Singular Manual: Type conversion and casting

3.5.5 Type conversion and casting

Type conversion

Assignments convert the type of the right-hand side to the type of the left-hand side of the assignment, if possible. Operators and functions which require certain types of operands can also implicitly convert the type of an expression. It is, for example, possible to multiply a polynomial by an integer because the integer is automatically converted to a polynomial. Type conversions do not act transitively. Possible conversions are:

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

intvec ==> intmat

poly ==> ideal

bigint ==> ideal

int ==> ideal

intmat ==> matrix

ideal ==> matrix

module ==> matrix

number ==> matrix

poly ==> matrix

vector ==> matrix

bigint ==> matrix

int ==> matrix

intvec ==> matrix

ideal ==> module

matrix ==> module

vector ==> module

bigint ==> number

int ==> number

number ==> poly

bigint ==> poly

int ==> poly

list ==> resolution

poly ==> vector (p ==> p*gen(1))

bigint ==> vector

int ==> vector (i ==> i*gen(1))

int ==> bigint

int ==> intvec

string ==> link

resolution ==> list

intvec ==> bigintvec

Type casting

An expression can be casted to another type by using a type cast expression:
type ( expression ).

Possible type casts are:

to from

bigint expression int, number, poly

bigintvec expression int, bigint

ideal expression lists of int, number, poly

ideal int, matrix, module, number, poly, vector

int number, poly

intvec expression lists of int, intmat, bigintvec

intmat intvec (see intmat type cast)

list expression lists of any type

matrix module, ideal, vector, matrix.
There are two forms to convert something to a matrix: if matrix( expression ) is used then the size of the matrix is determined by the size of expression.
But matrix( expression , m , n ) may also be used - the result is a $m \times n$ matrix (see matrix type cast)

module expression lists of int, number, poly, vector

module ideal, matrix, vector

number poly

poly int, number

ring list (the inverse of ringlist)

string any type (see string type cast)

Example:

ring r=0,x,(c,dp); number(3x); ==> 0 number(poly(3)); ==> 3 ideal i=1,2,3,4,5,6; print(matrix(i)); ==> 1,2,3,4,5,6 print(matrix(i,3,2)); ==> 1,2, ==> 3,4, ==> 5,6 vector v=[1,2]; print(matrix(v)); ==> 1, ==> 2 module(matrix(i,3,2)); ==> _[1]=[1,3,5] ==> _[2]=[2,4,6] // generators are columns of a matrix

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