purePower -- determine whether a ring element is a pure power of a variable
Synopsis
Usage:
purePower f
Inputs:
f, a ring element, an element of a polynomial ring or quotient of a polynomial ring
Outputs:
a Boolean value, returns true if f is a nonzero power of a variable and false otherwise.
Description
purePower tests a ring element in a polynomial ring or quotient of a polynomial ring to determine whether or not it is nonzero and a power of a variable. purePower is used in the lex-plus-powers (LPP) code.
i1 : R=ZZ/32003[a..c];
i2 : purePower a^4
o2 = true
i3 : purePower (a*b^5)
o3 = false
i4 : purePower (a^3-b^3)
o4 = false
i5 : Q=R/ideal(a^3,a*b^3);
i6 : purePower b^4
o6 = true
i7 : purePower a^3 --false since a^3 is zero in the quotient
o7 = false
See also
LPP -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence
isLPP -- determine whether an ideal is an LPP ideal