| 2 | | On Tue, Jul 29, 2008 at 6:05 PM, jamlatino <medrano.antonio@gmail.com> wrote: |
| 3 | | > |
| 4 | | > While working on the video tutorial for Sage I tried the following |
| 5 | | > equation: |
| 6 | | > |
| 7 | | > (sin(x) - 8*cos(x)*sin(x))*(sin(x)^2 + cos(x)) - (2*cos(x)*sin(x) - |
| 8 | | > sin(x))*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x)) |
| 9 | | > |
| 10 | | > if I use find_root in the interval 1,2 I get the following answer: |
| 11 | | > 1.9106332362490561 |
| 12 | | > |
| 13 | | > but when I use solve to find the solution I get |
| 14 | | > [x == pi, x == pi/2, x == 0] |
| 15 | | > |
| 16 | | > pi/2 is 1.57, but when I try find_root in the interval 1.5,1.6 it |
| 17 | | > tells me that the equation has no zero in that interval, can someone |
| 18 | | > explain?? |
| 19 | | |
| 20 | | This appears to me to be a bug as pi/2 is not a solution. |
| 21 | | If you do the following it is pretty clear that the 0's are |
| 22 | | at 0, 1.9..., etc. and not at pi/2: |
| 23 | | |
| 24 | | sage: f = (sin(x) - 8*cos(x)*sin(x))*(sin(x)^2 + cos(x)) - |
| 25 | | (2*cos(x)*sin(x) - sin(x))*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x)) |
| | 4 | sage: f(x) = sin(x) - 8*cos(x)*sin(x))*(sin(x)^2 + cos(x)) - (2*cos(x)*sin(x) - sin(x))*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x) |
| | 5 | sage: solve(f(x), x) |
| | 6 | [x == pi, x == 1/2*pi, x == 0] |
| 28 | | sage: f.plot(-1,4) |
| 29 | | |
| 30 | | Sage finds the numerical 0's using a numerical root |
| 31 | | finder (from scipy). |
| 32 | | |
| 33 | | Sage finds the exact solutions by calling the computer |
| 34 | | algebra system Maxima, which indeed strangely claims that pi/2 is a solution: |
| 35 | | |
| 36 | | (%i1) solve((sin(x)-8*cos(x)*sin(x))*(sin(x)^2+cos(x))-(2*cos(x)*sin(x)-sin(x))*(-2*sin(x)^2+2*cos(x)^2-cos(x))=0, |
| 37 | | x); |
| 38 | | |
| 39 | | `solve' is using arc-trig functions to get a solution. |
| 40 | | Some solutions will be lost. |
| 41 | | %pi |
| 42 | | (%o1) [x = %pi, x = ---, x = 0] |
| 43 | | 2 |
| 44 | | |
| 45 | | It looks like this might be a bug in Maxima's solve function. |
| 46 | | |
| 47 | | There's not much for me to do besides: |
| 48 | | * report this to the maxima folks (I've cc'd Robert Dodier |
| 49 | | in this email), |
| 50 | | * completely rewrite Sage's solve to not use Maxima. |
| 51 | | |
| 52 | | From Robert Dodier: |
| 53 | | |
| 54 | | |
| 55 | | Yup, that's a bug, all right ... I'll make a bug report. |
| 56 | | |
| 57 | | > * completely rewrite Sage's solve to not use Maxima. |
| 58 | | |
| 59 | | Well, if you do that, please write it in pure Python so it is easier |
| 60 | | to translate to Lisp. |
| 61 | | |
| 62 | | Maxima's code for solving equations has more than a few bugs, |
| 63 | | and it's not clear what classes of problems it can handle, nor is |
| 64 | | it clear what method is used for each class, and there certainly |
| 65 | | are interesting and useful equations which it just can't handle. |
| 66 | | All of this motivates a complete rewrite. Not that I'm volunteering; |
| 67 | | not yet, anyway. |
| 68 | | |
| 69 | | FWIW |
| 70 | | |
| 71 | | Robert Dodier |
