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).

$M,N≔\mathrm{Matrix}\left(3\,\mathrm{symbol}=m\right),\mathrm{Matrix}\left(3\,\mathrm{symbol}=n\right)$

$M,N≔\left[\begin{array}{ccc}{m}_{1,1}& m_{1,2}& m_{1,3}\\ m_{2,1}& m_{2,2}& m_{2,3}\\ m_{3,1}& m_{3,2}& m_{3,3}\end{array}\right],\left[\begin{array}{ccc}{n}_{1,1}& n_{1,2}& n_{1,3}\\ n_{2,1}& n_{2,2}& n_{2,3}\\ n_{3,1}& n_{3,2}& n_{3,3}\end{array}\right]$

$\mathrm{convert}\left(M=N\,\mathrm{setofequations}\right)$

$\left\{m_{1,1}=n_{1,1}\,m_{1,2}=n_{1,2}\,m_{1,3}=n_{1,3}\,m_{2,1}=n_{2,1}\,m_{2,2}=n_{2,2}\,m_{2,3}=n_{2,3}\,m_{3,1}=n_{3,1}\,m_{3,2}=n_{3,2}\,m_{3,3}=n_{3,3}\right\}$

$\mathrm{convert}\left(M=N\,\mathrm{listofequations}\right)$

$\left[m_{1,1}=n_{1,1}\,m_{2,1}=n_{2,1}\,m_{3,1}=n_{3,1}\,m_{1,2}=n_{1,2}\,m_{2,2}=n_{2,2}\,m_{3,2}=n_{3,2}\,m_{1,3}=n_{1,3}\,m_{2,3}=n_{2,3}\,m_{3,3}=n_{3,3}\right]$

$\mathrm{convert}\left(M\,\mathrm{listofequations}\right)$

$\left[m_{1,1}=0\,m_{1,2}=0\,m_{1,3}=0\,m_{2,1}=0\,m_{2,2}=0\,m_{2,3}=0\,m_{3,1}=0\,m_{3,2}=0\,m_{3,3}=0\right]$

$V\left[1\right]≔⟨a\,b\,c⟩$

$V_1≔\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$

$V\left[2\right]≔⟨A\,B\,C⟩$

$V_2≔\left[\begin{array}{c}A\\ B\\ C\end{array}\right]$

$\mathrm{convert}\left(V\left[1\right]=V\left[2\right]\,\mathrm{setofequations}\right)$

$\left\{a=A\,b=B\,c=C\right\}$

$\mathrm{with}\left(\mathrm{Physics}:-\mathrm{Vectors}\right)\:$$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)\:$

$\mathrm{A\_}≔A\left[x\right]\mathrm{\_i}+A\left[y\right]\mathrm{\_j}+A\left[z\right]\mathrm{\_k}$

$\overrightarrow{A}≔A_x\stackrel{\wedge }{i}+A_y\stackrel{\wedge }{j}+A_z\stackrel{\wedge }{k}$

$\mathrm{B\_}≔B\left[x\right]\mathrm{\_i}+B\left[y\right]\mathrm{\_j}+b\left[z\right]\mathrm{\_k}$

$\overrightarrow{B}≔B_x\stackrel{\wedge }{i}+B_y\stackrel{\wedge }{j}+b_z\stackrel{\wedge }{k}$

$\mathrm{convert}\left(\mathrm{A\_}=\mathrm{B\_}\,\mathrm{setofequations}\right)$

$\left\{A_x=B_x\,A_y=B_y\,A_z=b_z\right\}$