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.

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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