Re: recursively solve equation and save the values only

*To*: mathgroup at smc.vnet.net*Subject*: [mg125806] Re: recursively solve equation and save the values only*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 3 Apr 2012 04:48:59 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 4/2/12 at 4:27 AM, wsmjy2012 at gmail.com (wyn smjy) wrote: >I am new to Mathematica. I am trying to recursively solve equation >and saving the values into Table. Since I need the real solutions >only so I use Reduce. >The following is my code: >f = 5.68672 T + 6.46776 T^3 It is generally a bad habit to use a single upper case letter as a variable in Mathematica. There are too many instances where this conflicts with built-in symbols. Avoiding this habit ensures such conflicts cannot arise. >t = Table[i, {i, 0.2, 3, 0.2}] >sols = Table[Reduce[f == t[[i]], T, Reals], {i, Length[t]}] {T == >0.0351204, T == 0.06995, T == 0.104221, T == 0.137708, T == >0.170237, T == 0.201687, T == 0.231988, T == 0.26111, T === 0.289058, >T == 0.315857, T == 0.34155, T == 0.366188, T == 0.389828,= T == >0.412529, T == 0.434347} More efficient would be: sols = Table[Reduce[f == i, t, Reals], {i, 0.2, 3, 0.2}]; >The solution is OK as I compared it to other software as well. The >only thing that matters me is how to remove the T== , i.e. I just >need the solution and then to copy this into another table, say >sols2 that contains >sols2 = {0.0351204, 0.06995, 0.104221, T == 0.137708,.., 0.434347} >I tried the following: sols2 = T/.sols but produce the following >error: This won't work since t == value isn't a replacement rule. Given usage of Reduce the numeric values can be extracted using Cases. That is: In[17]:= Cases[sols, _?NumericQ, Infinity] Out[17]= {0.0351204,0.06995,0.104221,0.137709,0.170237,0.201687,0.231988,0.26111,0.289058,0.315857,0.34155,0.366188,0.389828,0.412529,0.434347} But do note, you could have obtained exactly the same result using NSolve. For example, In[18]:= sols = Flatten@Table[t /. NSolve[f == i, t, Reals], {i, .2, 3, .2}] Out[18]= {0.0351204,0.06995,0.104221,0.137709,0.170237,0.201687,0.231988,0.26111,0.289058,0.315857,0.34155,0.366188,0.389828,0.412529,0.434347} I've used Flatten since NSolve returns a list rather than a number.