# Singular

### 4.16.2 poly expressions

A polynomial expression is (optional parts in square brackets):

1. a monomial (there are NO spaces allowed inside a monomial)
 ``` [coefficient] ring_variable [ exponent] [ring_variable [exponent] ...]. ```
Monomials which contain an indexed ring variable must be built from `ring_variable` and `coefficient` with the operations `*` and `^`
2. an identifier of type poly
3. a function returning poly
4. polynomial expressions combined by the arithmetic operations `+`, `-`, `*`, `/`, or `^`
5. an int expression (see Type conversion and casting)
6. a type cast to poly

Example:

 ```ring S=0,(x,y,z,a(1)),dp; 2x, x3, 2x2y3, xyz, 2xy2; // are monomials 2*x, x^3, 2*x^2*y^3, x*y*z, 2*x*y^2; // are poly expressions 2*a(1); // is a valid polynomial expression (a(1) is a name of a variable), // but not 2a(1) (is a syntax error) 2*x^3; // is a valid polynomial expression equal to 2x3 (a valid monomial) // but not equal to 2x^3 which will be interpreted as (2x)^3 // since 2x is a monomial ring r=0,(x,y),dp; poly f = 10x2y3 +2x2y2-2xy+y -x+2; lead(f); ==> 10x2y3 leadmonom(f); ==> x2y3 simplify(f,1); // normalize leading coefficient ==> x2y3+1/5x2y2-1/5xy-1/10x+1/10y+1/5 poly g = 1/2x2 + 1/3y; cleardenom(g); ==> 3x2+2y int i = 102; poly(i); ==> 102 typeof(_); ==> poly ```

### Misc 