How expressions are evaluated

Some computer algebra systems evaluate an expression over and over until it stops changing. Eigenmath does not work that way. Eigenmath evaluates an expression once and then returns the result. For example,

Enter
	A = B
	B = C
	A

Result
	B

In the above example the symbol A evaluates to B and then stops. B is not converted to C. However, the eval function can be used to do another evaluation.

Enter
	eval(A)

Result
	C

Here A evaluates to B then the eval function evaluates B and returns C.

Although it is rarely needed, the eval function can be applied multiple times.

Enter
	C = D
	eval(eval(A))

Result
	D

Here is a more practical example of when to use eval. Suppose a general electromagnetic field tensor is defined.

Enter
	F = ((0,EX,EY,EZ),(EX,0,BZ,-BY),(EY,-BZ,0,BX),(EZ,BY,-BX,0))

Next, the components of the tensor are defined.

Enter
	EX = sin(z - t)
	EY = 0
	EZ = 0

	BX = 0
	BY = sin(z - t)
	BZ = 0

Although the components have been defined, the symbol F has not changed.

Enter
	F

Result
	 0    EX    EY    EZ

	EX     0    BZ    -BY

	EY    -BZ    0    BX

	EZ    BY    -BX    0

The components of F can be updated by using eval.

Enter
	F = eval(F)
	F

Result
	     0        -sin(t - z)        0             0

	-sin(t - z)        0             0        sin(t - z)

	     0             0             0             0

	     0        -sin(t - z)        0             0

So, a general rule of thumb is to use eval when the definition of a symbol changes.