# How can I get scheme product of two polynomials like this?

I use LaTeX by hand to make this table With Mathematica, I get the answer dirrectly

Expand[(x^2 + x - 1) (2 x^2 - 7 x + 9)]


-9 + 16 x - 5 x^3 + 2 x^4

or my code here How can I tell Mathematica to get the scheme like my picture. My purpose is to use the results of Mathematica to convert to LaTeX.

• I've added a new answer on the TeX stackexchange question that was mentioned by Nasser. Now the LaTeX code allows to display powers of $x$ (or any other variable). Jun 23 at 10:40
• Thank you very much. Can you write a code fot this question tex.stackexchange.com/questions/79182/… Jun 23 at 12:39
• @BrunoLeFloch Please see another version here. Note that, this version is different from this style Jun 23 at 13:24
• These questions are about polynomial divisions and already have answers. It's not clear why the answers are not suitable for you. Perhaps you could ask a new question on the TeX stackexchange website. Jun 23 at 13:51

In Latex, you could use how-can-i-make-a-scheme-to-multiply-polynomials but that answer only uses the coefficients. i.e. there will be no $$x$$ displayed in the process as you can see and one have to know the degree of $$x$$ by its position by inspection.

In Mathematica, here is a quick hack. But conversion this to Latex will need extra credit ;) and I am not sure now how much more effort it will take. The result is in a Grid.

mulp[x^2+x-1,2x^2-7x+9,x] mulp[1+x,x^2,x] mulp[x^6-x^2+x-1,2x^2-7x+x^3+9,x] ## Code

ClearAll["Global*"];
ClearAll[mulp]
(*version June 23, 2023. Bug reports are welcome*)
mulp[p1_,p2_,x_Symbol]:=Module[{max,min,cmin,cmax,g,n,m,pmin,pmax,tmp,w,currentRow,e,sum,currentCol,gridLines},
If[Not[PolynomialQ[p1,x]]||Not[PolynomialQ[p2,x]],Abort[]];
If[Length[CoefficientList[p1,x]]<=Length[CoefficientList[p2,x]],
pmin=p1;pmax=p2
,
pmin=p2;pmax=p1
];
cmin=CoefficientList[pmin,x];
cmax=CoefficientList[pmax,x];

w=Length@cmax+Length@cmin-1;
g=Table[0,{n,2+Length[cmin]+1},{m,w}];

Do[g[[1,w-n+1]]=cmax[[n]]*x^(n-1),{n,1,Length[cmax]}];
Do[g[[2,w-n+1]]=cmin[[n]]*x^(n-1),{n,1,Length[cmin]}];

Do[ currentRow=2+n;
e=g[[2,w-n+1]];

Do[ currentCol=w-m+1-n+1;
g[[currentRow,currentCol]]=e*g[[1,w-m+1]],
{m,1,Length[cmax]}],
{n,1,Length[cmin]}
];

currentRow=Length@g;
Do[ e=Total[g[[3;;,n]]];
g[[currentRow,n]]=If[n>1,If[InternalSyntacticNegativeQ[e]||e===0,e,"+"<>ToString[InputForm@e]],e]
,
{n,1,w}
];

gridLines=Table[If[n==3||n==Length[g],True,False],{n,Length@g}];
Grid[Replace[g,0->"",{2}],Spacings->{1, 1},Dividers->{{False},gridLines}]
]