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Hi there!

Concerning "slowness of the interface": That ist a general problem for the pexpect-interfaces. The idea of these interfaces is that Sage pretends to be a user who is interactively working with a GAP/Singular/Magma/... session. So, Sage sends strings that GAP/Singular/Magma interpretes as commands; then Sage waits for the result; when they appear, the strings printed by GAP/Singular/Magma are transferred back to Sage and interpreted.

Of course, this has one big disadvantage: Communication with a sub-process by ascii strings and parsing of printed results has a huge overhead. Therefore, when using such pexpect interfaces, it is sometimes needed to do, for example, a loop in Singular, even though a loop in Sage (using Cython, at least) is much faster.

I give you some examples using the Singular pexpect interface:

sage: P.<x,y,z> = QQ[]
sage: sP = singular(P)
sage: M = singular.matrix(100,100,0)
sage: def test1(M):
....:     for i in range(1,101):
....:         for j in range(1,101):
....:             M[i,j] = singular(i)*singular(j)
sage: def test2(M):
....:     for i in range(1,101):
....:         for j in range(1,101):
....:             M[i,j] = i*j
sage: def test3(M):
....:     singular.eval('int i')
....:     singular.eval('int j')
....:     singular.eval('for (i=1;i<=100;i++){for (j=1;j<=100;j++){%s[i,j]=i*j;}}'

The three functions are equivalent:

sage: M = singular.matrix(100,100,0)
sage: test1(M)
sage: N = singular.matrix(100,100,0)
sage: test2(N)
sage: O = singular.matrix(100,100,0)
sage: test3(O)
sage: list(M)==list(N)==list(O)

However the running times are vastly different, since the first two functions use the interface very inefficiently:

sage: M = singular.matrix(100,100,0)
sage: %time test1(M)
CPU times: user 8.50 s, sys: 1.96 s, total: 10.46 s
Wall time: 10.57 s
sage: M = singular.matrix(100,100,0)
sage: %time test2(M)
CPU times: user 4.44 s, sys: 1.06 s, total: 5.50 s
Wall time: 5.65 s
sage: M = singular.matrix(100,100,0)
sage: %time test3(M)
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.14 s

The overhead of a pexpect interface can be completely avoided by using a C library instead. In the case of Singular, such library is available: libSingular. But, as Volker said, LibGAP is not totally ready, yet.

After stating so many negative things about pexpect, you might wonder why it exists. In fact, the pexpect approach has at least two advantages:

  • The same interface (after modifying certain details: "What is the prompt?", "How is equality tested?" and so on) can be used for interacting with any command line program. In particular, we can offer a pexpect interface to Magma and Maple, but it would be illegal to include them in Sage as C libraries
  • It gives you full access to all features of a program. For example, libSingular currently only covers the commutative polynomial rings in Singular. If you want to use non-commutative g-algebras, you currently have to use the pexpect interface. That will soon change, though, by trac ticket #4539.