Let $f=f(t)=\sum_{i=0}^{4}a_ix^i ,g=g(t)=\sum_{j=0}^{4}b_jx^j \in L[x]$, $L$ is a commutative ring. I would like to compute the resultant of $f$ and $g$.
I wish to check a few examples in low dimensions, but even in low dimension (with $\deg(f)=\deg(g)$) such as four, the computation is quite lengthy-- the matrix is of order $8$.
I know that there are computer algebra systems that can do these calculations, but unfortunately I have not succeeded to install Macaulay2 on my computer, so I ask for help here; see the answer to this question.
What is the resultant of $f$ and $g$ as above?
I really apologize if my question is not so appropriate (I would prefer to get help in installing Macaulay2 or a link where one can compute the resultant on-line, but asking for that seems totally not appropriate to this site, and I do not know where to ask these questions).
Thank you very much!
Using Maple, there are $219$ terms: $$ \eqalign{&{a_{{0}}}^{4}{b_{{4}}}^{4}-{a_{{0}}}^{3}a_{{1}}b_{{3}}{b_{{4}}}^{3}-2 \,{a_{{0}}}^{3}a_{{2}}b_{{2}}{b_{{4}}}^{3}+{a_{{0}}}^{3}a_{{2}}{b_{{3} }}^{2}{b_{{4}}}^{2}-3\,{a_{{0}}}^{3}a_{{3}}b_{{1}}{b_{{4}}}^{3}+3\,{a_ {{0}}}^{3}a_{{3}}b_{{2}}b_{{3}}{b_{{4}}}^{2}-{a_{{0}}}^{3}a_{{3}}{b_{{ 3}}}^{3}b_{{4}} \cr & -4\,{a_{{0}}}^{3}a_{{4}}b_{{0}}{b_{{4}}}^{3}+4\,{a_{{0}}}^{3}a_{{4}}b_ {{1}}b_{{3}}{b_{{4}}}^{2}+2\,{a_{{0}}}^{3}a_{{4}}{b_{{2}}}^{2}{b_{{4}} }^{2}-4\,{a_{{0}}}^{3}a_{{4}}b_{{2}}{b_{{3}}}^{2}b_{{4}}+{a_{{0}}}^{3} a_{{4}}{b_{{3}}}^{4}+{a_{{0}}}^{2}{a_{{1}}}^{2}b_{{2}}{b_{{4}}}^{3}+3 \,{a_{{0}}}^{2}a_{{1}}a_{{2}}b_{{1}}{b_{{4}}}^{3} \cr & -{a_{{0}}}^{2}a_{{1}}a_{{2}}b_{{2}}b_{{3}}{b_{{4}}}^{2}+4\,{a_{{0}}}^{ 2}a_{{1}}a_{{3}}b_{{0}}{b_{{4}}}^{3}-{a_{{0}}}^{2}a_{{1}}a_{{3}}b_{{1} }b_{{3}}{b_{{4}}}^{2}-2\,{a_{{0}}}^{2}a_{{1}}a_{{3}}{b_{{2}}}^{2}{b_{{ 4}}}^{2}+{a_{{0}}}^{2}a_{{1}}a_{{3}}b_{{2}}{b_{{3}}}^{2}b_{{4}}-{a_{{0 }}}^{2}a_{{1}}a_{{4}}b_{{0}}b_{{3}}{b_{{4}}}^{2}-5\,{a_{{0}}}^{2}a_{{1 }}a_{{4}}b_{{1}}b_{{2}}{b_{{4}}}^{2} \cr & +{a_{{0}}}^{2}a_{{1}}a_{{4}}b_{{1}}{b_{{3}}}^{2}b_{{4}}+3\,{a_{{0}}}^{2 }a_{{1}}a_{{4}}{b_{{2}}}^{2}b_{{3}}b_{{4}}-{a_{{0}}}^{2}a_{{1}}a_{{4}} b_{{2}}{b_{{3}}}^{3}+2\,{a_{{0}}}^{2}{a_{{2}}}^{2}b_{{0}}{b_{{4}}}^{3} -2\,{a_{{0}}}^{2}{a_{{2}}}^{2}b_{{1}}b_{{3}}{b_{{4}}}^{2}+{a_{{0}}}^{2 }{a_{{2}}}^{2}{b_{{2}}}^{2}{b_{{4}}}^{2}-5\,{a_{{0}}}^{2}a_{{2}}a_{{3} }b_{{0}}b_{{3}}{b_{{4}}}^{2} \cr & +{a_{{0}}}^{2}a_{{2}}a_{{3}}b_{{1}}b_{{2}}{b_{{4}}}^{2}+2\,{a_{{0}}}^{2 }a_{{2}}a_{{3}}b_{{1}}{b_{{3}}}^{2}b_{{4}}-{a_{{0}}}^{2}a_{{2}}a_{{3}} {b_{{2}}}^{2}b_{{3}}b_{{4}}+2\,{a_{{0}}}^{2}a_{{2}}a_{{4}}b_{{0}}b_{{2 }}{b_{{4}}}^{2}+2\,{a_{{0}}}^{2}a_{{2}}a_{{4}}b_{{0}}{b_{{3}}}^{2}b_{{ 4}}-3\,{a_{{0}}}^{2}a_{{2}}a_{{4}}{b_{{1}}}^{2}{b_{{4}}}^{2}+4\,{a_{{0 }}}^{2}a_{{2}}a_{{4}}b_{{1}}b_{{2}}b_{{3}}b_{{4}} \cr & -2\,{a_{{0}}}^{2}a_{{2}}a_{{4}}b_{{1}}{b_{{3}}}^{3}-2\,{a_{{0}}}^{2}a_ {{2}}a_{{4}}{b_{{2}}}^{3}b_{{4}}+{a_{{0}}}^{2}a_{{2}}a_{{4}}{b_{{2}}}^ {2}{b_{{3}}}^{2}-3\,{a_{{0}}}^{2}{a_{{3}}}^{2}b_{{0}}b_{{2}}{b_{{4}}}^ {2}+3\,{a_{{0}}}^{2}{a_{{3}}}^{2}b_{{0}}{b_{{3}}}^{2}b_{{4}}+3\,{a_{{0 }}}^{2}{a_{{3}}}^{2}{b_{{1}}}^{2}{b_{{4}}}^{2}-3\,{a_{{0}}}^{2}{a_{{3} }}^{2}b_{{1}}b_{{2}}b_{{3}}b_{{4}} \cr & +{a_{{0}}}^{2}{a_{{3}}}^{2}{b_{{2}}}^{3}b_{{4}}+5\,{a_{{0}}}^{2}a_{{3}} a_{{4}}b_{{0}}b_{{1}}{b_{{4}}}^{2}+2\,{a_{{0}}}^{2}a_{{3}}a_{{4}}b_{{0 }}b_{{2}}b_{{3}}b_{{4}}-3\,{a_{{0}}}^{2}a_{{3}}a_{{4}}b_{{0}}{b_{{3}}} ^{3}-5\,{a_{{0}}}^{2}a_{{3}}a_{{4}}{b_{{1}}}^{2}b_{{3}}b_{{4}}+{a_{{0} }}^{2}a_{{3}}a_{{4}}b_{{1}}{b_{{2}}}^{2}b_{{4}}+3\,{a_{{0}}}^{2}a_{{3} }a_{{4}}b_{{1}}b_{{2}}{b_{{3}}}^{2} \cr & -{a_{{0}}}^{2}a_{{3}}a_{{4}}{b_{{2}}}^{3}b_{{3}}+6\,{a_{{0}}}^{2}{a_{{ 4}}}^{2}{b_{{0}}}^{2}{b_{{4}}}^{2}-8\,{a_{{0}}}^{2}{a_{{4}}}^{2}b_{{0} }b_{{1}}b_{{3}}b_{{4}}-4\,{a_{{0}}}^{2}{a_{{4}}}^{2}b_{{0}}{b_{{2}}}^{ 