Release 0.8-3

January 30, 2013

1 Introduction

1.1 Interfaces

1.2 Ring Declarations

1.3 Ordering

1.4 Arithmetic

1.5 Set operations

1.6 Gröbner bases

2 How to program efficiently

2.1 Low level friendly programming

2.2 Replace algebra by set operations

2.3 Direct constructions of diagrams

2.4 Case study: Graded part of a polynomial

2.5 Case study: Evaluation of a polynomial

3 Other techniques

3.1 Storing polynomial data in a ﬁle

3.2 Reinterpretation of Boolean sets as subsets of the vector space ℤ_{2}^{n}

3.3 Lexicographical normal form of a polynomial against a variety

3.4 Partial Boolean functions

3.5 Building your own Gröbner basis algorithm

4 Alternative user interfaces

4.1 PolyGUI

4.2 Singular’s pyobject extension

References

1.1 Interfaces

1.2 Ring Declarations

1.3 Ordering

1.4 Arithmetic

1.5 Set operations

1.6 Gröbner bases

2 How to program efficiently

2.1 Low level friendly programming

2.2 Replace algebra by set operations

2.3 Direct constructions of diagrams

2.4 Case study: Graded part of a polynomial

2.5 Case study: Evaluation of a polynomial

3 Other techniques

3.1 Storing polynomial data in a ﬁle

3.2 Reinterpretation of Boolean sets as subsets of the vector space ℤ

3.3 Lexicographical normal form of a polynomial against a variety

3.4 Partial Boolean functions

3.5 Building your own Gröbner basis algorithm

4 Alternative user interfaces

4.1 PolyGUI

4.2 Singular’s pyobject extension

References