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5.7. List of GEL Operators

As everything in gel is really just an expression, it is really just all connected together with operators. Here is a list of the operators in GEL. 

a;b

The separator, just evaluates both a and b, but returns only the result of b. 

a=b

The assignment operator. This assigns b to a (a must be a valid lvalue) (note however that this operator may be translated to == if used in a place where boolean expression is expected) 

a:=b

The assignment operator. Assigns b to a (a must be a valid lvalue). This is different from = because it never gets translated to a ==. 

|a|

Absolute value or modulus (if a is a complex number).

See Mathworld for more information. 

a^b

Exponentiation, raises a to the bth power. 

a.^b

Element by element exponentiation. Raise each element of a matrix a to the bth power. Or if b is a matrix of the same size as a, then do the operation element by element. If a is a number and b is a matrix then it creates matrix of the same size as b with a raised to all the different powers in b. 

a+b

Addition. Adds two numbers, matrices, functions or strings. If you add a string to anything the result will just be a string. 

a-b

Subtraction. Subtract two numbers, matrices or functions. 

a*b

Multiplication. This is the normal matrix multiplication. 

a.*b

Element by element multiplication if a and b are matrices. 

a/b

Division. 

a./b

Element by element division. 

a\b

Back division. That is this is the same as b/a. 

a.\b

Element by element back division. 

a%b

The mod operator. This does not turn on the modular mode, but just returns the remainder of a/b. 

a.%b

Element by element the mod operator. Returns the remaineder after element by element a./b. 

a mod b

Modular evaluation operator. The expression a is evaluated modulo b. See Section 5.6. Some functions and operators behave differently modulo an integer. 

a!

Factorial operator. This is like 1*...*(n-2)*(n-1)*n. 

a!!

Double factorial operator. This is like 1*...*(n-4)*(n-2)*n. 

a==b

Equality operator (returns true or false). 

a!=b

Inequality operator, returns true if a does not equal b else returns false. 

a<>b

Alternative inequality operator, returns true if a does not equal b else returns false. 

a<=b

Less than or equal operator, returns true if a is less than or equal to b else returns false. 

a>=b

Greater than or equal operator, returns true if a is greater than or equal to b else returns false. 

a<=>b

Comparison operator. If a is equal to b it returns 0, if a is less than b it returns -1 and if a is greater than b it returns 1. 

a and b

Logical and. 

a or b

Logical or. 

a xor b

Logical xor. 

not a

Logical not. 

-a

Negation operator. 

&a

Variable referencing (to pass a reference to something). See Section 6.8. 

*a

Variable dereferencing (to access a referenced varible). See Section 6.8. 

a'

Matrix conjugate transpose. 

a.'

Matrix transpose, does not conjugate the entries. 

a@(b,c)

Get element of a matrix in row b and column c. If b, c are vectors, then this gets the corresponding rows columns or submatrices. 

a@(b,)

Get row of a matrix (or rows if b is a vector). 

a@(b,:)

Same as above. 

a@(,c)

Get column of a matrix (or columns if c is a vector). 

a@(:,c)

Same as above. 

a@(b)

Get an element from a matrix treating it as a vector. This will traverse the matrix row-wise. 

a:b

Build a vector from a to b (or specify a row, column region for the @ operator). For example to get rows 2 to 4 of mamtrix A we could do 

A@(2:4,)
as 2:4 will return a vector [2,3,4]. 

a:b:c

Build a vector from a to c with b as a step. That is for example 

genius> 1:2:9
=
`[1, 3, 5, 7, 9]


(a)i

Make a imaginary number (multiply a by the imaginary). Note that normally the number i is written as 1i. So the above is equal to 

(a)*1i
	     

`a

Quote an identifier so that it doesn't get evaluated. Or quote a matrix so that it doesn't get expanded.

Note

The @() operator makes the : operator most useful. With this you can specify regions of a matrix. So that a@(2:4,6) is the rows 2,3,4 of the column 6. Or a@(,1:2) will get you the first two columns of a matrix. You can also assign to the @() operator, as long as the right value is a matrix that matches the region in size, or if it is any other type of value.

Note

The comparison operators (except for the <=> operator which behaves normally), are not strictly binary operators, they can in fact be grouped in the normal mathematical way, e.g.: (1<x<=y<5) is a legal boolean expression and means just what it should, that is (1<x and x≤y and y<5)

Note

The unitary minus operates in a different fashion depending on where it appears. If it appears before a number it binds very closely, if it appears in front of an expression it binds less than the power and factorial operators. So for example -1^k is really (-1)^k, but -foo(1)^k is really -(foo(1)^k). So be careful how you use it and if in doubt, add parentheses.

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