Difference between revisions of "Factors Command"
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
− | ;Factors | + | ;Factors( <Polynomial> ) |
:Gives a list of lists of the type ''{factor, exponent}'' such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in ascending order. | :Gives a list of lists of the type ''{factor, exponent}'' such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in ascending order. | ||
:{{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| 1=Not all of the factors are irreducible over the reals.}} | :{{note| 1=Not all of the factors are irreducible over the reals.}} | ||
− | ;Factors | + | ;Factors( <Number> ) |
:Gives matrix of the type <math>\left( \begin{array}{} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) </math> such that the product of all these primes raised to the power of the corresponding ''exponents'' equals the given number. The primes are sorted in ascending order. | :Gives matrix of the type <math>\left( \begin{array}{} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) </math> such that the product of all these primes raised to the power of the corresponding ''exponents'' equals the given number. The primes are sorted in ascending order. | ||
Revision as of 17:15, 7 October 2017
- Factors( <Polynomial> )
- Gives a list of lists of the type {factor, exponent} such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in ascending order.
- 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> )
- Gives matrix of the type \left( \begin{array}{} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order.
- Example:
Factors[1024]
yields ( 2 10 ), since 1024 = 2^{10}.Factors[42]
yields \left( \begin{array}{} 2 & 1 \\ 3 & 1 \\7 & 1 \\ \end{array} \right) , since 42 = 2^1・3^1・7^1.
Note: See also PrimeFactors Command and Factor Command.
Note: In the CAS View undefined variables can be used as input and the results are returned as proper matrices.
- Example:
Factors[a^8 - 1]
yields \left( \begin{array}{} a - 1 & 1 \\ a +1 & 1 \\a^2 + 1& 1 \\a^4 + 1& 1 \\ \end{array} \right).