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content -- the content of a polynomial

Synopsis

Usage:

content f

content(f, x)
Inputs:
- f, a ring element,
- x, a ring element, a variable in the ring of f
Outputs:
- an ideal, the content of a matrix or polynomial

Description

The content is the ideal in the base ring generated by the coefficients.

i1 : R = ZZ[x,y]

o1 = R

o1 : PolynomialRing

i2 : content(4*x + 6*x^5)

o2 = ideal (6, 4)

o2 : Ideal of ZZ

i3 : content(4*x + 6*x^5, x)

o3 = ideal (6, 4)

o3 : Ideal of R

i4 : content(4*x + 6*x^5, y)

             5
o4 = ideal(6x  + 4x)

o4 : Ideal of R

i5 : generator oo

       5
o5 = 6x  + 4x

o5 : R

Code

../../../../../Macaulay2/m2/matrix1.m2:657:37-657:65: --source code:
content(RingElement) := Ideal => (f) -> ideal \\ last \ listForm f
../../../../../Macaulay2/m2/matrix1.m2:658:52-658:96: --source code:
content(RingElement, RingElement) := Ideal => (f,x) -> ideal last coefficients(f, Variables => {x})

See also

exponents -- the exponents of a polynomial
coefficients -- monomials and their coefficients
listForm -- convert to list form
standardForm -- convert to standard form
monomials -- matrix of monomials in a ring element or matrix

Ways to use content :

content(RingElement)
content(RingElement,RingElement)

For the programmer

The object content is a method function.