Get started

Example gallery¶

Every program listed here is checked against its expected output. The pages include its source, a download link, and a run command. Begin with the first tutorial, then use the later examples to see how operations fit together.

Tutorials and guides¶

Program	Walkthrough
`tutorial_first.mojo`, `tutorial_steps.mojo`	Your first polynomial
`array_api.mojo`, `array_operations.mojo`, `array_surface_scalars.mojo`, `array_surface_format.mojo`	Polynomial arrays
`array_access_inspection.mojo`, `array_exact_algebra.mojo`, `array_factor_fields.mojo`, `array_exact_samples.mojo`	Exact algebra
`array_parity_checked.mojo`, `array_exact_choices.mojo`	Check exact algebra results
`array_solver_roots.mojo`, `array_access_sturm.mojo`, `array_complex_roots.mojo`, `array_solver_streams.mojo`	Roots
`array_algebraic_points.mojo`, `array_root_diagnostics.mojo`, `array_extension_algebraic_roots.mojo`	Evaluate at exact roots and inspect candidates
`array_workflow_specialization.mojo`, `array_workflow_covers.mojo`, `array_workflow_root_stream.mojo`	Algebraic coefficients in root searches
`array_algebraic_coefficients.mojo`, `array_algebraic_factor.mojo`, `array_algebraic_multivariate_factor.mojo`	Algebraic coefficients
`array_solver_ideals.mojo`	Gröbner bases and membership
`array_solver_cad.mojo`	Inequalities and CAD
`array_parity_cad.mojo`, `array_fixed_cad.mojo`, `array_algebraic_cad.mojo`	Specialized CAD workflows
`array_toolkit_series.mojo`	Formal series
`array_toolkit_basis.mojo`	Alternative bases
`array_toolkit_rational.mojo`, `array_algebraic_rational.mojo`, `array_fraction_enclosures.mojo`, `array_workflow_fraction.mojo`	Rational functions
`array_numeric.mojo`, `array_access_dtype.mojo`, `array_algebraic_numeric.mojo`, `array_extension_numerical.mojo`, `array_extension_representations.mojo`	Numerical coefficients
`array_extension_certified.mojo`, `array_parity_stream.mojo`, `array_algebraic_stream.mojo`	Certified evaluation
`array_batching.mojo`, `array_batch_reductions.mojo`, `array_workflow_accumulate.mojo`, `array_batch_interop.mojo`	Batch calculations
`array_value_serialization.mojo`, `array_checked_serialization.mojo`, `array_serialization.mojo`, `array_algebraic_serialization.mojo`, `array_surface_kernel.mojo`	Save and restore values
`tutorial_errors.mojo`	Typed errors and budget exhaustion

Core API examples¶

These programs use the core polynomials package directly. They are for developers extending the library; applications use the programs above.

Program	Where to find it
`array_exact_core.mojo`, `array_access_interop.mojo`, `array_surface_interop.mojo`	Exchange arrays with core values
`arithmetic.mojo`	Arithmetic and the kernel codec
`gcd.mojo`, `tutorial_division.mojo`	Division, gcds, and cancellation certificates
`algebra.mojo`, `tutorial_factor.mojo`	Factorization, bases, and roots
`tutorial_groebner.mojo`, `complex_groebner.mojo`	Gröbner bases and membership
`tutorial_roots.mojo`	Rational and irrational real roots
`toolkit.mojo`, `tutorial_calculus.mojo`, `tutorial_interpolation.mojo`, `tutorial_rational.mojo`, `tutorial_bases.mojo`, `tutorial_series.mojo`	Polynomial toolkit
`streaming.mojo`	Incremental text and proof checking
`numerical.mojo`, `tutorial_numerical.mojo`, `tutorial_refinement.mojo`	Numerical certificates and refinement
`algebraic_numbers.mojo`	Exact real algebraic arithmetic
`cad.mojo`	CAD and selective coverings

To run a downloaded example, install the package and run it with pixi run mojo run, or run it with mojo -I build inside a checkout's Pixi environment.