2}b_{{4}}+4\,{a_{{0}}}^{2}{a_{{4}}}^{2}b_{{0}}b_{{2}}{b_{{3}}}^{2}+4\, {a_{{0}}}^{2}{a_{{4}}}^{2}{b_{{1}}}^{2}b_{{2}}b_{{4}}+2\,{a_{{0}}}^{2} {a_{{4}}}^{2}{b_{{1}}}^{2}{b_{{3}}}^{2} \cr & -4\,{a_{{0}}}^{2}{a_{{4}}}^{2}b_{{1}}{b_{{2}}}^{2}b_{{3}}+{a_{{0}}}^{2 }{a_{{4}}}^{2}{b_{{2}}}^{4}-a_{{0}}{a_{{1}}}^{3}b_{{1}}{b_{{4}}}^{3}-4 \,a_{{0}}{a_{{1}}}^{2}a_{{2}}b_{{0}}{b_{{4}}}^{3}+a_{{0}}{a_{{1}}}^{2} a_{{2}}b_{{1}}b_{{3}}{b_{{4}}}^{2}+a_{{0}}{a_{{1}}}^{2}a_{{3}}b_{{0}}b _{{3}}{b_{{4}}}^{2}+2\,a_{{0}}{a_{{1}}}^{2}a_{{3}}b_{{1}}b_{{2}}{b_{{4 }}}^{2} \cr & -a_{{0}}{a_{{1}}}^{2}a_{{3}}b_{{1}}{b_{{3}}}^{2}b_{{4}}+2\,a_{{0}}{a_{ {1}}}^{2}a_{{4}}b_{{0}}b_{{2}}{b_{{4}}}^{2}-a_{{0}}{a_{{1}}}^{2}a_{{4} }b_{{0}}{b_{{3}}}^{2}b_{{4}}+3\,a_{{0}}{a_{{1}}}^{2}a_{{4}}{b_{{1}}}^{ 2}{b_{{4}}}^{2}-3\,a_{{0}}{a_{{1}}}^{2}a_{{4}}b_{{1}}b_{{2}}b_{{3}}b_{ {4}}+a_{{0}}{a_{{1}}}^{2}a_{{4}}b_{{1}}{b_{{3}}}^{3}+3\,a_{{0}}a_{{1}} {a_{{2}}}^{2}b_{{0}}b_{{3}}{b_{{4}}}^{2} \cr & -a_{{0}}a_{{1}}{a_{{2}}}^{2}b_{{1}}b_{{2}}{b_{{4}}}^{2}+4\,a_{{0}}a_{{ 1}}a_{{2}}a_{{3}}b_{{0}}b_{{2}}{b_{{4}}}^{2}-3\,a_{{0}}a_{{1}}a_{{2}}a _{{3}}b_{{0}}{b_{{3}}}^{2}b_{{4}}-3\,a_{{0}}a_{{1}}a_{{2}}a_{{3}}{b_{{ 1}}}^{2}{b_{{4}}}^{2}+a_{{0}}a_{{1}}a_{{2}}a_{{3}}b_{{1}}b_{{2}}b_{{3} }b_{{4}}+2\,a_{{0}}a_{{1}}a_{{2}}a_{{4}}b_{{0}}b_{{1}}{b_{{4}}}^{2}-8 \,a_{{0}}a_{{1}}a_{{2}}a_{{4}}b_{{0}}b_{{2}}b_{{3}}b_{{4}} \cr & +3\,a_{{0}}a_{{1}}a_{{2}}a_{{4}}b_{{0}}{b_{{3}}}^{3}+a_{{0}}a_{{1}}a_{{ 2}}a_{{4}}{b_{{1}}}^{2}b_{{3}}b_{{4}}+2\,a_{{0}}a_{{1}}a_{{2}}a_{{4}}b _{{1}}{b_{{2}}}^{2}b_{{4}}-a_{{0}}a_{{1}}a_{{2}}a_{{4}}b_{{1}}b_{{2}}{ b_{{3}}}^{2}-5\,a_{{0}}a_{{1}}{a_{{3}}}^{2}b_{{0}}b_{{1}}{b_{{4}}}^{2} +a_{{0}}a_{{1}}{a_{{3}}}^{2}b_{{0}}b_{{2}}b_{{3}}b_{{4}}+2\,a_{{0}}a_{ {1}}{a_{{3}}}^{2}{b_{{1}}}^{2}b_{{3}}b_{{4}} \cr & -a_{{0}}a_{{1}}{a_{{3}}}^{2}b_{{1}}{b_{{2}}}^{2}b_{{4}}-8\,a_{{0}}a_{{ 