thank you very much. 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 4:35 PM Peter Stahlecker <peter.stahlec...@gmail.com> wrote: > 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 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 sympy+unsubscr...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/CA%2B1XYLOkAu3fHK8Fm1eRoO8CQxkN70mnO%3DM7iNqeRg3bt44yZQ%40mail.gmail.com >> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLOkAu3fHK8Fm1eRoO8CQxkN70mnO%3DM7iNqeRg3bt44yZQ%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/CABKqA0aeQ%3D47NmCUei%3DvtXwFyjs4dw%3DfZ%3DjQGqpJvsk68BRYHA%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CABKqA0aeQ%3D47NmCUei%3DvtXwFyjs4dw%3DfZ%3DjQGqpJvsk68BRYHA%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%2B1XYLMg7bq4X3iedc0u_9nwiKHXrFd8GV1%3DdUt9n255dcwJxw%40mail.gmail.com.
