Sorry, no online dictionaries contain the exact phrase birational map.
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Reverse dictionary results:
1. bijective
2. conformal
3. affine
4. homotopic
5. projective
6. bilinear
7. contractive
8. differentiable
9. euclidean
10. fourier
11. holomorphic
12. homographic
13. homomorphic
14. homothetic
15. homotopy
16. injective
17. invertible
18. irrational
19. non-birational
20. non-rational
21. polynomial
22. symplectic
23. topological
24. aaa
25. acre
26. acres
27. act
28. acy
29. allocation
30. alt
31. aps
32. area
33. arrow
34. asia
35. assignment
36. atlas
37. avenue
38. browse
39. cadastre
40. card

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You can look up the words in the phrase individually using these links:   birational ?   map ?
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bira*to search for words beginning with bira, or
* mapto search for words ending with map
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