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Equate

convert a pair of rectangular objects into a list of equations

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Equate(u, v)

Parameters

u

-

list, Array, Matrix, Vector, or algebraic structure representing a vector of the Physics[Vectors] package

v

-

list, Array, Matrix, Vector, or algebraic structure representing a vector of the Physics[Vectors] package

Description

• 

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.

Examples

Equate1,2,a,b

1=a,2=b

(1)

Equate1,2|3,4|5,6,a,b,c,d,e,f

1=a,3=b,5=c,2=d,4=e,6=f

(2)

Equate1,2,3,a|b|c

1=a,2=b,3=c

(3)

EquateArray1..2,1..2,a,b,c,d,Matrix1,2,3,4

a=1,b=2,c=3,d=4

(4)

EquateVector3,a,b,c,Vector3,1,2,3

a=1,b=2,c=3

(5)

EquateVector3,a,b,c,1,2,3

a=1,b=2,c=3

(6)

EquateMatrix2,2,a,b,c,d,1,2|3,4

a=1,b=3,c=2,d=4

(7)

EquateArray1..2,1..2,a,b,c,d,1,2|3,4

a=1,b=3,c=2,d=4

(8)

This is invalid because the dimensions do not match.

Equate1,2,3,4,Array1..4,a,b,c,d

Error, (in Equate) unable to equate these objects

This is invalid because the index origins do not match.

EquateArray2..1,1,2,3,4,Array1..4,a,b,c,d

Error, (in Equate) unable to equate these objects

To handle vectors of the Vectors subpackage of Physics, first load Vectors

withPhysics:-Vectors

&x,`+`,`.`,ChangeBasis,ChangeCoordinates,Component,Curl,DirectionalDiff,Divergence,Gradient,Identify,Laplacian,Nabla,Norm,Setup,diff

(9)

Equate the components of two vectors

Rx_i+y_j+z_k

R:=_ix+_jy+_kz

(10)

Vz_i+yx_k

V:=z_i+yx_k

(11)

EquateR,V

x=z,y=0,z=yx

(12)

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)

Cρ_ρ+z_k

C:=_kz+_ρρ

(13)

Sr_r

S:=r_r

(14)

EquateR,C

x=ρcosφ,y=ρsinφ,z=z

(15)

EquateR,S

x=rsinθcosφ,y=rsinθsinφ,z=rcosθ

(16)

See Also

Array

convert

Matrix

Physics/Vectors

Vector

 


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