Stability parameters

Stability function

EXAMPLES:

sage: from msinvar import Stability
sage: z=Stability([1,0]); z
Stability function [[1, 0], [1, 1]]
sage: z([1,2]) #slope
0.333333333333

class msinvar.stability.Stability(a, b=None)

Bases: object

Stability function corresponding to the vectors a, b.

EXAMPLES:

sage: from msinvar import Stability
sage: z=Stability([1,0]); z
Stability function [[1, 0], [1, 1]]
sage: z([1,2]) #slope
0.333333333333
sage: z([1,0],[0,1]) #difference of slopes
1
sage: z.less([1,0],[0,1])
False

slope(d)

Slope of the vector d.

compare(d, e)

Difference of slopes.

has_slope(d, slope)

less(d, e)

Return True if slope(d)<slope(e).

lesseq(d, e)

Return True if slope(d)<=slope(e).

equal(d, e=None)

Return True if slope(d)=slope(e).

dim()

Rank of the lattice.

weight(d)

Return vector w such that w*e<0 iff slope(e)<slope(d).

normalize(d)

Return function f such that f(e)<0 iff slope(e)<slope(d).

randomize()

Generic perturbation of self.

is_generic(prec)

Return True if slope(d)=slope(e) for d,e<=prec implies that d, e are proportional.

static trivial(n)

Return trivial stability of dimension n.

static check(z)

Check if z is a stability. If it is a vector, convert it to a stability.