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Read the lecture notes and complete the definition of the instance for |Num| for the datatype |ComplexP|. Also add a constructor for variables to enable writing expressions like |(Var "z") :*: toComplex 1|.
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Read the next few pages of Appendix I (in [Adams & Essex]) defining the polar view of Complex Numbers and try to implement complex numbers again, this time based on magnitude and phase for the semantics.
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Implement a simplifier |simp :: ComplexP r -> ComplexP r| that handles a few cases like |0 * x = 0|, |1 * x = x|, |(a + b) * c = a * c + b * c|, ... What class context do you need to add to the type of simp?
References:
- Adams & Essex (2010): Calculus: a complete course, 7th edition. Pearson Canada. "Appendix I. Definition of Complex Numbers"
TBD
Preparation: Read the TFPIE'15 paper