Complex-valued variables (JuliaAlgebra#213)

* First draft for complex-valued interface

* Adjust imaginary part

* Slight updates

* Add exports

* Rename ordvar to ordinary_variable

* Change assert to error

* Code style

* Remove real_coefficient_type_polynomial_like

* Change comparisons to comparison functions

* Explain _show in comment

* Shortcuts for conj

* Add explicit isreal/iscomplex for monomial vectors

* Fix

* Improve real/imag of APL

* Replace zip by powers

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

* Fix

* Explain choice of function signature

* Format

* Documentation

* Fix iscomplex detection

* Docstring update, new function spelling

* Test for complex case

* Remove missing references to Base functions

* Format test

* Format

* Compatibility in tests

* Fix adjoint issues with new interface

* Revert APL adjoint implementation (mutable coefficients would be aliased)

* Add copy_if_mutable safeguards

* Remove complex branch CI

* Update src/complex.jl

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

* Update src/complex.jl

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

* Update src/complex.jl

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

* Avoid splatting

* Remove iscomplex

* Improve documentation

---------

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

Author: projekter

docs/src/types.md

@@ -14,6 +14,14 @@ name_base_indices
 variable_union_type
 similar_variable
 @similar_variable
+conj(::AbstractVariable)
+real(::AbstractVariable)
+imag(::AbstractVariable)
+isreal(::AbstractVariable)
+isrealpart
+isimagpart
+isconj
+ordinary_variable
 ```
 
 ## Monomials
@@ -47,6 +55,8 @@ coefficient_type
 monomial
 constant_term
 zero_term
+degree_complex
+halfdegree
 ```
 
 ## Polynomials
@@ -75,6 +85,16 @@ monic
 map_coefficients
 map_coefficients!
 map_coefficients_to!
+conj(::_APL)
+real(::_APL)
+imag(::_APL)
+isreal(::_APL)
+mindegree_complex
+minhalfdegree
+maxdegree_complex
+maxhalfdegree
+extdegree_complex
+exthalfdegree
 ```
 
 ## Rational Polynomial Function
@@ -90,4 +110,8 @@ monomial_vector_type
 empty_monomial_vector
 sort_monomial_vector
 merge_monomial_vectors
+conj(::AbstractVector{<:AbstractMonomial})
+real(::AbstractVector{<:AbstractMonomial})
+imag(::AbstractVector{<:AbstractMonomial})
+isreal(::AbstractVector{<:AbstractMonomial})
 ```

src/MultivariatePolynomials.jl

@@ -77,6 +77,7 @@ include("hash.jl")
 include("promote.jl")
 include("conversion.jl")
 
+include("complex.jl")
 include("operators.jl")
 include("comparison.jl")