This chapter presents the study of set theory with Sage, starting with a
description of the Set function and its variations, then how to use
it to calculate the basic set operations.
3
Counting techniques arise naturally in computer algebra as well as in basic applications in daily life. This chapter covers the treatment in Sage of the enumeration problem, like counting combinations and counting permutations as well as listing them.
4
We introduce in this chapter different ways to create boolean formulas using the logical functions not, and, or, if then, and if and only if. Then we show how to ask Sage to create a truth table from a formula and determine if an expression is a contradiction or a tautology.
5
Building on the Cartesian product introduced earlier, this chapter deals with relations between the elements in sets. We will first see how to visualize with Sage some relations and then we introduce some new functions to decide if they are equivalence or partial order relations.
6
This chapter will discuss briefly the implementation of functions in Sage and delve deeper into the sequences defined by recursion, including the Fibonacci one. We show how to solve a recurrence relation using Sage.
7
Sage is extremely powerful for graph theory. This chapter presents the study of graph theory with Sage, starting with a description of the Graph class to the implementation of optimization algorithms. We also illustrate the graphical capabilities of Sage to visualize graphs.
8
This chapter completes the preceding one by explaining how to ask Sage to decide whether a given graph is a tree and then introduce further searching algorithms for trees.
9
Building on the partial order sets introduced earlier, this chapter explains how to ask Sage to decide whether a given poset is a lattice. Then we show how to calculate the meet and join tables using build-in functions in Sage as well as customized ones.
10
This chapter completes the preceding one by explaining how to ask Sage to decide whether a given lattice is a Boolean algebra. We also illustrate basic operations with Boolean functions.
Samuel-Lubliner
commented
5 months ago
Add intros to all sections:
2
This chapter presents the study of set theory with Sage, starting with a description of the Set function and its variations, then how to use it to calculate the basic set operations.
3
Counting techniques arise naturally in computer algebra as well as in basic applications in daily life. This chapter covers the treatment in Sage of the enumeration problem, like counting combinations and counting permutations as well as listing them.
4
We introduce in this chapter different ways to create boolean formulas using the logical functions not, and, or, if then, and if and only if. Then we show how to ask Sage to create a truth table from a formula and determine if an expression is a contradiction or a tautology.
5
Building on the Cartesian product introduced earlier, this chapter deals with relations between the elements in sets. We will first see how to visualize with Sage some relations and then we introduce some new functions to decide if they are equivalence or partial order relations.
6
This chapter will discuss briefly the implementation of functions in Sage and delve deeper into the sequences defined by recursion, including the Fibonacci one. We show how to solve a recurrence relation using Sage.
7
Sage is extremely powerful for graph theory. This chapter presents the study of graph theory with Sage, starting with a description of the Graph class to the implementation of optimization algorithms. We also illustrate the graphical capabilities of Sage to visualize graphs.
8
This chapter completes the preceding one by explaining how to ask Sage to decide whether a given graph is a tree and then introduce further searching algorithms for trees.
9
Building on the partial order sets introduced earlier, this chapter explains how to ask Sage to decide whether a given poset is a lattice. Then we show how to calculate the meet and join tables using build-in functions in Sage as well as customized ones.
10
This chapter completes the preceding one by explaining how to ask Sage to decide whether a given lattice is a Boolean algebra. We also illustrate basic operations with Boolean functions.