Difference between revisions of "Factors Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=4.0}}</noinclude> | <noinclude>{{Manual Page|version=4.0}}</noinclude> | ||
{{command|function}} | {{command|function}} | ||
| − | ;Factors[ <Polynomial> ]:Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given polynomial. | + | ;Factors[ <Polynomial> ] |
| + | :Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given polynomial. | ||
:{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}''.</div>}} | :{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}''.</div>}} | ||
:{{note|Not all of the factors are irreducible over the reals.}} | :{{note|Not all of the factors are irreducible over the reals.}} | ||
| − | ;Factors[ <Number> ]:Returns list of lists ''{prime,exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | + | ;Factors[ <Number> ] |
| + | :Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | ||
| + | :{{example|1=<div> | ||
| + | :* <code>Factors[1024]</code> returns ''<nowiki>{{2,10}}</nowiki>'', because ''1024 = 2<sup>10</sup>''. | ||
| + | :* <code>Factors[42]</code> returns ''{{2, 1}, {3, 1}, {7, 1}}'', because ''42 = 2<sup>1</sup> 3<sup>1</sup> 7<sup>1</sup>''.</div>}} | ||
| + | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | ||
| + | ==CAS Syntax== | ||
| + | ;Factors[ <Polynomial> ] | ||
| + | :Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given polynomial. | ||
| + | :{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}''.</div>}} | ||
| + | :{{note|Not all of the factors are irreducible over the reals.}} | ||
| + | ;Factors[ <Number> ] | ||
| + | :Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | ||
:{{example|1=<div> | :{{example|1=<div> | ||
:* <code>Factors[1024]</code> returns ''<nowiki>{{2,10}}</nowiki>'', because ''1024 = 2<sup>10</sup>''. | :* <code>Factors[1024]</code> returns ''<nowiki>{{2,10}}</nowiki>'', because ''1024 = 2<sup>10</sup>''. | ||
:* <code>Factors[42]</code> returns ''{{2, 1}, {3, 1}, {7, 1}}'', because ''42 = 2<sup>1</sup> 3<sup>1</sup> 7<sup>1</sup>''.</div>}} | :* <code>Factors[42]</code> returns ''{{2, 1}, {3, 1}, {7, 1}}'', because ''42 = 2<sup>1</sup> 3<sup>1</sup> 7<sup>1</sup>''.</div>}} | ||
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | ||
Revision as of 12:09, 23 August 2011
- Factors[ <Polynomial> ]
- Returns list of lists {factor,exponent} such that product of all these factors raised to corresponding exponents equals the given polynomial.
- Example:
Factors[x^8 - 1]yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.
- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Returns list of lists {prime, exponent} such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order.
- Example:
Factors[1024]returns {{2,10}}, because 1024 = 210.Factors[42]returns {{2, 1}, {3, 1}, {7, 1}}, because 42 = 21 31 71.
Note: See also PrimeFactors Command and Factor Command.
CAS Syntax
- Factors[ <Polynomial> ]
- Returns list of lists {factor,exponent} such that product of all these factors raised to corresponding exponents equals the given polynomial.
- Example:
Factors[x^8 - 1]yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.
- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Returns list of lists {prime, exponent} such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order.
- Example:
Factors[1024]returns {{2,10}}, because 1024 = 210.Factors[42]returns {{2, 1}, {3, 1}, {7, 1}}, because 42 = 21 31 71.
Note: See also PrimeFactors Command and Factor Command.
