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## 4.iii. Further extensions of the Schubert calculus

This special Schubert calculus admits further extensions, some of which are
known to be fully real.
Interestingly, some problems involving the Lagrangian
Grassmannian 4.ii.e are known to be
*fully unreal*, a new phenomenon.
Further investigation is encouraged; in particular, the Lagrangian Schubert
calculus may yield the first class of enumerative which are *not* fully
real.

**Subsections**
- General Schubert calculus
- Quantum Schubert calculus
- Schubert calculus of flags
- Reality in the orthogonal Schubert
calculus
- Unreality in the Lagrangian Schubert
calculus

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** Previous:** 4.ii. The Special Schubert Calculus