The Equate(u,v) command receives the rectangular structures u and v, typically of type list, Array, Matrix or Vector, and returns a list of equations, where the left-hand sides of the equations are taken from u and the right-hand sides from the corresponding components of v. The two input objects, u and v, must have the same shapes and sizes, and if only one is an Array then its indices must start at 1.

Equate can also receive two algebraic structures u and v representing vectors of the Vectors subpackage of the Physics package, in which case the list of equations returned is constructed equating the components of u and v. When u and v are projected into different orthonormal basis, the second one is first reprojected onto the basis of the first one; then the components are equated.

$\mathrm{Equate}\left(\left[1\,2\right]\,⟨a\,b⟩\right)$

$\left[1=a\,2=b\right]$

$\mathrm{Equate}\left(⟨⟨1\,2⟩\|⟨3\,4⟩\|⟨5\,6⟩⟩\,\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\right]\right)$

$\left[1=a\,3=b\,5=c\,2=d\,4=e\,6=f\right]$

$\mathrm{Equate}\left(⟨1\,2\,3⟩\,⟨a\|b\|c⟩\right)$

$\left[1=a\,2=b\,3=c\right]$

$\mathrm{Equate}\left(\mathrm{Array}\left(1..2\,1..2\,\left[\left[a\,b\right]\,\left[c\,d\right]\right]\right)\,\mathrm{Matrix}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\right)\right)$

$\left[a=1\,b=2\,c=3\,d=4\right]$

$\mathrm{Equate}\left(\mathrm{Vector}\left(3\,\left[a\,b\,c\right]\right)\,\mathrm{Vector}\left(3\,\left[1\,2\,3\right]\right)\right)$

$\left[a=1\,b=2\,c=3\right]$

$\mathrm{Equate}\left(\mathrm{Vector}\left(3\,\left[a\,b\,c\right]\right)\,⟨1\,2\,3⟩\right)$

$\left[a=1\,b=2\,c=3\right]$

$\mathrm{Equate}\left(\mathrm{Matrix}\left(2\,2\,\left[\left[a\,b\right]\,\left[c\,d\right]\right]\right)\,⟨⟨1\,2⟩\|⟨3\,4⟩⟩\right)$

$\left[a=1\,b=3\,c=2\,d=4\right]$

$\mathrm{Equate}\left(\mathrm{Array}\left(1..2\,1..2\,\left[\left[a\,b\right]\,\left[c\,d\right]\right]\right)\,⟨⟨1\,2⟩\|⟨3\,4⟩⟩\right)$

$\left[a=1\,b=3\,c=2\,d=4\right]$

$\mathrm{Equate}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\,\mathrm{Array}\left(1..4\,\left[a\,b\,c\,d\right]\right)\right)$

Error, (in Equate) unable to equate these objects

$\mathrm{Equate}\left(\mathrm{Array}\left(-2..1\,\left[1\,2\,3\,4\right]\right)\,\mathrm{Array}\left(1..4\,\left[a\,b\,c\,d\right]\right)\right)$

Error, (in Equate) unable to equate these objects

$\mathrm{with}\left(\mathrm{Physics}:-\mathrm{Vectors}\right)$

$\left[\mathrm{\&x}\,\mathrm{`+`}\,\mathrm{`.`}\,\mathrm{Assume}\,\mathrm{ChangeBasis}\,\mathrm{ChangeCoordinates}\,\mathrm{CompactDisplay}\,\mathrm{Component}\,\mathrm{Curl}\,\mathrm{DirectionalDiff}\,\mathrm{Divergence}\,\mathrm{Gradient}\,\mathrm{Identify}\,\mathrm{Laplacian}\,\nabla \,\mathrm{Norm}\,\mathrm{ParametrizeCurve}\,\mathrm{ParametrizeSurface}\,\mathrm{ParametrizeVolume}\,\mathrm{Setup}\,\mathrm{Simplify}\,\mathrm{`^`}\,\mathrm{diff}\,\mathrm{int}\right]$

$R≔x\mathrm{\_i}\+y\mathrm{\_j}\+z\mathrm{\_k}$

$R≔x\mathrm{\_i}+y\mathrm{\_j}+z\mathrm{\_k}$

$V≔-z\mathrm{\_i}\+\left(y-x\right)\mathrm{\_k}$

$V≔-z\mathrm{\_i}+\left(y-x\right)\mathrm{\_k}$

$\mathrm{Equate}\left(R\,V\right)$

$\left[x=-z\,y=0\,z=y-x\right]$

$C≔\mathrm{\ρ}\mathrm{\_\ρ}\+z\mathrm{\_k}$

$C≔z\mathrm{\_k}+\mathrm{\rho }\mathrm{\_\ρ}$

$S≔r\mathrm{\_r}$

$S≔r\mathrm{\_r}$

$\mathrm{Equate}\left(R\,C\right)$

$\left[x=\cos \left(\mathrm{\phi }\right)\mathrm{\rho }\,y=\sin \left(\mathrm{\phi }\right)\mathrm{\rho }\,z=z\right]$

$\mathrm{Equate}\left(R\,S\right)$

$\left[x=\sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\phi }\right)r\,y=\sin \left(\mathrm{\theta }\right)\sin \left(\mathrm{\phi }\right)r\,z=r\cos \left(\mathrm{\theta }\right)\right]$