| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Is there a polynomial whose square has fewer terms? Are there two polynomials with m and n terms, respectively, whose product has fewer than min(m,n) terms?
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 79.1 | AURORA::HALLYB | Mon Jun 11 1984 21:44 | 2 | ||
Presumably Stan is referring to polynomials over the reals. An easy counterexample (otherwise) would be 2x+y, over the integers modulo 4. | |||||
| 79.2 | HARE::STAN | Tue Jun 12 1984 02:24 | 1 | ||
I intended that the coefficients be (non-zero) complex numbers. | |||||
| 79.3 | HARE::GILBERT | Tue Jun 12 1984 18:00 | 10 | ||
Here are two polynomials with 4 terms each, and a product with 2 terms:
3 2 2 3 2 2
p = x - 2x y + 2xy - y = (x - y)(x - xy + y )
3 2 2 3 2 2
q = x + 2x y + 2xy + y = (x + y)(x + xy + y )
6 6
pq = x - y
| |||||
| 79.4 | ORPHAN::BRETT | Tue Jun 12 1984 19:50 | 4 | ||
Okay, now for only one variable.... /Bevin | |||||
| 79.5 | TURTLE::STAN | Tue Jun 12 1984 22:37 | 1 | ||
Let y=1. | |||||