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# SimisStrategy -- a strategy for determining whether a map is birational and computing its inverse

## Description

SimisStrategy is a valid value for the Strategy Option of inverseOfMap, isBirationalMap, and isEmbedding. Considering the bigraded structure of the equations of the ideal of definition of a Rees algebra, SimisStrategy looks for all Gröbner bases where the degree is (1, n) for some natural number n. The advantage of this restriction is that this part of the Rees ideal is enough to decide birationality and to compute the inverse map; this strategy reduces computation time. A disadvantage of this Strategy is that if the given map is not birational this Strategy may never end because the jacobianDualMatrix will not attain its maximum rank. To circumvent this problem we implemented HybridStrategy.

## See also

- ReesStrategy -- a strategy for determining whether a map is birational and computing its inverse
- SaturationStrategy -- a strategy for determining whether a map is birational and computing its inverse
- HybridStrategy -- A strategy for determining whether a map is birational and computing its inverse

## For the programmer

The object SimisStrategy is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RationalMaps.m2:1528:0.