M2SingularBook -- Macaulay2 examples for the Singular book

M2SingularBook consists of Macaulay2 translations of the examples in the book A Singular introduction to commutative algebra

Each example is numbered as it is in Greuel and Pfister's book. Links to Macaulay2 routines and concepts are also provided.

Macaulay2 implementation bugs and problems

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Chapter 1

• Singular Book 1.1.8 -- computation in fields
• Singular Book 1.1.9 -- computation in polynomial rings
• Singular Book 1.1.10 -- methods for creating ring maps
• Singular Book 1.2.3 -- leading data
• Singular Book 1.2.13 -- monomial orderings
• Singular Book 1.3.3 -- properties of ring maps
• Singular Book 1.3.13 -- computation in quotient rings
• Singular Book 1.3.15 -- computing with radicals
• Singular Book 1.4.9 -- global versus local rings
• Singular Book 1.5.10 -- realization of rings
• Singular Book 1.6.13 -- normal form
• Singular Book 1.7.10 -- standard bases
• Singular Book 1.7.12 -- highest corner
• Singular Book 1.8.1 -- ideal membership
• Singular Book 1.8.2 -- linear combination of ideal members
• Singular Book 1.8.4 -- elimination of variables
• Singular Book 1.8.6 -- Zariski closure of the image
• Singular Book 1.8.7 -- solving equations
• Singular Book 1.8.9 -- radical membership
• Singular Book 1.8.11 -- intersection of ideals
• Singular Book 1.8.13 -- quotient of ideals
• Singular Book 1.8.15 -- saturation
• Singular Book 1.8.18 -- kernel of a ring map
• Singular Book 1.8.19 -- algebraic dependence
• Singular Book 1.8.20 -- subalgebra membership

Chapter 2

• Singular Book 2.1.6 -- matrix operations
• Singular Book 2.1.7 -- maps induced by Hom
• Singular Book 2.1.10 -- Submodules of A^n
• Singular Book 2.1.13 -- kernel, image and cokernel of a module homomorphism
• Singular Book 2.1.20 -- sum, intersection, module quotient
• Singular Book 2.1.24 -- submodules, presentation of a module
• Singular Book 2.1.26 -- computation of Hom
• Singular Book 2.1.34 -- minimal presentations, prune
• Singular Book 2.2.15 -- graded rings and modules
• Singular Book 2.3.10 -- normal form
• Singular Book 2.3.12 -- standard bases
• Singular Book 2.4.12 -- resolution and Betti numbers
• Singular Book 2.4.15 -- homogeneous resolution and graded Betti numbers
• Singular Book 2.5.5 -- syzygies
• Singular Book 2.5.18 -- Schreyer resolution
• Singular Book 2.6.3 -- diagonal form
• Singular Book 2.6.11 -- cyclic decomposition
• Singular Book 2.6.15 -- Jordan normal form
• Singular Book 2.7.5 -- tensor product of maps
• Singular Book 2.7.9 -- tensor product of modules
• Singular Book 2.7.14 -- tensor product of rings
• Singular Book 2.8.1 -- module membership
• Singular Book 2.8.3 -- elimination of module components
• Singular Book 2.8.5 -- intersection of modules
• Singular Book 2.8.6 -- quotient of modules
• Singular Book 2.8.7 -- radical, zerodivisors of modules
• Singular Book 2.8.8 -- annihilator and Fitting ideal
• Singular Book 2.8.9 -- kernel of a module homomorphism
• Singular Book 2.8.10 -- solving linear equations