Overview "Algorithmic Task" (199 entries)

• ➔ Boundary Value Problem
• ➔ Combined State and Parameter Reduction
• ➔ Compute a graded (and minimal) free resolution of a finitely generated graded R-module
• ➔ Compute a Gröbner basis of a submodule U⊂R^t with respect to a global module order
• ➔ Compute a Gröbner basis of an ideal from generators using S-polynomials and reductions
• ➔ Compute a minimal primary decomposition of a monomial ideal
• ➔ Compute a normal form NF(v;G) in a free module R^t with respect to a module term order and generators G
• ➔ Compute a presentation of subquot(A,B) = (im(A)+im(B))/im(B) as a cokernel
• ➔ Compute a primary decomposition of a general (not necessarily monomial) ideal in K[x1,…,xn]
• ➔ Compute an irredundant irreducible decomposition of a monomial ideal
• ➔ Compute generators of the kernel of a matrix over a polynomial ring using Gröbner/syzygy techniques
• ➔ Compute Hilbert series and Hilbert polynomial (and derive dimension, degree, genus) from a graded free resolution
• ➔ Compute Hom_R(M,N) (and graded pieces) from presentations via kernel/image operations
• ➔ Compute the greatest common divisor of two integers and Bézout representation
• ➔ Compute the Hermite normal form of a matrix over a principal ideal domain