What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variables

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The documentation for polynomial sequences is here:

http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html

It says

We call a finite list of polynomials a Polynomial Sequence.

To see all the polynomials in the sequence, you can use the list command.

Example.

sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)

This outputs the list of all polynomials in the polynomial sequence.

Note that the representation of F is a string of the list itself if the sequence F has less than 20 elements, while if F has 20 elements or more, a summary is printed.

Example: compare

sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
4
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]

and

sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
20
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables

Note that this information is in the documentation for the _repr_ method of F, which you can access by typing

sage: F._repr_?

See also the source code by typing

sage: F._repr_??