| 1 | | Just wondering if there's any update to this issue ? I think this behavior is related to the problem in |
| 2 | | http://trac.sagemath.org/sage_trac/ticket/11309 |
| | 1 | From the following sage-devel thread: |
| | 2 | |
| | 3 | http://groups.google.com/group/sage-devel/t/951d510c814f894f |
| | 4 | |
| | 5 | |
| | 6 | Arithmetic with inequalities can be confusing, since Sage does nothing to keep the inequality ``correct``. For example: |
| | 7 | |
| | 8 | {{{ |
| | 9 | On Thu, 10 Dec 2009 00:37:10 -0800 (PST) |
| | 10 | "marik@mendelu.cz" <marik@mendelu.cz> wrote: |
| | 11 | |
| | 12 | > sage: f = x + 3 < y - 2 |
| | 13 | > sage: f*(-1) |
| | 14 | > -x - 3 < -y + 2 |
| | 15 | }}} |
| | 16 | |
| | 17 | It seems MMA doesn't apply any automatic simplification in this case: |
| | 18 | |
| | 19 | {{{ |
| | 20 | On Thu, 10 Dec 2009 09:54:36 -0800 |
| | 21 | William Stein <wstein@gmail.com> wrote: |
| | 22 | |
| | 23 | > Mathematica does something weird and formal: |
| | 24 | > |
| | 25 | > In[1]:= f := x+3 < y-2; |
| | 26 | > In[3]:= f*(-1) |
| | 27 | > Out[3]= -(3 + x < -2 + y) |
| | 28 | }}} |
| | 29 | |
| | 30 | Maple acts more intuitively, though the way ``formal products`` are printed leaves something to be desired, IMHO: |
| | 31 | |
| | 32 | {{{ |
| | 33 | On Thu, 10 Dec 2009 14:15:53 -0800 |
| | 34 | William Stein <wstein@gmail.com> wrote: |
| | 35 | |
| | 36 | > Here is what Maple does: |
| | 37 | > |
| | 38 | > flat:release_notes wstein$ maple |
| | 39 | > |\^/| Maple 13 (APPLE UNIVERSAL OSX) |
| | 40 | > ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple |
| | 41 | > Inc. 2009 \ MAPLE / All rights reserved. Maple is a trademark of |
| | 42 | > <____ ____> Waterloo Maple Inc. |
| | 43 | > | Type ? for help. |
| | 44 | > > f := x < y; |
| | 45 | > f := x < y |
| | 46 | > |
| | 47 | > > f*(-3); |
| | 48 | > -3 y < -3 x |
| | 49 | > |
| | 50 | > > f*z; |
| | 51 | > *(x < y, z) |
| | 52 | > |
| | 53 | > > f*a; |
| | 54 | > *(x < y, a) |
| | 55 | }}} |
| | 56 | |
| | 57 | |
| | 58 | We should multiply both sides of the inequality only if the argument is a real number (as opposed to a symbol with real domain), and invert the relation when the argument is negative. |
| | 59 | |
| | 60 | Note that GiNaC leaves everything formal, like MMA, by default: |
| | 61 | |
| | 62 | {{{ |
| | 63 | ginsh - GiNaC Interactive Shell (ginac V1.5.3) |
| | 64 | __, _______ Copyright (C) 1999-2009 Johannes Gutenberg University Mainz, |
| | 65 | (__) * | Germany. This is free software with ABSOLUTELY NO WARRANTY. |
| | 66 | ._) i N a C | You are welcome to redistribute it under certain conditions. |
| | 67 | <-------------' For details type `warranty;'. |
| | 68 | |
| | 69 | Type ?? for a list of help topics. |
| | 70 | > f= x < y; |
| | 71 | x<y |
| | 72 | > f*-1; |
| | 73 | -(x<y) |
| | 74 | > f*-5; |
| | 75 | -5*(x<y) |
| | 76 | > f*-z; |
| | 77 | -z*(x<y) |
| | 78 | > f*z; |
| | 79 | z*(x<y) |
| | 80 | }}} |
