DEtools - Maple Help

DEtools

 load intermediate computation as saved using the 'store' options of rifsimp

Parameters

 filename - (optional) name of the file containing the partial rifsimp computation.

Description

 • The rifread command loads a partial rifsimp computation that was run using the store or storeall options (see rifsimp[adv_options]).
 The storage options are most useful for large or complex computations, where the resources required to complete the computation may exceed the capability of the machine. The state of the system at the last iteration  (using store), or at all previous iterations and/or cases (using storeall), can be retrieved using this command.
 When called with no arguments, the file "RifStorage.m" is used. This is the default file name for use with the store option of rifsimp. If a file name was specified for the rifsimp run, or if the storeall option was used (storing all iterations and/or cases in separate files), the file name must be included in the rifread command.
 • Please note that the system obtained using rifread is not in final form and may have redundant equations or unresolved integrability conditions.

Examples

 > $\mathrm{with}\left(\mathrm{DEtools}\right):$

Consider the following system, run with rifsimp.

 > $\mathrm{sys1}≔\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right),\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{η}\left(x,y\right)-2\left(\frac{{\partial }^{2}}{\partial y\partial x}\mathrm{ξ}\left(x,y\right)\right),-3{y}^{2}\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)+2\left(\frac{{\partial }^{2}}{\partial y\partial x}\mathrm{η}\left(x,y\right)\right)-\left(\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{ξ}\left(x,y\right)\right),-2\mathrm{η}\left(x,y\right)y-2{y}^{2}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right)+{y}^{2}\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right)+\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{η}\left(x,y\right)\right]$
 ${\mathrm{sys1}}{:=}\left[\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){,}\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){-}{2}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){,}{-}{3}{}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){+}{2}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){-}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){,}{-}{2}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}{y}{-}{2}{}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){+}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){+}\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]$ (1)
 > $\mathrm{ans1}≔\mathrm{rifsimp}\left(\mathrm{sys1},\left[\mathrm{ξ},\mathrm{η}\right],\mathrm{store}\right)$
 ${\mathrm{ans1}}{:=}{\mathrm{table}}\left(\left[{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}\right]\right]\right)$ (2)

Partial results can be obtained using rifread, even if the full computation did not succeed (notice the presence of the redundant equation ${\mathrm{\eta }}_{\mathrm{yy}}=0$).

 > $\mathrm{temp1}≔\mathrm{rifread}\left(\right)$
 ${\mathrm{temp1}}{:=}{\mathrm{table}}\left(\left[{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}\right]\right]\right)$ (3)

Note that the results obtained above were stored in the file "RifStorage.m".

The same example can have results stored under a different name. Here the temp results are stored in "tmpstore.m":

 > $\mathrm{ans1}≔\mathrm{rifsimp}\left(\mathrm{sys1},\left[\mathrm{ξ},\mathrm{η}\right],\mathrm{store}="tmpstore"\right)$
 ${\mathrm{ans1}}{:=}{\mathrm{table}}\left(\left[{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}\right]\right]\right)$ (4)
 > $\mathrm{temp1}≔\mathrm{rifread}\left("tmpstore"\right)$
 ${\mathrm{temp1}}{:=}{\mathrm{table}}\left(\left[{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}\right]\right]\right)$ (5)

It is also possible to store the results at the end of each iteration and for each separate case using storeall. Increasing the infolevel will display the file name as each partial calculation is saved.

 > $\mathrm{sys2}≔\left[-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)y-\left(\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)\right){y}^{2},\mathrm{η}\left(x,y\right)-2\left(\frac{{\partial }^{2}}{\partial y\partial x}\mathrm{ξ}\left(x,y\right)\right){y}^{2}+\left(\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{η}\left(x,y\right)\right){y}^{2}-\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right)y-2\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)y+2\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)a{y}^{2},-2y\left(\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)\right)-\left(\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{ξ}\left(x,y\right)\right){y}^{2}+2\left(\frac{{\partial }^{2}}{\partial y\partial x}\mathrm{η}\left(x,y\right)\right){y}^{2}+\mathrm{η}\left(x,y\right)-\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right)y+\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right)a{y}^{2}+3{y}^{3}\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right){a}^{2}-3{y}^{4}\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right){b}^{2}-3{y}^{5}\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right){b}^{2}+3{y}^{2}\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right){a}^{2},\left(\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{η}\left(x,y\right)\right){y}^{2}+{y}^{2}\left(\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)\right)a-y\left(\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)\right)+2{y}^{3}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right){a}^{2}-2{y}^{4}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right){b}^{2}-{y}^{3}\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right){a}^{2}+{y}^{4}\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right){b}^{2}+\mathrm{η}\left(x,y\right){y}^{2}{a}^{2}-2\mathrm{η}\left(x,y\right){y}^{3}{b}^{2}-{y}^{2}\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right){a}^{2}-3\mathrm{η}\left(x,y\right){y}^{4}{b}^{2}-2{y}^{5}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right){b}^{2}+2{y}^{2}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right){a}^{2}+{y}^{5}\left(\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)\right){b}^{2}\right]$
 ${\mathrm{sys2}}{:=}\left[{-}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{y}{-}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{,}{\mathrm{η}}{}\left({x}{,}{y}\right){-}{2}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{+}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{-}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{y}{-}{2}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{y}{+}{2}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{a}{}{{y}}^{{2}}{,}{-}{2}{}{y}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){-}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{+}{2}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{+}{\mathrm{η}}{}\left({x}{,}{y}\right){-}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{y}{+}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{a}{}{{y}}^{{2}}{+}{3}{}{{y}}^{{3}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{-}{3}{}{{y}}^{{4}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}{-}{3}{}{{y}}^{{5}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}{+}{3}{}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{,}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{y}}^{{2}}{+}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{a}{-}{y}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){+}{2}{}{{y}}^{{3}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{-}{2}{}{{y}}^{{4}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}{-}{{y}}^{{3}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{+}{{y}}^{{4}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}{+}{\mathrm{η}}{}\left({x}{,}{y}\right){}{{y}}^{{2}}{}{{a}}^{{2}}{-}{2}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}{{y}}^{{3}}{}{{b}}^{{2}}{-}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{-}{3}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}{{y}}^{{4}}{}{{b}}^{{2}}{-}{2}{}{{y}}^{{5}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}{+}{2}{}{{y}}^{{2}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right)\right){}{{a}}^{{2}}{+}{{y}}^{{5}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right)\right){}{{b}}^{{2}}\right]$ (6)

