APL(NARS), 76 chars
{⍵⊥⌽⍺⍵⊥⍺}∂
For the input of polynom the list
$$ a_0 a_1 ... a_n $$$$ a_n a_{n-1} ... a_1 a_0 $$
means polynom
$$ a_0+a_1 X^1+ ... +a_n X^n $$
test:$$ a_n X^n+a_{n-1} X^{n-1} ... a_1 X+a_0 $$
f←{⍵⊥⌽⍺⍵⊥⍺}∂
4 5 4 f ̄13
5
05 0 0 4 ̄2 0 0 0 ̄2 4 0 0 50 f 19
1.613438484E13
0 0 0 0 0 f 400
0
0 f 400
0
04.14 0 48 0 4.140 f ̄3
̄735.12
̄51 0 0 1 ̄5 f 5.4
87.48
APL(NARS), 7 chars
{⍵⊥⌽⍺}∂
For the input of polynom the list
$$ a_0 a_1 ... a_n $$
means polynom
$$ a_0+a_1 X^1+ ... +a_n X^n $$
test:
f←{⍵⊥⌽⍺}∂
4 5 f ̄13
5
0 0 0 4 ̄2 0 0 0 0 0 5 f 19
1.613438484E13
0 0 0 0 0 f 400
0
0 f 400
0
0 0 48 0 4.14 f ̄3
̄735.12
̄5 0 0 1 f 5.4
87.48
APL(NARS), 6 chars
{⍵⊥⍺}∂
For the input of polynom the list
$$ a_n a_{n-1} ... a_1 a_0 $$
means polynom
$$ a_n X^n+a_{n-1} X^{n-1} ... a_1 X+a_0 $$
f←{⍵⊥⍺}∂
5 4 f ̄13
5
5 0 0 0 0 0 ̄2 4 0 0 0 f 19
1.613438484E13
0 0 0 0 0 f 400
0
0 f 400
0
4.14 0 48 0 0 f ̄3
̄735.12
1 0 0 ̄5 f 5.4
87.48
APL(NARS), 7 chars
{⍵⊥⌽⍺}∂
For the input of polynom the list
$$ a_0 a_1 ... a_n $$
means polynom
$$ a_0+a_1 X^1+ ... +a_n X^n $$
test:
f←{⍵⊥⌽⍺}∂
4 5 f ̄13
5
0 0 0 4 ̄2 0 0 0 0 0 5 f 19
1.613438484E13
0 0 0 0 0 f 400
0
0 f 400
0
0 0 48 0 4.14 f ̄3
̄735.12
̄5 0 0 1 f 5.4
87.48