1}}a_{{3}}a_{{4}}{b_{{0}}}^{2}{b_{{4}}}^{2}+10\,a_{{0}}a_{{1}}a_{{3}}a _{{4}}b_{{0}}b_{{1}}b_{{3}}b_{{4}}-a_{{0}}a_{{1}}a_{{3}}a_{{4}}b_{{0}} b_{{2}}{b_{{3}}}^{2}-a_{{0}}a_{{1}}a_{{3}}a_{{4}}{b_{{1}}}^{2}b_{{2}}b _{{4}}-2\,a_{{0}}a_{{1}}a_{{3}}a_{{4}}{b_{{1}}}^{2}{b_{{3}}}^{2}+a_{{0 }}a_{{1}}a_{{3}}a_{{4}}b_{{1}}{b_{{2}}}^{2}b_{{3}} \cr & +5\,a_{{0}}a_{{1}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{3}}b_{{4}}+2\,a_{{0}}a_ {{1}}{a_{{4}}}^{2}b_{{0}}b_{{1}}b_{{2}}b_{{4}}-5\,a_{{0}}a_{{1}}{a_{{4 }}}^{2}b_{{0}}b_{{1}}{b_{{3}}}^{2}+a_{{0}}a_{{1}}{a_{{4}}}^{2}b_{{0}}{ b_{{2}}}^{2}b_{{3}}-3\,a_{{0}}a_{{1}}{a_{{4}}}^{2}{b_{{1}}}^{3}b_{{4}} +3\,a_{{0}}a_{{1}}{a_{{4}}}^{2}{b_{{1}}}^{2}b_{{2}}b_{{3}}-a_{{0}}a_{{ 1}}{a_{{4}}}^{2}b_{{1}}{b_{{2}}}^{3} \cr & -2\,a_{{0}}{a_{{2}}}^{3}b_{{0}}b_{{2}}{b_{{4}}}^{2}+a_{{0}}{a_{{2}}}^{ 3}{b_{{1}}}^{2}{b_{{4}}}^{2}+a_{{0}}{a_{{2}}}^{2}a_{{3}}b_{{0}}b_{{1}} {b_{{4}}}^{2}+2\,a_{{0}}{a_{{2}}}^{2}a_{{3}}b_{{0}}b_{{2}}b_{{3}}b_{{4 }}-a_{{0}}{a_{{2}}}^{2}a_{{3}}{b_{{1}}}^{2}b_{{3}}b_{{4}}-4\,a_{{0}}{a _{{2}}}^{2}a_{{4}}{b_{{0}}}^{2}{b_{{4}}}^{2}+4\,a_{{0}}{a_{{2}}}^{2}a_ {{4}}b_{{0}}{b_{{2}}}^{2}b_{{4}} \cr & -2\,a_{{0}}{a_{{2}}}^{2}a_{{4}}b_{{0}}b_{{2}}{b_{{3}}}^{2}-2\,a_{{0}}{ a_{{2}}}^{2}a_{{4}}{b_{{1}}}^{2}b_{{2}}b_{{4}}+a_{{0}}{a_{{2}}}^{2}a_{ {4}}{b_{{1}}}^{2}{b_{{3}}}^{2}+4\,a_{{0}}a_{{2}}{a_{{3}}}^{2}{b_{{0}}} ^{2}{b_{{4}}}^{2}-a_{{0}}a_{{2}}{a_{{3}}}^{2}b_{{0}}b_{{1}}b_{{3}}b_{{ 4}}-2\,a_{{0}}a_{{2}}{a_{{3}}}^{2}b_{{0}}{b_{{2}}}^{2}b_{{4}}+a_{{0}}a _{{2}}{a_{{3}}}^{2}{b_{{1}}}^{2}b_{{2}}b_{{4}} \cr & +2\,a_{{0}}a_{{2}}a_{{3}}a_{{4}}{b_{{0}}}^{2}b_{{3}}b_{{4}}-8\,a_{{0}}a _{{2}}a_{{3}}a_{{4}}b_{{0}}b_{{1}}b_{{2}}b_{{4}}+a_{{0}}a_{{2}}a_{{3}} a_{{4}}b_{{0}}b_{{1}}{b_{{3}}}^{2}+2\,a_{{0}}a_{{2}}a_{{3}}a_{{4}}b_{{0 }}{b_{{2}}}^{2}b_{{3}}+3\,a_{{0}}a_{{2}}a_{{3}}a_{{4}}{b_{{1}}}^{3}b_{ {4}}-a_{{0}}a_{{2}}a_{{3}}a_{{4}}{b_{{1}}}^{2}b_{{2}}b_{{3}}+2\,a_{{0} }a_{{2}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{2}}b_{{4}} \cr & -3\,a_{{0}}a_{{2}}{a_{{4}}}^{2}{b_{{0}}}^{2}{b_{{3}}}^{2}+2\,a_{{0}}a_ {{2}}{a_{{4}}}^{2}b_{{0}}{b_{{1}}}^{2}b_{{4}}+4\,a_{{0}}a_{{2}}{a_{{4} }}^{2}b_{{0}}b_{{1}}b_{{2}}b_{{3}}-2\,a_{{0}}a_{{2}}{a_{{4}}}^{2}b_{{0 }}{b_{{2}}}^{3}-2\,a_{{0}}a_{{2}}{a_{{4}}}^{2}{b_{{1}}}^{3}b_{{3}}+a_{ {0}}a_{{2}}{a_{{4}}}^{2}{b_{{1}}}^{2}{b_{{2}}}^{2}-3\,a_{{0}}{a_{{3}}} ^{3}{b_{{0}}}^{2}b_{{3}}b_{{4}} \cr & +3\,a_{{0}}{a_{{3}}}^{3}b_{{0}}b_{{1}}b_{{2}}b_{{4}}-a_{{0}}{a_{{3}}}^{ 3}{b_{{1}}}^{3}b_{{4}}+2\,a_{{0}}{a_{{3}}}^{2}a_{{4}}{b_{{0}}}^{2}b_{{ 2}}b_{{4}}+3\,a_{{0}}{a_{{3}}}^{2}a_{{4}}{b_{{0}}}^{2}{b_{{3}}}^{2}-a_ {{0}}{a_{{3}}}^{2}a_{{4}}b_{{0}}{b_{{1}}}^{2}b_{{4}}-3\,a_{{0}}{a_{{3} }}^{2}a_{{4}}b_{{0}}b_{{1}}b_{{2}}b_{{3}}+a_{{0}}{a_{{3}}}^{2}a_{{4}}{ b_{{1}}}^{3}b_{{3}} \cr & -a_{{0}}a_{{3}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{1}}b_{{4}}-5\,a_{{0}}a_{{ 3}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{2}}b_{{3}}+a_{{0}}a_{{3}}{a_{{4}}}^{2 }b_{{0}}{b_{{1}}}^{2}b_{{3}}+3\,a_{{0}}a_{{3}}{a_{{4}}}^{2}b_{{0}}b_{{ 1}}{b_{{2}}}^{2}-a_{{0}}a_{{3}}{a_{{4}}}^{2}{b_{{1}}}^{3}b_{{2}}-4\,a_ {{0}}{a_{{4}}}^{3}{b_{{0}}}^{3}b_{{4}}+4\,a_{{0}}{a_{{4}}}^{3}{b_{{0}} }^{2}b_{{1}}b_{{3}} \cr & +2\,a_{{0}}{a_{{4}}}^{3}{b_{{0}}}^{2}{b_{{2}}}^{2}-4\,a_{{0}}{a_{{4}}}^ {3}b_{{0}}{b_{{1}}}^{2}b_{{2}}+a_{{0}}{a_{{4}}}^{3}{b_{{1}}}^{4}+{a_{{ 1}}}^{4}b_{{0}}{b_{{4}}}^{3}-{a_{{1}}}^{3}a_{{2}}b_{{0}}b_{{3}}{b_{{4} }}^{2}-2\,{a_{{1}}}^{3}a_{{3}}b_{{0}}b_{{2}}{b_{{4}}}^{2}+{a_{{1}}}^{3 }a_{{3}}b_{{0}}{b_{{3}}}^{2}b_{{4}} \cr & -3\,{a_{{1}}}^{3}a_{{4}}b_{{0}}b_{{1}}{b_{{4}}}^{2}+3\,{a_{{1}}}^{3}a_ {{4}}b_{{0}}b_{{2}}b_{{3}}b_{{4}}-{a_{{1}}}^{3}a_{{4}}b_{{0}}{b_{{3}}} ^{3}+{a_{{1}}}^{2}{a_{{2}}}^{2}b_{{0}}b_{{2}}{b_{{4}}}^{2}+3\,{a_{{1}} }^{2}a_{{2}}a_{{3}}b_{{0}}b_{{1}}{b_{{4}}}^{2}-{a_{{1}}}^{2}a_{{2}}a_{ {3}}b_{{0}}b_{{2}}b_{{3}}b_{{4}}+4\,{a_{{1}}}^{2}a_{{2}}a_{{4}}{b_{{0} }}^{2}{b_{{4}}}^{2} \cr & -{a_{{1}}}^{2}a_{{2}}a_{{4}}b_{{0}}b_{{1}}b_{{3}}b_{{4}}-2\,{a_{{1}}}^ {2}a_{{2}}a_{{4}}b_{{0}}{b_{{2}}}^{2}b_{{4}}+{a_{{1}}}^{2}a_{{2}}a_{{4 }}b_{{0}}b_{{2}}{b_{{3}}}^{2}+2\,{a_{{1}}}^{2}{a_{{3}}}^{2}{b_{{0}}}^{ 2}{b_{{4}}}^{2}-2\,{a_{{1}}}^{2}{a_{{3}}}^{2}b_{{0}}b_{{1}}b_{{3}}b_{{ 4}}+{a_{{1}}}^{2}{a_{{3}}}^{2}b_{{0}}{b_{{2}}}^{2}b_{{4}}-5\,{a_{{1}}} ^{2}a_{{3}}a_{{4}}{b_{{0}}}^{2}b_{{3}}b_{{4}} \cr & +{a_{{1}}}^{2}a_{{3}}a_{{4}}b_{{0}}b_{{1}}b_{{2}}b_{{4}}+2\,{a_{{1}}}^{ 2}a_{{3}}a_{{4}}b_{{0}}b_{{1}}{b_{{3}}}^{2}-{a_{{1}}}^{2}a_{{3}}a_{{4} }b_{{0}}{b_{{2}}}^{2}b_{{3}}-3\,{a_{{1}}}^{2}{a_{{4}}}^{2}{b_{{0}}}^{2 }b_{{2}}b_{{4}}+3\,{a_{{1}}}^{2}{a_{{4}}}^{2}{b_{{0}}}^{2}{b_{{3}}}^{2 }+3\,{a_{{1}}}^{2}{a_{{4}}}^{2}b_{{0}}{b_{{1}}}^{2}b_{{4}}-3\,{a_{{1}} }^{2}{a_{{4}}}^{2}b_{{0}}b_{{1}}b_{{2}}b_{{3}} \cr & +{a_{{1}}}^{2}{a_{{4}}}^{2}b_{{0}}{b_{{2}}}^{3}-a_{{1}}{a_{{2}}}^{3}b_{ {0}}b_{{1}}{b_{{4}}}^{2}-4\,a_{{1}}{a_{{2}}}^{2}a_{{3}}{b_{{0}}}^{2}{b _{{4}}}^{2}+a_{{1}}{a_{{2}}}^{2}a_{{3}}b_{{0}}b_{{1}}b_{{3}}b_{{4}}+a_ {{1}}{a_{{2}}}^{2}a_{{4}}{b_{{0}}}^{2}b_{{3}}b_{{4}}+2\,a_{{1}}{a_{{2} }}^{2}a_{{4}}b_{{0}}b_{{1}}b_{{2}}b_{{4}}-a_{{1}}{a_{{2}}}^{2}a_{{4}}b _{{0}}b_{{1}}{b_{{3}}}^{2} \cr & +3\,a_{{1}}a_{{2}}{a_{{3}}}^{2}{b_{{0}}}^{2}b_{{3}}b_{{4}}-a_{{1}}a_{{2 }}{a_{{3}}}^{2}b_{{0}}b_{{1}}b_{{2}}b_{{4}}+4\,a_{{1}}a_{{2}}a_{{3}}a_ {{4}}{b_{{0}}}^{2}b_{{2}}b_{{4}}-3\,a_{{1}}a_{{2}}a_{{3}}a_{{4}}{b_{{0 }}}^{2}{b_{{3}}}^{2}-3\,a_{{1}}a_{{2}}a_{{3}}a_{{4}}b_{{0}}{b_{{1}}}^{ 2}b_{{4}}+a_{{1}}a_{{2}}a_{{3}}a_{{4}}b_{{0}}b_{{1}}b_{{2}}b_{{3}}-5\, a_{{1}}a_{{2}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{1}}b_{{4}} \cr & +a_{{1}}a_{{2}}{a_{{4}}}^{2}{b_{{0}}}^{2}b_{{2}}b_{{3}}+2\,a_{{1}}a_{{2 }}{a_{{4}}}^{2}b_{{0}}{b_{{1}}}^{2}b_{{3}}-a_{{1}}a_{{2}}{a_{{4}}}^{2} b_{{0}}b_{{1}}{b_{{2}}}^{2}-2\,a_{{1}}{a_{{3}}}^{3}{b_{{0}}}^{2}b_{{2} }b_{{4}}+a_{{1}}{a_{{3}}}^{3}b_{{0}}{b_{{1}}}^{2}b_{{4}}+a_{{1}}{a_{{3 }}}^{2}a_{{4}}{b_{{0}}}^{2}b_{{1}}b_{{4}}+2\,a_{{1}}{a_{{3}}}^{2}a_{{4 }}{b_{{0}}}^{2}b_{{2}}b_{{3}} \cr & -a_{{1}}{a_{{3}}}^{2}a_{{4}}b_{{0}}{b_{{1}}}^{2}b_{{3}}+4\,a_{{1}}a_{{ 3}}{a_{{4}}}^{2}{b_{{0}}}^{3}b_{{4}}-a_{{1}}a_{{3}}{a_{{4}}}^{2}{b_{{0 }}}^{2}b_{{1}}b_{{3}}-2\,a_{{1}}a_{{3}}{a_{{4}}}^{2}{b_{{0}}}^{2}{b_{{ 2}}}^{2}+a_{{1}}a_{{3}}{a_{{4}}}^{2}b_{{0}}{b_{{1}}}^{2}b_{{2}}-3\,a_{ {1}}{a_{{4}}}^{3}{b_{{0}}}^{3}b_{{3}}+3\,a_{{1}}{a_{{4}}}^{3}{b_{{0}}} ^{2}b_{{1}}b_{{2}} \cr & -a_{{1}}{a_{{4}}}^{3}b_{{0}}{b_{{1}}}^{3}+{a_{{2}}}^{4}{b_{{0}}}^{2}{b _{{4}}}^{2}-{a_{{2}}}^{3}a_{{3}}{b_{{0}}}^{2}b_{{3}}b_{{4}}-2\,{a_{{2} }}^{3}a_{{4}}{b_{{0}}}^{2}b_{{2}}b_{{4}}+{a_{{2}}}^{3}a_{{4}}{b_{{0}}} ^{2}{b_{{3}}}^{2}+{a_{{2}}}^{2}{a_{{3}}}^{2}{b_{{0}}}^{2}b_{{2}}b_{{4} }+3\,{a_{{2}}}^{2}a_{{3}}a_{{4}}{b_{{0}}}^{2}b_{{1}}b_{{4}} \cr & -{a_{{2}}}^{2}a_{{3}}a_{{4}}{b_{{0}}}^{2}b_{{2}}b_{{3}}+2\,{a_{{2}}}^{ 2}{a_{{4}}}^{2}{b_{{0}}}^{3}b_{{4}}-2\,{a_{{2}}}^{2}{a_{{4}}}^{2}{b_{{0 }}}^{2}b_{{1}}b_{{3}}+{a_{{2}}}^{2}{a_{{4}}}^{2}{b_{{0}}}^{2}{b_{{2}}} ^{2}-a_{{2}}{a_{{3}}}^{3}{b_{{0}}}^{2}b_{{1}}b_{{4}}-4\,a_{{2}}{a_{{3} }}^{2}a_{{4}}{b_{{0}}}^{3}b_{{4}}+a_{{2}}{a_{{3}}}^{2}a_{{4}}{b_{{0}}} ^{2}b_{{1}}b_{{3}} \cr & +3\,a_{{2}}a_{{3}}{a_{{4}}}^{2}{b_{{0}}}^{3}b_{{3}}-a_{{2}}a_{{3}}{a_{{ 4}}}^{2}{b_{{0}}}^{2}b_{{1}}b_{{2}}-2\,a_{{2}}{a_{{4}}}^{3}{b_{{0}}}^{ 3}b_{{2}}+a_{{2}}{a_{{4}}}^{3}{b_{{0}}}^{2}{b_{{1}}}^{2}+{a_{{3}}}^{4} {b_{{0}}}^{3}b_{{4}}-{a_{{3}}}^{3}a_{{4}}{b_{{0}}}^{3}b_{{3}}+{a_{{3}} }^{2}{a_{{4}}}^{2}{b_{{0}}}^{3}b_{{2}} \cr & -a_{{3}}{a_{{4}}}^{3}{b_{{0}}}^{3}b_{{1}}+{a_{{4}}}^{4}{b_{{0}}}^{4} \cr}$$