##  [S-Polynomial](/s-polynomial) 

  ##  [S-Polynomial](https://algebra.quantumdictionary.io/s-polynomial-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For two polynomials f and g with leading terms lt(f) and lt(g), the S-polynomial is the combination S(f,g) = (lcm(lt(f),lt(g))/lt(f)) * f - (lcm(lt(f),lt(g))/lt(g)) * g that cancels the leading terms; it measures the compatibility of leading terms in Gröbner-basis computations.