# Singular

### 4.6.2 int expressions

An int expression is:

1. a sequence of digits (if the number represented by this sequence is too large to fit into the range of integers it is automatically converted to the type number, if a basering is defined)
2. an identifier of type int
3. a function returning int
4. an expression involving ints and the arithmetic operations `+`, `-`, `*`, `div` (`/`), `%` (`mod`), or `^`
5. a boolean expression
6. a type cast to int

Note: Variables of type int represent the compiler integers and are, therefore, limited in their range (see Limitations). If this range is too small the expression must be converted to the type number over a ring with characteristic 0.

Example:

 ```12345678901; // too large ==> 12345678901 typeof(_); ==> bigint ring r=0,x,dp; 12345678901; ==> 12345678901 typeof(_); ==> bigint // Note: 11*13*17*100*200*2000*503*1111*222222 // returns a machine integer: 11*13*17*100*200*2000*503*1111*222222; ==> // ** int overflow(*), result may be wrong ==> // ** int overflow(*), result may be wrong ==> // ** int overflow(*), result may be wrong ==> // ** int overflow(*), result may be wrong ==> -1875651584 // using the type cast number for a greater allowed range number(11)*13*17*100*200*2000*503*1111*222222; ==> 12075748128684240000000 ring rp=32003,x,dp; 12345678901; ==> 12345678901 typeof(_); ==> bigint intmat m[2][2] = 1,2,3,4; m; ==> 1,2, ==> 3,4 m[2,2]; ==> 4 typeof(_); ==> int det(m); ==> -2 m[1,1] + m[2,1] == trace(m); ==> 0 ! 0; ==> 1 1 and 2; ==> 1 intvec v = 1,2,3; def d =transpose(v)*v; // scalarproduct gives an 1x1 intvec typeof(d); ==> intvec int i = d[1]; // access the first (the only) entry in the intvec ring rr=31,(x,y,z),dp; poly f = 1; i = int(f); // cast to int // Integers may be converted to constant polynomials by an assignment, poly g=37; // define the constant polynomial g equal to the image of // the integer 37 in the actual coefficient field, here it equals 6 g; ==> 6 ```