List of GEL Operators

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

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

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

See Mathworld for more information.

Exponentiation, raises a to the bth power.

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.

Addition. Adds two numbers, matrices, functions or strings. If you add a string to anything the result will just be a string. If one is a square matrix and the other a number, then the number is multiplied by the identity matrix.

Subtraction. Subtract two numbers, matrices or functions.

Multiplication. This is the normal matrix multiplication.

Element by element multiplication if a and b are matrices.

Division. When a and b are just numbers this is the normal division. When they are matrices, then this is equivalent to a*b^-1.

Element by element division. Same as a/b for numbers, but operarates element by element on matrices.

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

Element by element back division.

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

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

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

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

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

Equality operator. Returns true or false depending on a and b being equal or not.

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

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

Less than or equal operator, returns true if a is less than or equal to b else returns false. These can be chained as in a <= b <= c (can also be combined with the less than operator).

Greater than or equal operator, returns true if a is greater than or equal to b else returns false. These can be chained as in a >= b >= c (can also be combine with the greater than operator).

Less than operator, returns true if a is less than or equal to b else returns false. These can be chained as in a < b < c (can also be combine with the less than or equal to operator).

Greater than operator, returns true if a is greater than or equal to b else returns false. These can be chained as in a > b > c (can also be combine with the greater than or equal to operator).

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.

Logical and. Returns true if both a and b are true, else returns false. If given numbers, nonzero numbers are treated as true.

Logical or. Returns true if both a or b are true, else returns false. If given numbers, nonzero numbers are treated as true.

Logical xor. Returns true exactly one of a or b is true, else returns false. If given numbers, nonzero numbers are treated as true.

Logical not. Returns the logical negation of a

Negation operator.

Variable referencing (to pass a reference to something). See the Section called References in the Chapter called Programming with GEL.

Variable dereferencing (to access a referenced variable). See the Section called References in the Chapter called Programming with GEL.

Matrix conjugate transpose.

Matrix transpose, does not conjugate the entries.

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.

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

Same as above.

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

Same as above.

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

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 matrix A we could do

A@(2:4,)
	     

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]

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
	     

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

Swap value of a with the value of b. Currently does not operate on ranges of matrix elements. It returns null. Available from version 1.0.13.

Increment the variable a by 1. If a is a matrix, then increment each element. This is equivalent to a=a+1, but it is somewhat faster. It returns null. Available from version 1.0.13.

Increment the variable a by b. If a is a matrix, then increment each element. This is equivalent to a=a+b, but it is somewhat faster. It returns null. Available from version 1.0.13.