2022, 01:17 Aaron Meurer, <asmeu...@gmail.com> 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 < >>>>>>>> z.karimza...@gmail.com> 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 >>>>>>>>> z.karimza...@gmail.com >>>>>>>>> +989102116325 >>>>>>>>> >>>>>>>>> ((((((((((((((((Value Water))))))))))))))) >>>>>>>>> >>>>>>>>> >>>>>>>>> On Wed, Aug 17, 2022 at 7:46 PM Peter Stahlecker < >>>>>>>>> peter.stahlec...@gmail.com> 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 < >>>>>>>>>> z.karimza...@gmail.com> 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 sympy+unsubscr...@googlegroups.com. >>>>>>>>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>>>>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>>>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>>> >>>>> 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 sympy+unsubscr...@googlegroups.com. >>>>> 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 sympy+unsubscr...@googlegroups.com. >>>> >>> 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 sympy+unsubscr...@googlegroups.com. >>> 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 sympy+unsubscr...@googlegroups.com. >> > To 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