Short proofs of ideal membership

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Cites Work

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On the complexity of the generalized MinRank problem
A generalization of the Sherman-Morrison-Woodbury formula
Moore-Penrose inverse in rings with involution
Reverse order law for the Moore-Penrose inverse
Generalized inverses of morphisms with kernels
A new efficient algorithm for computing Gröbner bases \((F_4)\)
Interior-point methods
A survey on signature-based algorithms for computing Gröbner bases
The complexity of the word problems for commutative semigroups and polynomial ideals
Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra
Formally verifying proofs for algebraic identities of matrices
Formal proofs of operator identities by a single formal computation
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
The Moore-Penrose inverses of products and differences of projections in a \(C^*\)-algebra
On the effective Nullstellensatz
Atomic Decomposition by Basis Pursuit
Handbook of Linear Algebra
Heights of varieties in multiprojective spaces and arithmetic Nullstellensatze
Sparse Gröbner bases
Solving Polynomial Equation Systems
Decoding by Linear Programming
Complexity of Membership Problems of Different Types of Polynomial Ideals
Sharp Effective Nullstellensatz
Matching pursuits with time-frequency dictionaries
Entropy-based algorithms for best basis selection
The Complexity of the Ideal Membership Problem for Constrained Problems Over the Boolean Domain
Membership in polynomial ideals over Q is exponential space complete
Compatible rewriting of noncommutative polynomials for proving operator identities
Letterplace
Proof simplification and automated theorem proving
Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane
Certifying operator identities via noncommutative Gröbner bases
Compressed sensing
Finding shortest proofs: An application of linked inference rules
On the complexity of computing Gröbner bases for weighted homogeneous systems
Signature Gröbner bases in free algebras over rings
On the complexity of CSP-based ideal membership problems
Axioms for a theory of signature bases
The Ideal Membership Problem and Abelian Groups
How to Automatise Proofs of Operator Statements: Moore–Penrose Inverse; A Case Study

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