The class is for algebraic number represented by coefficient of standard basis.
polynomial must be a monic irreducible polynomial defining the number field. type of polynomial must be a list. valuelist is made from integer coefficient and denominator for standard basis.
Ex.1
>>> a = algfield.BasicAlgNumber([[1, 1], 1], [-3, 0, 1]) >>> print a BasicAlgNumber([[1, 1], 1], [-3, 0, 1])
Ex.2
>>> b = algfield.BasicAlgNumber([[0, 1, 1], 2], [-2, 0, 0, 1]) >>> print b BasicAlgNumber([[0, 1, 1], 2], [-2, 0, 0, 1])
integer coefficient and denominator.
integer coefficient of the algebraic number.
denominator of the algebraic number.
defining polynomial of the field including the algebraic number.
degree of the polynomial.
field defined by the polynomial.
Return the inverse of the algebraic number.
Compute the trace of the algebraic number.
Compute the norm of the algebraic number.
Determine whether the algebraic number is an algebraic integer or not.
Change class to MatAlgNumber.
Change class to ApproxAlgNuber with approx.
operator | explanation |
a + b | Return a + b. |
a - b | Return a - b. |
a * b | Return a * b. a must be algebraic number or integer. |
a / b | Return a / b. b must not be zero unit. |
a ** b | Return a ** b. b must be integer. |