Difference between revisions of "Factors Command"

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;Factors[ <Polynomial> ]
 
;Factors[ <Polynomial> ]
 
:Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given 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^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 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> ]
 
;Factors[ <Number> ]
Line 14: Line 14:
 
;Factors[ <Polynomial> ]
 
;Factors[ <Polynomial> ]
 
:Returns list of lists ''{factor, exponent}'' such that product of all these factors raised to corresponding exponents equals the given 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}}'', displayed as <math>\begin{pmatrix}
+
:{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}'', displayed as <math>\begin{pmatrix}
x-1&1\\
+
x^4+1&1\\
 +
x^2+1&1\\
 
x+1&1\\
 
x+1&1\\
x^2+1&1\\
+
x-1&1
x^4+1&1
 
 
\end{pmatrix}</math>.</div>}}
 
\end{pmatrix}</math>.</div>}}
 
:{{note|Not all of the factors are irreducible over the reals.}}
 
:{{note|Not all of the factors are irreducible over the reals.}}

Revision as of 12:07, 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^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> ]
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] yields {{2, 10}}, because 1024 = 210.
  • Factors[42] yields {{2, 1}, {3, 1}, {7, 1}}, because 42 = 21 31 71.

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^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> ]
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] yields {{2, 10}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, because 1024 = 210.

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

      \end{pmatrix}
      , because 42 = 21 31 71.
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