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convert/setofequations

convert a matrix equality into a set of equations

convert/listsofequations

convert a matrix equality into a list of equations

 Calling Sequence convert(E, setofequations) convert(E, listofequations)

Parameters

 E - any Maple object, typically a Matrix, a Vector, possibly from the Physics:-Vectors package, or an expression or equation involving them

Description

 • The convert/setofequations function converts an equality between matrices into a set of equations equating the matrix components, or an equality between Vectors, typically from the Physics:-Vectors package, into an set of equations for the components of these vectors. When only one object (Matrix or vector) is passed, in the set of equations returned all the components are equated to 0.
 • The convert/listofequations works the same way as convert/setofequations but the output is a list instead of a set. In the case of an equation of matrices, the list is ordered from line to columns (see the Examples).

Examples

 > $M,N≔\mathrm{Matrix}\left(3,\mathrm{symbol}=m\right),\mathrm{Matrix}\left(3,\mathrm{symbol}=n\right)$
 ${M}{,}{N}{≔}\left[\begin{array}{ccc}{{m}}_{{1}{,}{1}}& {{m}}_{{1}{,}{2}}& {{m}}_{{1}{,}{3}}\\ {{m}}_{{2}{,}{1}}& {{m}}_{{2}{,}{2}}& {{m}}_{{2}{,}{3}}\\ {{m}}_{{3}{,}{1}}& {{m}}_{{3}{,}{2}}& {{m}}_{{3}{,}{3}}\end{array}\right]{,}\left[\begin{array}{ccc}{{n}}_{{1}{,}{1}}& {{n}}_{{1}{,}{2}}& {{n}}_{{1}{,}{3}}\\ {{n}}_{{2}{,}{1}}& {{n}}_{{2}{,}{2}}& {{n}}_{{2}{,}{3}}\\ {{n}}_{{3}{,}{1}}& {{n}}_{{3}{,}{2}}& {{n}}_{{3}{,}{3}}\end{array}\right]$ (1)
 > $\mathrm{convert}\left(M=N,\mathrm{setofequations}\right)$
 $\left\{{{m}}_{{1}{,}{1}}{=}{{n}}_{{1}{,}{1}}{,}{{m}}_{{1}{,}{2}}{=}{{n}}_{{1}{,}{2}}{,}{{m}}_{{1}{,}{3}}{=}{{n}}_{{1}{,}{3}}{,}{{m}}_{{2}{,}{1}}{=}{{n}}_{{2}{,}{1}}{,}{{m}}_{{2}{,}{2}}{=}{{n}}_{{2}{,}{2}}{,}{{m}}_{{2}{,}{3}}{=}{{n}}_{{2}{,}{3}}{,}{{m}}_{{3}{,}{1}}{=}{{n}}_{{3}{,}{1}}{,}{{m}}_{{3}{,}{2}}{=}{{n}}_{{3}{,}{2}}{,}{{m}}_{{3}{,}{3}}{=}{{n}}_{{3}{,}{3}}\right\}$ (2)
 > $\mathrm{convert}\left(M=N,\mathrm{listofequations}\right)$
 $\left[{{m}}_{{1}{,}{1}}{=}{{n}}_{{1}{,}{1}}{,}{{m}}_{{2}{,}{1}}{=}{{n}}_{{2}{,}{1}}{,}{{m}}_{{3}{,}{1}}{=}{{n}}_{{3}{,}{1}}{,}{{m}}_{{1}{,}{2}}{=}{{n}}_{{1}{,}{2}}{,}{{m}}_{{2}{,}{2}}{=}{{n}}_{{2}{,}{2}}{,}{{m}}_{{3}{,}{2}}{=}{{n}}_{{3}{,}{2}}{,}{{m}}_{{1}{,}{3}}{=}{{n}}_{{1}{,}{3}}{,}{{m}}_{{2}{,}{3}}{=}{{n}}_{{2}{,}{3}}{,}{{m}}_{{3}{,}{3}}{=}{{n}}_{{3}{,}{3}}\right]$ (3)

When a single matrix is passed, each element is equated to 0 and the related set or list is returned.

 > $\mathrm{convert}\left(M,\mathrm{listofequations}\right)$
 $\left[{{m}}_{{1}{,}{1}}{=}{0}{,}{{m}}_{{1}{,}{2}}{=}{0}{,}{{m}}_{{1}{,}{3}}{=}{0}{,}{{m}}_{{2}{,}{1}}{=}{0}{,}{{m}}_{{2}{,}{2}}{=}{0}{,}{{m}}_{{2}{,}{3}}{=}{0}{,}{{m}}_{{3}{,}{1}}{=}{0}{,}{{m}}_{{3}{,}{2}}{=}{0}{,}{{m}}_{{3}{,}{3}}{=}{0}\right]$ (4)

Converting vectorial equations:

 > $V\left[1\right]≔⟨a,b,c⟩$
 $\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$ (5)
 > $V\left[2\right]≔⟨A,B,C⟩$
 $\left[\begin{array}{c}A\\ B\\ C\end{array}\right]$ (6)
 > $\mathrm{convert}\left(V\left[1\right]=V\left[2\right],\mathrm{setofequations}\right)$
 $\left\{{a}{=}{A}{,}{b}{=}{B}{,}{c}{=}{C}\right\}$ (7)

Vectorial equations with vectors of the Physics package are also handled:

 > $\mathrm{with}\left(\mathrm{Physics}:-\mathrm{Vectors}\right):$$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right):$
 > $\mathrm{A_}≔A\left[x\right]\mathrm{_i}+A\left[y\right]\mathrm{_j}+A\left[z\right]\mathrm{_k}$
 $\stackrel{{\to }}{{A}}{≔}{{A}}_{{x}}{}\stackrel{{\wedge }}{{i}}{+}{{A}}_{{y}}{}\stackrel{{\wedge }}{{j}}{+}{{A}}_{{z}}{}\stackrel{{\wedge }}{{k}}$ (8)
 > $\mathrm{B_}≔B\left[x\right]\mathrm{_i}+B\left[y\right]\mathrm{_j}+b\left[z\right]\mathrm{_k}$
 $\stackrel{{\to }}{{B}}{≔}{{B}}_{{x}}{}\stackrel{{\wedge }}{{i}}{+}{{B}}_{{y}}{}\stackrel{{\wedge }}{{j}}{+}{{b}}_{{z}}{}\stackrel{{\wedge }}{{k}}$ (9)
 > $\mathrm{convert}\left(\mathrm{A_}=\mathrm{B_},\mathrm{setofequations}\right)$
 $\left\{{{A}}_{{x}}{=}{{B}}_{{x}}{,}{{A}}_{{y}}{=}{{B}}_{{y}}{,}{{A}}_{{z}}{=}{{b}}_{{z}}\right\}$ (10)
 > 

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