Difference between revisions of "Factors Command"

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:{{example|1=<div>
 
:* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', since <math>1024 = 2^{10}</math>.
 
:* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', since <math>1024 = 2^{10}</math>.
:* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', since <math>42 = 2^1 * 3^1 * 7^1</math>.</div>}}
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:* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', since <math>42 = 2^1・3^1・7^1</math>.</div>}}
 
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}}
 
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}}
 
==CAS Syntax==
 
==CAS Syntax==
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3&1\\
 
3&1\\
 
7&1
 
7&1
\end{pmatrix}</math>, since <math>42 = 2^1 * 3^1 * 7^1</math>.</div>}}
+
\end{pmatrix}</math>, since <math>42 = 2^1・3^1・7^1</math>.</div>}}
 
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}}
 
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}}

Revision as of 09:25, 8 July 2013



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 descending order.
Example:
Factors[x^8 - 1] yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}.
Note: Not all of the factors are irreducible over the reals.
Factors[ <Number> ]
Gives a list of lists of the type {prime, exponent} 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 {{2, 1}, {3, 1}, {7, 1}}, since 42 = 2^1・3^1・7^1.

CAS Syntax

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 descending order.
Example:
Factors[x^8 - 1] yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}, displayed as \begin{pmatrix} x^4+1&1\\ x^2+1&1\\ x+1&1\\ x-1&1

\end{pmatrix}
.
Note: Not all of the factors are irreducible over the reals.
Factors[ <Number> ]
Gives a list of lists of the type {prime, exponent} 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}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, since 1024 = 2^{10}.

    • Factors[42] yields {{2, 1}, {3, 1}, {7, 1}}, displayed as \begin{pmatrix} 2&1\\ 3&1\\ 7&1

      \end{pmatrix}
      , since 42 = 2^1・3^1・7^1.
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