Unravel the mysteries of complex shapes called algebraic varieties! Computational algebraic
geometry embarks on a journey with two powerful tools: toric and tropical varieties.Imagine a
hidden world built from equations. Toric geometry acts as a translator converting these
equations into a structured grid revealing hidden symmetries and patterns within the variety.
Like a decoder ring it unlocks the secrets of its form.Tropical geometry takes a different
path. It creates a simpler shadow - a collection of flat shapes glued together - capturing the
essence of the variety's geometry. This tropicalization allows us to analyze its interactions
with other shapes and understand its overall structure with greater ease.Computational
algebraic geometry leverages the power of both these approaches. By switching between these
lenses mathematicians can gain a deeper understanding of these intricate shapes making this
journey a fascinating exploration of the hidden worlds defined by equations