If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation method is displayed.

 > ${\mathrm{infolevel}}_{\mathrm{rifsimp}}≔1$
 ${{\mathrm{infolevel}}}_{{\mathrm{rifsimp}}}{:=}{1}$ (7)
 > $\mathrm{rr}≔\mathrm{rifsimp}\left(\mathrm{sys2},\left[\mathrm{ξ},\mathrm{η}\right],\mathrm{storeall},\mathrm{casesplit}\right)$
 Storing current system in RifStorage_1_1.mStoring current system in RifStorage_1_2.m       Storing current system in RifStorage_1_3.m       Storing current system in RifStorage_1_4.m       Storing current system in RifStorage_1_5.m       Storing current system in RifStorage_1_6.m       Storing current system in RifStorage_1_7.m       Storing current system in RifStorage_1_8.m       Storing current system in RifStorage_1_9.m       Storing current system in RifStorage_1_10.m       Storing current system in RifStorage_1_11.m       Storing current system in RifStorage_1_12.m       Storing current system in RifStorage_1_13.m       Storing current system in RifStorage_1_14.m       Storing current system in RifStorage_2_13.m       Storing current system in RifStorage_2_14.m       Storing current system in RifStorage_2_15.m       Storing current system in RifStorage_3_14.m       Storing current system in RifStorage_3_15.m       Storing current system in RifStorage_3_16.m       Storing current system in RifStorage_4_15.m
 ${\mathrm{The system has been identified as follows:}}$
 ${\mathrm{The system has the following dependent variables:}}$
 ${\mathrm{ξ}}{,}{\mathrm{η}}$
 ${\mathrm{The system has the following independent variables:}}$
 ${x}{,}{y}$
 ${\mathrm{The system has the following constants:}}$
 ${a}{,}{b}$
 ${\mathrm{The following are to be treated as solve variables:}}$
 ${\mathrm{ξ}}{,}{\mathrm{η}}{,}{a}{,}{b}$
 ${\mathrm{rr}}{:=}{\mathrm{table}}\left(\left[{1}{=}{\mathrm{table}}\left(\left[{\mathrm{Case}}{=}\left[\left[{b}{\ne }{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]\right]{,}{\mathrm{Pivots}}{=}\left[{b}{\ne }{0}\right]{,}{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}\right]\right]\right){,}{2}{=}{\mathrm{table}}\left(\left[{\mathrm{Case}}{=}\left[\left[{b}{=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]{,}\left[{a}{}\left({a}{-}{1}\right){\ne }{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]\right]{,}{\mathrm{Pivots}}{=}\left[{a}{\ne }{0}{,}{a}{-}{1}{\ne }{0}\right]{,}{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}{b}{=}{0}\right]\right]\right){,}{3}{=}{\mathrm{table}}\left(\left[{\mathrm{Case}}{=}\left[\left[{b}{=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]{,}\left[{a}{}\left({a}{-}{1}\right){=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]{,}\left[{a}{\ne }{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]\right]{,}{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}{a}{=}{1}{,}{b}{=}{0}\right]\right]\right){,}{4}{=}{\mathrm{table}}\left(\left[{\mathrm{Case}}{=}\left[\left[{b}{=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]{,}\left[{a}{}\left({a}{-}{1}\right){=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]{,}\left[{a}{=}{0}{,}{\mathrm{η}}{}\left({x}{,}{y}\right)\right]\right]{,}{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}{a}{=}{0}{,}{b}{=}{0}\right]\right]\right){,}{\mathrm{casecount}}{=}{4}\right]\right)$ (8)
 > $\mathrm{rifread}\left("RifStorage_2_13"\right)$
 ${\mathrm{table}}\left(\left[{\mathrm{DiffConstraint}}{=}\left[{0}{=}{a}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}\left({a}{-}{1}\right){,}{0}{=}{a}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}\left({a}{-}{1}\right){,}{0}{=}{a}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}\left({a}{-}{1}\right){,}{0}{=}{a}{}{\mathrm{η}}{}\left({x}{,}{y}\right){}\left({9}{}{{a}}^{{3}}{}{y}{-}{9}{}{{a}}^{{2}}{}{y}{+}{4}{}{a}{}{y}{-}{2}{}{a}{+}{2}\right)\right]{,}{\mathrm{Solved}}{=}\left[\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}{0}{,}{b}{=}{0}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}{a}{}\left({3}{}{a}{-}{2}\right){}{\mathrm{η}}{}\left({x}{,}{y}\right){,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{η}}{}\left({x}{,}{y}\right)}{{y}}\right]\right]\right)$ (9)

A description of the meaning of each entry appearing in the output tables can be found on the rifsimp[output] page.