User guide examples

There's a ton of undocumented functionality. The user guide needs sections on all the core functionality, with each section containing an overview of the mathematics involved and example code blocks.

Checklist of things to document in order to close this issue:

• Natural numbers and their operations including factoring. (#62)
• Integers and their operations including factoring. (#77)
• Integer factoring.
• Rationals and their operations (#83).
• Polynomials in one variable, operations with them, factoring over different rings.
• Multivariable polynomials, operations with them, factoring over different rings.
• Symmetric polynomials and obtaining expressions in terms of elementary symmetric polynomials.
• Combinatorical functions: partitions of sets, partitions of numbers, compositions of numbers, subsets of a fixed size, etc.
• Matricies, hermite normal form, smith normal form, jordan normal form, solving systems of linear equations.
• Algebraic real and complex numbers.
• Algebraic p-adic numbers.
• Algebraic number fields, integral bases, ring of integers, ideals, factoring ideals, etc.
• Finite groups, enumerating subgroups and normal subgroups, finding isomorphisms, enumerating cosets in finitely generated groups, etc.
• Simplicial complexes: convex hull of points, boolean operations.

Start with the user guide and review the checklist to identify which core functionality remains undocumented. Use the completed sections as a model for the mathematics overviews and example code blocks, then document the remaining polynomial, combinatorial, matrix, algebraic-number, and group functionality until the unchecked items are complete.