square-free factorization function - Maple Help

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sqrfree - square-free factorization function

Calling Sequence

sqrfree(a)

sqrfree(a, x)

Parameters

a

-

multivariate polynomial or rational function

x

-

name or list or set of names

Description

• 

The sqrfree function computes the square-free factorization of the multivariate polynomial or the rational function a in the variable(s) x over an algebraic number field.

• 

The square-free factorization is returned in the form [u,[[f1,ⅇ1],...,[fn,ⅇn]] such that a=uf1ⅇ1...fnⅇn where fi is primitive and square-free, that is, gcdfi,xfi=1 for all i and gcdfi,fj=1 for all ij hence u is the content(a,x) times a unit.

• 

In the case of two arguments, the second argument x denotes the main variable(s).  In the case of one argument, all the names in the polynomial a are used as variables.

• 

Note that the ei are not necessarily distinct as partial factorizations in the input are preserved as much as possible.

Examples

sqrfree12x3+9x+3

3,x1,1,1+2x,2

(1)

f:=x3yx3x2y2+x2y

f:=x3yx2y2x3+x2y

(2)

sqrfreef,x

y1,x,2,y+x,1

(3)

sqrfreef,y

x2,xy+y2+xy,1

(4)

sqrfreef,x,y

1,y1,1,x,2,y+x,1

(5)

g:=x+y+1expandx+y+12xy333x+6y21

g:=x+y+1x2+2xy+y2+2x+2y+1xy333x+6y21

(6)

sqrfreeg,x,y

3,x+2y7,1,x+y+1,3,xy3,3

(7)

h:=x+y3expandx2y22x2+1

h:=x+y3x62x4y2+x2y4+x42x2y2+y4

(8)

sqrfreeh

1,x+y,1,x2+1,1,y+x,2

(9)

sqrfreeh,y

1x2+1,x+y,1,x+y,2

(10)

See Also

convert/sqrfree, factor, isqrfree, PolynomialTools[Split], Sqrfree


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