Timeline for How to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2013 at 18:24 | comment | added | gpap | Thanks a lot - I edited to match the example in the documentation. | |
| Oct 4, 2013 at 18:21 | history | edited | gpap | CC BY-SA 3.0 | added 895 characters in body |
| Oct 4, 2013 at 14:06 | comment | added | Daniel Lichtblau | This is reasonable (I upvoted..) I'd recommend separating into a GB followed by polynomial reduction though. In[607]:= vars = {a, b, x, y}; In[608]:= PolynomialReduce[(a + b)^3 - (a^3 + b^3), GroebnerBasis[{a + b - x, a*b - y}, vars], vars][[2]] Out[608]= 3 x y Reason being that the replacement will not in general result in certain variables being eliminated, so a GB alone might not suffice. | |
| Oct 4, 2013 at 13:48 | vote | accept | kiss my armpit | ||
| Oct 4, 2013 at 13:42 | comment | added | gpap | GroebnerBasis[{a^10 + b^10, a + b - x, a b - y}, {x, y}, {a, b}] produces the expected result. | |
| Oct 4, 2013 at 13:38 | comment | added | kiss my armpit | If I want to find $a^{10}+b^{10}$ in terms of $x$ and $y$, why does Simplify[(a + b)^10 - Expand[(a + b)^10 - a^10 - b^10], a b == x && a + b == y] not produce the expected result? | |
| Oct 4, 2013 at 13:27 | history | answered | gpap | CC BY-SA 3.0 |