convert a pair of rectangular objects into a list of equations
list, Array, Matrix, Vector, or algebraic structure representing a vector of the Physics[Vectors] package
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.
This is invalid because the dimensions do not match.
Error, (in Equate) unable to equate these objects
This is invalid because the index origins do not match.
To handle vectors of the Vectors subpackage of Physics, first load Vectors
Equate the components of two vectors
R ≔ x⁢_i+y⁢_j+z⁢_k
V ≔ −z⁢_i+y−x⁢_k
When the two vectors are not projected onto the same orthonormal basis, the second one is reprojected onto the basis of the first one. In the following examples C and S are the same vector as R but expressed in cylindrical and spherical coordinates and corresponding orthonormal bases (see Vectors)
C ≔ ρ⁢_ρ+z⁢_k
S ≔ r⁢_r
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