Basic Operators

Operator	Argument(s) -> Result(s)	Brief Description
+, -, *	(int,int->int)	usual integer arithmetic operations
-	(int->int)	integral unary minus
^	(int,int->int)	integer exponentiation (whenever result integral)
\, %	(int,int->int)	integer (Euclidian) division and remainder
\%	(int,int->int,int)	Euclidian division with remainder
+, -, \*, /	(rat,rat->rat)	usual rational arithmetic operations
+, -, \*, /	(rat,int->rat)	more efficient in applicable bcases
%	(rat,int->rat)	remainder after removing greatest integer multiple
%	(rat,rat->rat)	remainder after removing greatest integer multiple
-	(rat->rat)	rational unary minus
/	(rat->rat)	rational unary divide (in other words: inverse)
^	(rat,int->rat)	rational exponentiation (whenever result defined)
%	(rat->int,int)	pair of numerator and denominator
+, -	(vec,vec->vec)	addition/subtraction of vectors of equal size
-	(vec->vec)	vector unary minus
*	(vec,int->vec)	scalar multiplication (note the operand order)
\	(vec,int->vec)	scalar division, rounding down
%	(vec,int->vec)	remainder in scalar division
*	(vec,vec->int)	scalar product
+, -	(mat,mat->mat)	matrix addition and subtraction
*	(mat,vec->vec)	matrix-vector product
*	(mat,mat->mat)	matrix-matrix product
*	(vec,mat->mat)	vector-matrix product (vector is transposed)
^	(mat->mat)	(unary use of ^) matrix transposition
^	(vec->mat)	(unary use of ^) (transposed) vector as 1-line matrix
+, -	(mat,int->mat)	addition/subtraction of multiple of identity
+, -	(int,mat->mat)	addition/subtraction from multiple of identity
/	(vec,int->ratvec)	vector division giving rational vector
%	(ratvec->vec,int)	pair of numerator vector and denominator
+, -	(ratvec,ratvec->ratvec)	additive rational vector arithmetic
*, /, %	(ratvec,int->ratvec)	scalar rational vector operations
*, /	(ratvec,rat->ratvec)	scalar rational vector operations
-	(ratvec->ratvec)	unary minus of rational vectors
*	(mat,ratvec->ratvec)	left-multiplication my matrix of ratvec
*	(ratvec,mat->ratvec)	right-multiplication my matrix of ratvec
=, !=	(int->bool)	test for equality/inequality against 0
>=, >	(int->bool)	non-negative, positive (note op. on wrong side)
<=, <	(int->bool)	non-positive, negative (note op. on wrong side)
>, >=, <, <=, =, !=	(int,int->bool)	usual relational operators
=, !=	(rat->bool)	test for equality/inequality against 0/1
>=, >	(rat->bool)	non-negative, positive (note op. on wrong side)
<=, <	(rat->bool)	non-positive, negative (note op. on wrong side)
>, >=, <, <=, =, !=	(rat,rat->bool)	usual relational operators
=, !=	(bool,bool->bool)	Boolean equivalence, inequivalence (xor)
=, !=	(string->bool)	test for being (or not being) the empty string
>, >=, <, <=, =, !=	(string,string->bool)	relational operators
=, !=	(vec->bool)	test for being (or not being) a zero vector
>=, >	(vec->bool)	test for all entries being non-negative/positive
=, !=	(vec,vec->bool)	vector equality and inequality
=, !=	(ratvec->bool)	test for being a (or not) zero rational vector
>=, >	(ratvec->bool)	test for all entries non-negative/positive
=, !=	(ratvec,ratvec->bool)	rational vector equality, inequality
=, !=	(mat->bool)	test for being a (or not) zero matrix
=, !=	(mat,mat->bool)	matrix equality and inequality
#	(string->int)	length of string
#	(vec->int)	number of components of vector
#	(ratvec->int)	number of components of rational vector
#	(mat->int,int)	dimensions (rows, columns) of a matrix
#	([T]->int)	number of components of row (T is any type)
#	(string,string->string)	string concatenation
#	(vec,vec->vec)	concatenation of vectors
#	(vec,int->vec)	append element to a vector
#	(int,vec->vec)	prepend element to a vector
#	([T],[T]->[T])	concatenation of rows (T is any type)
#	([T],T->[T])	append element to a row (T is any type)
#	(T,[T]->[T])	prepend element to a row (T is any type)
#	(int,[vec]->mat)	combine columns of given fixed height into matrix
^	(int,[vec]->mat)	combine rows of given fixed length into matrix