Compute Algebra Systems and SageMath

Symbolic Computation and Computer Algebra Systems

1. Compare and contrast numerical computation and symbolic computation.
2. Give examples of symbolic computation from your previous schoolwork.
3. Define Computer Algebra System (CAS).
4. Give examples of commercial computer algebra systems.

SageMath Practicalities

1. Run SageMath through a Jupyter Notebook on your personal computer.
2. Use SageMath to perform arithmetic.
3. Use N() in SageMath to compute numerical approximations to numerical expressions.
4. Initialize symbolic variables.
5. Compare and contrast symbolic variables and “computer science” variables.

Basic Computer Algebra with SageMath

1. Define and store expressions.
2. Generate LaTeX commands for a given expression.
3. Use Jupyter’s %display option to display SageMath expressions as typeset LaTeX.
4. Expand expressions.
5. Factor expressions.
6. Simplify expressions.

Symbolic Functions in SageMath

1. Define a symbolic function.
2. Use defined symbolic functions algebraically.

Solving Equations with SageMath

1. Use solve() to solve an equation.
2. Use solve() to find the inverse of a symbolic function.
3. Access the solutions returned by solve() and the left and right hand sides of the solutions.

Plotting Symbolic Functions

1. Plot the graph of a symbolic function using plot().
2. Build plots programmatically using plot() and +.
3. Use iteration and conditional statements to built plots programmatically.