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A.1.2 Writing procedures and libraries

The user may add their own commands to the commands already available in SINGULAR by writing SINGULAR procedures. There are basically two kinds of procedures:

  • procedures written in the SINGULAR programming language (which are usually collected in SINGULAR libraries).
  • procedures written in C/C++ (collected in dynamic modules).

At this point, we restrict ourselves to describing the first kind of (library) procedures, which are sufficient for most applications. The syntax and general structure of a library (procedure) is described in Procedures, and Libraries.

The probably most efficient way of writing a new library is to use one of the official SINGULAR libraries, say ring.lib as a sample. On a Unix-like operating system, type LIB "ring.lib"; to get information on where the libraries are stored on your disk.

SINGULAR provides several commands and tools, which may be useful when writing a procedure, for instance, to have a look at intermediate results (see Debugging tools).

If such a libarary should be contributed to SINGULAR some formal requirements are needed:

  • the library header must explain the purpose of the library and (for non-trivial algorithm) a pointer to the algorithm (text book, article, etc.)
  • all global procedures must have a help string and an example which shows its usage.
  • it is strongly recommend also to provide test scripts which test the functionality: one should test the essential functionality of the library/command in a relatively short time (say, in no more than 30s), other tests should check the functionality of the library/command in detail so that, if possible, all relevant cases/results are tested. Nevertheless, such a test should not run longer than, say, 10 minutes.

We give short examples of procedures to demonstrate the following:

  • Write procedures which return an integer (ring independent), see also Milnor and Tjurina number. (Here we restrict ourselves to the main body of the procedures).
    • The procedure milnorNumber must be called with one parameter, a polynomial. The name g is local to the procedure and is killed automatically when leaving the procedure. milnorNumber returns the Milnor number (and displays a comment).
    • The procedure tjurinaNumber has no specified number of parameters. Here, the parameters are referred to by #[1] for the 1st, #[2] for the 2nd parameter, etc. tjurinaNumber returns the Tjurina number (and displays a comment).
    • the procedure milnor_tjurina which returns a list consisting of two integers, the Milnor and the Tjurina number.

  • Write a procedure which creates a new ring and returns data dependent on this new ring (two numbers) and an int. In this example, we also show how to write a help text for the procedure (which is optional, but recommended).

proc milnorNumber (poly g)
   "Milnor number:";

proc tjurinaNumber
   "Tjurina number:";

proc milnor_tjurina (poly f)
   ideal j=jacob(f);
   list L=vdim(std(j)),vdim(std(j+f));

proc real_sols (number b, number c)
"USAGE: real_sols (b,c);  b,c number
ASSUME: active basering has characteristic 0
RETURN: list: first entry is an integer (the number of different real
        solutions). If this number is non-negative, the list has as second
        entry a ring in which the list SOL of real solutions of x^2+bx+c=0
        is stored (as floating point number, precision 30 digits).
NOTE:   This procedure calls laguerre_solve from solve.lib.
  def oldring = basering;  // assign name to the ring active when
                           // calling the procedure
  number disc = b^2-4*c;
  if (disc>0) { int n_of_sols = 2; }
  if (disc==0) { int n_of_sols = 1; }
  string s = nameof(var(1));  // name of first ring variable
  if (disc>=0) {
    execute("ring rinC =(complex,30),("+s+"),lp;");
    if (not(defined(laguerre_solve))) { LIB "solve.lib"; }
    poly f = x2+imap(oldring,b)*x+imap(oldring,c);
                        // f is a local ring-dependent variable
    list SOL = laguerre_solve(f,30);
    export SOL;         // make SOL a global ring-dependent variable
                        // such variables are still accessible when the
                        // ring is among the return values of the proc
    setring oldring;
  else {

// We now apply the procedures which are defined by the
// lines of code above:
ring r = 0,(x,y),ds;
poly f = x7+y7+(x-y)^2*x2y2;

==> Milnor number:
==> 28
==> Tjurina number:
==> 24
milnor_tjurina(f);     // a list containing Milnor and Tjurina number
==> [1]:
==>    28
==> [2]:
==>    24

def L=real_sols(2,1);
L[1];                  // number of real solutions of x^2+2x+1
==> 1
def R1=L[2];
setring R1;
listvar(R1);           // only global ring-dependent objects are still alive
==> // R1                             [0]  *ring
==> // SOL                            [0]  list, size: 2
SOL;                   // the real solutions
==> [1]:
==> -1
==> [2]:
==> -1

setring r;
L[1];                  // number of reals solutions of x^2+x+1
==> 0

setring r;
L[1];                  // number of reals solutions of x^2+x-5
==> 2
def R3=L[2];
setring R3; SOL;       // the real solutions
==> [1]:
==> -2.79128784747792000329402359686
==> [2]:
==> 1.79128784747792000329402359686

Writing a dynamic module is not as simple as writing a library procedure, since it does not only require some knowledge of C/C++, but also about the way the SINGULAR kernel works. See also Dynamic modules.