How do I create new intrinsics in MAGMA (computer algebra system)?

Question

I am having trouble creating intrinsics in MAGMA. For example, the following code in MAGMA:

intrinsic Square(x::FldComElt) -> FldComElt
{Returns the square of x (x^2).}
return x^2;
end intrinsic;

produced the following error:

User error: Illegal intrinsic

I don't understand the error as to why this is an illegal intrinsic. Can someone help me to create intrinsics in MAGMA?

For example, the following code in MAGMA:

intrinsic Square(x::FldComElt) -> FldComElt
{Returns the square of x (x^2).}
return x^2;
end intrinsic;
Square(12);

produced the following errors in output:

User error: Illegal intrinsic

User error: Identifier 'Square' has not been declared or assigned

rather than the following output:

144

Can this error be fixed?

Answer 1

Intrinsics should be defined in a package file, and imported. For details, see http://magma.maths.usyd.edu.au/magma/handbook/text/24#164

In your example, the code looks good, I would just change 'FldComElt' to 'RngIntElt' in order to square the integer 12.

Save lines 1--4 of your code (the intrinsic definition) as a .m file. In the same directory, if you call

Attach("example.m");
Square(12);

you should get output 144.

Note: a) this cannot be done in the MAGMA online calculator, as you need directories; b) your example would be better suited as a function:

function Square(x)
// Returns the square of x (x^2).
return x^2;
end function;

Square(12);

so no extra file would be necessary (and the online calculator works fine). However, if you are creating and sharing detailed routines, intrinsics are the way to go.