Equations are acting inert

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Question:Equations are acting inert

Posted: Ronan 1311 Product: Maple 2022

October 10 2022

I have a matrix and generate difference tables from it's diagonals. Works fine. Then I make a polynomial from the first row of the difference table. I have three polynomials. They are all acting inert, just will not evaluate.

I cannot see what the problem is.

i) Recurrence relation

for i from 2 to Msize do for j from i to Msize do A[i, j] := A[i, j-1]*(j-2)+A[i-1, j-1] end do end do

Matrix(%id = 36893489695842121836)

viia) General formula for diagonals:-

Select diagonal & Difference Table procedures

diag := proc (M::Matrix, dg::posint) local i, rd, c, dt; rd := LinearAlgebra:-RowDimension(M); dt := Matrix(rd, rd); for i from dg to rd do dt[1+i-dg, 1] := M[1+i-dg, i] end do; return dt end proc

proc (M::Matrix, dg::posint) local i, rd, c, dt; rd := LinearAlgebra:-RowDimension(M); dt := Matrix(rd, rd); for i from dg to rd do dt[1+i-dg, 1] := M[1+i-dg, i] end do; return dt end proc

Matrix(%id = 36893489695866397388)

diftab := proc (M::Matrix) local i, j, cl, rd; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[i, 1] = 0 then rd := rd-1 else break end if end do; cl := rd; for i from 2 to cl do for j to rd-i do M[j, i] := M[j+1, i-1]-M[j, i-1] end do end do; print(M); return M end proc

proc (M::Matrix) local i, j, cl, rd; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[i, 1] = 0 then rd := rd-1 else break end if end do; cl := rd; for i from 2 to cl do for j to rd-i do M[j, i] := M[j+1, i-1]-M[j, i-1] end do end do; print(M); return M end proc

Matrix(%id = 36893489695866348116)

gnrpoly := proc (M::Matrix) local i, p, rd, n; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[1, i] = 0 then rd := rd-1 else break end if end do; p := 0; for i from 0 to rd-1 do p := p+M[1, i+1]*binomial(n, i) end do; return p end proc

proc (M::Matrix) local i, p, rd, n; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[1, i] = 0 then rd := rd-1 else break end if end do; p := 0; for i from 0 to rd-1 do p := p+M[1, i+1]*binomial(n, i) end do; return p end proc

"for i from 0 to 3 do print("Diagonal ",i); eqn:=gnrpoly(diftab(diag(A,i+1))); cat(poly,i):=unapply(factor(expand(eqn)),n); print("--------------------------------------------------------------"); end do"