rts=m-||m+||m--4++||m+-4++||m--4++||m+-4++
1
2
-5++2t
2
m
4
1/3
2
4
m
t
2/3
2
3
1
2
-5++2t
2
m
4
1/3
2
4
m
t
2/3
2
3
1
2
2
m
2
2
m
3
1+
3
4
m
3t
2/3
2
1-
3
t6
1/3
2
1
2
2
m
2
2
m
3
1+
3
4
m
3t
2/3
2
1-
3
t6
1/3
2
1
2
2
m
2
2
m
3
1-
3
4
m
3t
2/3
2
1+
3
t6
1/3
2
1
2
2
m
2
2
m
3
1-
3
4
m
3t
2/3
2
1+
3
t6
1/3
2
In[]:=
ReduceIm[rts[[1]]]==0&&t==&&m>=1&&L>=1&&m∈Integers&&L∈Integers
1/3
-27L+2+3
6
m
3
27-4L
2
L
6
m
Out[]=
(L|m)∈&&L≥1&&m≥Root[-64L+9&,2]&&t
6
#1
1/3
-27L+2+3
6
m
3
L(27L-4)
6
m
Therootindexingrepresentation[f,k]appliestopolynomialfunctionsfonly.Theindexingofrootstakestherealrootsfirst,inincreasingorder.Forpolynomialswithrationalcoefficients,thecomplexconjugatepairsofrootshaveconsecutiveindices.
In[]:=
ReduceIm[rts[[3]]]==0&&t==&&m>=1&&L>=1&&m∈Integers&&L∈Integers
1/3
-27L+2+3
6
m
3
27-4L
2
L
6
m
Out[]=
False
In[]:=
ReduceIm[rts[[5]]]==0&&t==&&m>=1&&L>=1&&m∈Integers&&L∈Integers
1/3
-27L+2+3
6
m
3
27-4L
2
L
6
m
Out[]=
False