A Guided Tour

This section is a guided tour of some of what is available in Sage. For many more examples, see “Sage Constructions”, which is intended to answer the general question “How do I construct …?”. See also the “Sage Reference Manual”, which has thousands more examples. Also note that you can interactively work through this tour in the Sage notebook by clicking the "Help" link.

(If you are viewing the tutorial in the Sage notebook, press "shift-enter" to evaluate any input cell. You can even edit the input before pressing shift-enter. On some Macs you might have to press "shift-return" rather than "shift-enter".)

Assignment, Equality, and Arithmetic

Getting Help

Functions, Indentation, and Counting

Basic Algebra and Calculus

Solving Equations

Solving Equations Exactly

Solving Equations Numerically

Differentiation, Integration, etc.

Solving Differential Equations

Euler’s Method for Systems of Differential Equations

Special functions

Plotting

Two-dimensional Plots

Three-Dimensional Plots

Some Common Issues with Functions

Basic Rings

Linear Algebra

Matrix spaces

Sparse Linear Algebra

Polynomials

Univariate Polynomials

Multivariate Polynomials

Parents, Conversion and Coercion

Elements

Parents and categories

Types versus parents

Conversion versus Coercion

Finite Groups, Abelian Groups

Number Theory

-adic Numbers

Some More Advanced Mathematics

Algebraic Geometry

Elliptic Curves

Dirichlet Characters

Modular Forms