Special rings

Some base rings in which our invariants take values

EXAMPLES:

sage: from msinvar.rings import RF
sage: R=RF('u,v')
sage: R.inject_variables(verbose=False)
sage: (u-v).adams(2)/(u+v)
u - v

class msinvar.rings.RationalFunctionField(vars='y', base=Rational Field)

Bases: sage.rings.fraction_field.FractionField_generic

Field of rational functions in several variables, meaning fractions P/Q, where P, Q are polynomials in several variables.

EXAMPLES:

sage: from msinvar.rings import RF
sage: R=RF(); R
Field of Rational Functions in y
sage: y=R.gen()
sage: f=(1-y)**3/(1+y)**2; f
(-y^3 + 3*y^2 - 3*y + 1)/(y^2 + 2*y + 1)
sage: factor(f)
(-1) * (y + 1)^-2 * (y - 1)^3
sage: f.adams(2)
(-y^6 + 3*y^4 - 3*y^2 + 1)/(y^4 + 2*y^2 + 1)

sage: R=RF('x,y'); R
Field of Rational Functions in x, y
sage: R.inject_variables(verbose=False)
sage: f=(1-y**2)**5/(1-y)**5*(x-y)
sage: f.factor()
(-1) * (-x + y) * (y + 1)^5

symbolic(f)

Symbolic expression of a given rational function f.

msinvar.rings.RF

alias of msinvar.rings.RationalFunctionField

class msinvar.rings.RationalFunction

Bases: sage.rings.fraction_field_element.FractionFieldElement

Element class for the parent class RationalFunctionField.

root_vars(k=2)

See root_vars().

simp()

msinvar.rings.root_vars(f, k=2)

Substitute every variable x in a fraction f by x^(1/k).

class msinvar.rings.SR1(vars)

Bases: sage.symbolic.ring.SymbolicRing

ngens()

Return the number of variables.

gen(i=0)

Return the i-th variable.

variable_names()

Return the tuple of all names of variables.