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RegularChains

  

MainDegree

  

main degree of a nonconstant polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MainDegree(p, R)

Parameters

R

-

polynomial ring

p

-

polynomial of R

Description

• 

The function call MainDegree(p,R) returns the main degree of p,   that is, the degree of p with respect to its main variable.

• 

It is assumed that p is a nonconstant polynomial.

• 

This command is part of the RegularChains package, so it can be used in the form MainDegree(..) only after executing the command with(RegularChains). However, it can always be accessed through the long form of the command by using RegularChains[MainDegree](..).

Examples

withRegularChains:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

py+1x3+z+4x+3

p:=y+1x3+z+4x+3

(2)

MainVariablep,R

x

(3)

Initialp,R

y+1

(4)

MainDegreep,R

3

(5)

Rankp,R

x3

(6)

Tailp,R

xz+4x+3

(7)

Change the ordering of the variable.

RPolynomialRingz,y,x

R:=polynomial_ring

(8)

pexpandy+1x3+z+4x+3

p:=x3y+x3+xz+4x+3

(9)

MainVariablep,R

z

(10)

Initialp,R

x

(11)

MainDegreep,R

1

(12)

Rankp,R

z

(13)

Tailp,R

x3y+x3+4x+3

(14)

Set the characteristic to 3.

RPolynomialRingz,y,x,3

R:=polynomial_ring

(15)

px+y3z3+3z2+2z+y+4

p:=x+y3z3+3z2+2z+y+4

(16)

MainVariablep,R

z

(17)

Initialp,R

x3+y3

(18)

MainDegreep,R

3

(19)

Rankp,R

z3

(20)

Tailp,R

y+2z+1

(21)

See Also

Initial

MainVariable

PolynomialRing

Rank

RegularChains

Separant

Tail

 


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