Monic polynomial
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Revision 6848
10/7/2026, 3:58:16 PM · Ancient Tree
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Revision 6847
10/7/2026, 3:57:56 PM · Ancient Tree
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10/7/2026, 3:57:54 PM · Ancient Tree
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Let $R$ be a [[Commutative ring|commutative ring]].##### Formal definitionA monic [[Polynomial|polynomial]] $P(X):=\sum_{n=0}^da_n X^n\in R[X]$ of degree $d$ is a polynomial of degree $d$ such that its dominant coefficient $a_{d}$ is $1$.A monic polynomial is a [[Polynôme|polynomial]] whose coefficient of highest degree is equal to $1$. ##### Examples : - $X^3-2X+5$ is a monic polynomial, while $2X^3-X+1$ is not. ##### Remarks- If $K$ is a field and $P\in K[X] /\{0\}$, then one can obtain a monic polynomial by dividing $P$ by its coefficient of highest degree.Revision 6844
10/7/2026, 3:57:35 PM · Ancient Tree
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Revision 6843
10/7/2026, 3:56:57 PM · Ancient Tree
Concept marked usable
Revision 572
7/23/2026, 2:54:00 PM · Ancient Tree
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Revision 571
7/23/2026, 2:53:41 PM · Ancient Tree
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Let $R$ be a [[Commutative ring|commutative ring]].A monic [[Polynomial|polynomial]] $P(X):=\sum_{n=0}^da_n X^d\in R[X]$ of degree $d$ is a polynomial of degree $d$ such that its dominant coefficient $a_{d}$ is $1$.A monic [[Polynomial|polynomial]] $P(X):=\sum_{n=0}^da_n X^n\in R[X]$ of degree $d$ is a polynomial of degree $d$ such that its dominant coefficient $a_{d}$ is $1$.Revision 570
7/23/2026, 2:53:13 PM · Ancient Tree
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This older revision predates detailed metadata tracking.
Revision 567
7/23/2026, 2:34:40 PM · Sequoia
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Compare with revision 5662 changed lines
Let $R$ be an [[integer domain|integer domain]].Let $R$ be a [[Commutative ring|commutative ring]].A monic [[Polynomial|polynomial]] $P(X):=\sum_{n=0}^da_n X^d\in R[X]$ of degree $d$ is a polynomial of degree $d$ such that its dominant coefficient $a_{d}$ is $1$.Revision 566
7/23/2026, 2:33:20 PM · Sequoia
Concept created
Let $R$ be an [[integer domain|integer domain]].
A monic [[Polynomial|polynomial]] $P(X):=\sum_{n=0}^da_n X^d\in R[X]$ of degree $d$ is a polynomial of degree $d$ such that its dominant coefficient $a_{d}$ is $1$.