The CalculationHistory module is a collection of three simple commands for storing and retrieving the results of intermediate calculations.  The command Update(S, exp) stores the Maple expression exp in a table (called the HistoryTable) with table index S.  Only the 10 most current values of exp are retained in the HistoryTable.  The command Get(S) retrieves these values.  The command Clear() clears all stored values in the HistoryTable.

At present, the commands Query/Indecomposable, Decompose and Nilradical use the CalculationHistory module and store intermediate results which can be recalled.

The number of calculations stored in the HistoryTable can be specified by the DifferentialGeometry:-Preferences command.

This command is part of the DifferentialGeometry:-Tools package, and so can be used in the form CalculationHistory:-Update(...) only after executing the commands with(DifferentialGeometry) and with(Tools) in that order.  It can always be used in the long form DifferentialGeometry:-Tools:-CalculationHistory:-Update.  The commands Get and Clear work the same way.

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{Tools}\right)\:$$\mathrm{with}\left(\mathrm{LieAlgebras}\right)\:$

$\mathrm{exports}\left(\mathrm{CalculationHistory}\right)$

$\mathrm{Clear},\mathrm{Get},\mathrm{Update}$

Test := proc(n)
local i, s, t;
s := 0;
for i to n do
t := i^2;
Tools:-CalculationHistory:-Update("Test", [i, t]);
s := s + t;
od;
s
end:

$\mathrm{Test}\left(25\right)$

$5525$

$\mathrm{Tools}:-\mathrm{CalculationHistory}:-\mathrm{Get}\left(''Test''\right)$

$\left[\left[25\,625\right]\,\left[24\,576\right]\,\left[23\,529\right]\,\left[22\,484\right]\,\left[21\,441\right]\,\left[20\,400\right]\,\left[19\,361\right]\,\left[18\,324\right]\,\left[17\,289\right]\,\left[16\,256\right]\right]$

$\mathrm{Tools}:-\mathrm{CalculationHistory}:-\mathrm{Clear}\left(''Test''\right)$

$L≔\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Alg3}\,\left[4\right]\right]\,\left[\left[\left[1\,3\,2\right]\,-2\right]\,\left[\left[1\,4\,1\right]\,-1\right]\,\left[\left[2\,3\,1\right]\,-1\right]\,\left[\left[2\,4\,2\right]\,-1\right]\right]\right]\right)$

$L≔\left[\left[\mathrm{e1}\,\mathrm{e3}\right]=-2\mathrm{e2}\,\left[\mathrm{e1}\,\mathrm{e4}\right]=-\mathrm{e1}\,\left[\mathrm{e2}\,\mathrm{e3}\right]=-\mathrm{e1}\,\left[\mathrm{e2}\,\mathrm{e4}\right]=-\mathrm{e2}\right]$

$\mathrm{DGsetup}\left(L\right)$

$\mathrm{Lie\; algebra:\; Alg3}$

$\mathrm{Decompose}\left(\right)\:$

Warning, the Lie algebra "Alg3:2" is decomposable but an explicit decomposition could not be constructed.  See CalculationHistory and rerun Decompose with optional argument hint.

$\mathrm{CalculationHistory}:-\mathrm{Get}\left(''Decompose''\right)$

$\left[\left[''Alg3''\,\left[-1+\mathrm{\_z5}\,-\frac{1}{2}+{\mathrm{\_z5}}^2\right]\right]\right]$

$\mathrm{Decompose}\left(\mathrm{hint}=\left[x\,\left[x^2-\frac{1}{2}\,\left[x-\frac{1}{\mathrm{sqrt}\left(2\right)}\,x+\frac{1}{\mathrm{sqrt}\left(2\right)}\right]\right]\right]\right)$

$\left[\left[\right]\,\left[\mathrm{e1}+\sqrt{2}\mathrm{e2}\,\mathrm{e3}+\sqrt{2}\mathrm{e4}\,\mathrm{e1}-\sqrt{2}\mathrm{e2}\,\mathrm{e3}-\sqrt{2}\mathrm{e4}\right]\right]$