Revision history [back]
 | 1 | initial version |
First note that written as-4536*sqrt(33)+61128, the number is part of Sage's
symbolic ring.
To work with algebraic numbers, the best is to work either
- in a number field,
- in the field of algebraic numbers, QQbar),
- in the field of real algebraic numbers, AA.
Example of working in AA:
sage: a = -4536*sqrt(33)+61128
sage: aa = AA(a)
sage: aa
35070.66383530351?
sage: aa.sqrt()
187.2716311545973?
sage: bb = aa.sqrt()
sage: bb
187.2716311545973?
sage: bb.radical_expression()
42*sqrt(33) - 54
| | 2 | No.2 Revision |
First note that written as-4536*sqrt(33)+61128, the number is part of Sage's
symbolic ring.
To work with algebraic numbers, the best is to work either
- in a number field,
- either
- in a number field,
- in the field of algebraic numbers,
QQbar), -), - in the field of real algebraic numbers,
AA.
Example of working in AA:
sage: a = -4536*sqrt(33)+61128
sage: aa = AA(a)
sage: aa
35070.66383530351?
sage: aa.sqrt()
187.2716311545973?
sage: bb = aa.sqrt()
sage: bb
187.2716311545973?
sage: bb.radical_expression()
42*sqrt(33) - 54
Example of working in a number field:
First we check the approximate value of sqrt(33):
sage: sqrt(33).n()
5.74456264653803
Create an embedded number field:
sage: K.<r33> = NumberField(x^2-33, 5.8)
Check if our number field element is a square:
sage: a = -4536*r33+61128
sage: a.is_square()
True
Take the square root:
sage: a.sqrt()
42*r33 - 54
| | 3 | No.3 Revision |
First note that written as-4536*sqrt(33)+61128, the number is part of Sage's
symbolic ring.
To work with algebraic numbers, the best is to work either
- in a number field,
- in the field of algebraic numbers,
QQbar), - in the field of real algebraic numbers,
AA.
Example of working in AA:
sage: a = -4536*sqrt(33)+61128
sage: aa = AA(a)
sage: aa
35070.66383530351?
sage: aa.sqrt()
187.2716311545973?
sage: bb = aa.sqrt()
sage: bb
187.2716311545973?
sage: bb.radical_expression()
42*sqrt(33) - 54
Example of working in a number field:
First we check the approximate value of sqrt(33):
sage: sqrt(33).n()
5.74456264653803
Create an embedded number field:
sage: K.<r33> = NumberField(x^2-33, 5.8)
Check if our number field element is a square:
sage: a = -4536*r33+61128
sage: a.is_square()
True
Take the square root:
sage: a.sqrt()
42*r33 - 54
Final note: in all cases, the method sqrt will return one of the two square roots.
Keep in mind that there is another one --- it's just the opposite of the one you got.
So if you let b = a.sqrt(), then remember that -b is also a square root of a.
