j4n bur53 wrote:
> I am unable to run derive 6.10 on my windows 10 machine.
> On the other hand I could run maxima, which has a groebner
> basis library, and I get:
>
> (%i27)
> poly_buchberger([(5+(5+a^2)*b-a*b^2)*t,(5*a^2*b-(a+4*a^2)*b^2)
(t-1)],[t,a,b]);
> The lcm is the polynomial 4*a^3*b^4 + .... Probably indeed
> a nasty example, 0.3281 secs isn?t that fast. Nevertheless
> I need to check what heuristic I am missing.
FriCAS results below. As you can see after usung Gebauer-Moeller
criteria there is only small number of S-pairs to consider.
groebner([(5 + (5 + a^2)+b - a*b^2)*t, (5*a^2*b - (a + 4*a^2)*b^2)*(1-t)],
"info")
you choose option -info-
abbrev. for the following information strings are
ci => Leading monomial for critpair calculation
tci => Number of terms of polynomial i
cj => Leading monomial for critpair calculation
tcj => Number of terms of polynomial j
c => Leading monomial of critpair polynomial
tc => Number of terms of critpair polynomial
rc => Leading monomial of redcritpair polynomial
trc => Number of terms of redcritpair polynomial
tF => Number of polynomials in reduction list F
tD => Number of critpairs still to do
[
2 2 2 2 2
[ci = a b t, tci = 6, cj = a b t, tcj = 4, c = a b t, tc = 8, rc = a b t,
trc = 10, tF = 2, tD = 1]
]
[
2 2 2 2
[ci = a b t, tci = 4, cj = a b t, tcj = 10, c = a b t, tc = 11, rc = b t,
trc = 15, tF = 2, tD = 1]
]
[
2 2 2
[ci = a b t, tci = 4, cj = b t, tcj = 15, c = a b t, tc = 16, rc = a b t,
trc = 17, tF = 2, tD = 2]
]
[
2
[ci = a b t, tci = 10, cj = a b t, tcj = 17, c = a b t, tc = 20, rc = b t,
trc = 20, tF = 1, tD = 2]
]
[
7
[ci = a b t, tci = 17, cj = b t, tcj = 20, c = b t, tc = 24, rc = a t,
trc = 22, tF = 2, tD = 2]
]
[
2 6 4 4
[ci = b t, tci = 15, cj = b t, tcj = 20, c = a b t, tc = 27, rc = a b ,
trc = 16, tF = 3, tD = 3]
]
[
7 4 4 6 4 3 7
[ci = a t, tci = 22, cj = a b , tcj = 16, c = a b t, tc = 34, rc = a b ,
trc = 25, tF = 4, tD = 4]
]
[
4 4 3 7 3 7
[ci = a b , tci = 16, cj = a b , tcj = 25, c = a b , tc = 29, rc = 0,
trc = 0, tF = 4, tD = 3]
]
[
7 6 3 4
[ci = b t, tci = 20, cj = a t, tcj = 22, c = a b t, tc = 40, rc = a b ,
trc = 11, tF = 3, tD = 3]
]
[
4 4 3 4 3 4
[ci = a b , tci = 16, cj = a b , tcj = 11, c = a b , tc = 11, rc = 0,
trc = 0, tF = 3, tD = 2]
]
[
3 4 2 4
[ci = b t, tci = 20, cj = a b , tcj = 11, c = a b t, tc = 28, rc = 0,
trc = 0, tF = 3, tD = 1]
]
[
3 7 3 4 3 6
[ci = a b , tci = 25, cj = a b , tcj = 11, c = a b , tc = 24, rc = 0,
trc = 0, tF = 3, tD = 0]
]
There are
3
Groebner Basis Polynomials.
THE GROEBNER BASIS POLYNOMIALS
(18)
[
6 5 4 3
2
13805 b + 92336 a - 115771 a + 1991015 a - 871670 a + 10690355 a
+
2860400 a + 138050
*
t
+
4 3 2 3
(- 115420 a + 85561 a + 28604 a )b
+
5 4 3 2 2
(- 92336 a + 115771 a - 952235 a - 371601 a - 42409 a)b
+
5 4 3 2
(115420 a + 6775 a + 1009825 a + 212045 a )b
,
7 6 5 4 3 2
(16 a - 17 a + 341 a - 85 a + 1820 a + 850 a + 100 a)t
+
5 4 3 2 3
(- 20 a + 11 a + 8 a + a )b
+
6 5 4 3 2 2
(- 16 a + 17 a - 161 a - 96 a - 18 a - a)b
+
6 5 4 3 2
(20 a + 5 a + 175 a + 70 a + 5 a )b
,
3 2 4 3 2 3 4 3 2 2
(4 a + a )b + (- 5 a - 4 a - a)b + (- 4 a - a - 35 a - 10 a)b
+
4 2
(5 a + 50 a )b
]
Type: List(Polynomial(Integer))
Time: 0.01 (IN) + 0.01 (EV) + 0.02 (OT) = 0.03 sec
--
Waldek Hebisch
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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