make the initial of a polynomial regular
RegularizeInitial(f, rc, R, 'normalized'='yes')
polynomial of R
regular chain of R
boolean flag (optional)
The command RegularizeInitial(f, rc, R) returns a list of pairs fi,rci where each rci is a regular chain of R and each fi is a polynomial of R.
The set of all the regular chains rci form a decomposition of in_rc in the sense of Kalkbrener.
Each polynomial fi is either constant or its initial is regular modulo rci.
Each polynomial fi is equal to f modulo the saturated ideal of rci.
The function is based on Regularize.
This command is part of the RegularChains package, so it can be used in the form RegularizeInitial(..) only after executing the command with(RegularChains). However, it can always be accessed through the long form of the command by using RegularChains[RegularizeInitial](..).
R ≔ PolynomialRing⁡x,y,z
R ≔ polynomial_ring
T ≔ Empty⁡R
T ≔ regular_chain
T ≔ Chain⁡z+1⁢z+2,y2+z,x−z⁢x−y,T,R
rtl ≔ RegularizeInitial⁡z+1⁢x3+5,T,R
rtl ≔ x3⁢z+x3+5⁢z+5,regular_chain,5⁢z+5,regular_chain
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