MathAction MyComplex

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      - MyComplex <-- You are here.

spad

)abbrev domain MYPLEX MyComplex
++ Description:
++ Based on \spadtype{Complex(R)},
++ \spadtype{MyComplex(R)} creates the domain of elements of the form
++ \spad{a + b * i} where \spad{a} and b come from the ring R,
++ and i is a new element such that \spad{i^2 = -1}.
MyComplex(R:CommutativeRing): ComplexCategory(R) with
     if R has OpenMath then OpenMath
   == add
       Rep := Record(real:R, imag:R)

       if R has OpenMath then
         writeOMComplex(dev: OpenMathDevice, x: %): Void ==
          OMputApp(dev)
          OMputSymbol(dev, "complex1", "complex__cartesian")
          OMwrite(dev, real x)
          OMwrite(dev, imag x)
          OMputEndApp(dev)

         OMwrite(x: %): String ==
          s: String := ""
          sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
          dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML)
          OMputObject(dev)
          writeOMComplex(dev, x)
          OMputEndObject(dev)
          OMclose(dev)
          s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
          s

         OMwrite(x: %, wholeObj: Boolean): String ==
          s: String := ""
          sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
          dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML)
          if wholeObj then
            OMputObject(dev)
          writeOMComplex(dev, x)
          if wholeObj then
            OMputEndObject(dev)
          OMclose(dev)
          s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
          s

         OMwrite(dev: OpenMathDevice, x: %): Void ==
          OMputObject(dev)
          writeOMComplex(dev, x)
          OMputEndObject(dev)

         OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void ==
          if wholeObj then
            OMputObject(dev)
          writeOMComplex(dev, x)
          if wholeObj then
            OMputEndObject(dev)

       0                == [0, 0]
       1                == [1, 0]
       zero? x          == zero?(x.real) and zero?(x.imag)
--       one? x           == one?(x.real) and zero?(x.imag)
       one? x           == ((x.real) = 1) and zero?(x.imag)
       coerce(r:R):%    == [r, 0]
       complex(r, i)   == [r, i]
       real x           == x.real
       imag x           == x.imag
       x + y            == [x.real + y.real, x.imag + y.imag]
                           -- by re-defining this here, we save 5 fn calls
       x:% * y:% ==
         [x.real * y.real - x.imag * y.imag,
          x.imag * y.real + y.imag * x.real] -- here we save nine!

       if R has IntegralDomain then
         _exquo(x:%, y:%) == -- to correct bad defaulting problem
           zero? y.imag => x exquo y.real
           x * conjugate(y) exquo norm(y)

spad

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4777213760436474437-25px001.spad
      using old system compiler.
   MYPLEX abbreviates domain MyComplex 
------------------------------------------------------------------------
   initializing NRLIB MYPLEX for MyComplex 
   compiling into NRLIB MYPLEX 
****** Domain: R already in scope
augmenting R: (OpenMath)
   compiling local writeOMComplex : (OpenMathDevice,$) -> Void
Time: 0.05 SEC.

   compiling exported OMwrite : $ -> String
Time: 0 SEC.

   compiling exported OMwrite : ($,Boolean) -> String
Time: 0 SEC.

   compiling exported OMwrite : (OpenMathDevice,$) -> Void
Time: 0 SEC.

   compiling exported OMwrite : (OpenMathDevice,$,Boolean) -> Void
Time: 0 SEC.

   compiling exported Zero : () -> $
Time: 0 SEC.

   compiling exported One : () -> $
Time: 0 SEC.

   compiling exported zero? : $ -> Boolean
Time: 0 SEC.

   compiling exported one? : $ -> Boolean
Time: 0 SEC.

   compiling exported coerce : R -> $
Time: 0 SEC.

   compiling exported complex : (R,R) -> $
      MYPLEX;complex;2R$;11 is replaced by CONS 
Time: 0 SEC.

   compiling exported real : $ -> R
      MYPLEX;real;$R;12 is replaced by QCAR 
Time: 0 SEC.

   compiling exported imag : $ -> R
      MYPLEX;imag;$R;13 is replaced by QCDR 
Time: 0 SEC.

   compiling exported + : ($,$) -> $
Time: 0 SEC.

   compiling exported * : ($,$) -> $
Time: 0 SEC.

****** Domain: R already in scope
augmenting R: (IntegralDomain)
   compiling exported exquo : ($,$) -> Union($,failed)
Time: 0 SEC.

****** Domain: R already in scope
augmenting R: (EuclideanDomain)
****** Domain: R already in scope
augmenting R: (PolynomialFactorizationExplicit)
****** Domain: R already in scope
augmenting R: (RadicalCategory)
****** Domain: R already in scope
augmenting R: (TranscendentalFunctionCategory)
****** Domain: R already in scope
augmenting R: (RealNumberSystem)
****** Domain: R already in scope
augmenting R: (TranscendentalFunctionCategory)
****** Domain: R already in scope
augmenting R: (Comparable)
****** Domain: R already in scope
augmenting R: (ConvertibleTo (InputForm))
****** Domain: R already in scope
augmenting R: (ConvertibleTo (Pattern (Float)))
****** Domain: R already in scope
augmenting R: (ConvertibleTo (Pattern (Integer)))
****** Domain: R already in scope
augmenting R: (DifferentialRing)
****** Domain: R already in scope
augmenting R: (Eltable R R)
****** Domain: R already in scope
augmenting R: (EuclideanDomain)
****** Domain: R already in scope
augmenting R: (Evalable R)
****** Domain: R already in scope
augmenting R: (Field)
****** Domain: R already in scope
augmenting R: (Finite)
****** Domain: R already in scope
augmenting R: (FiniteFieldCategory)
****** Domain: R already in scope
augmenting R: (InnerEvalable (Symbol) R)
****** Domain: R already in scope
augmenting R: (IntegerNumberSystem)
****** Domain: R already in scope
augmenting R: (IntegralDomain)
****** Domain: R already in scope
augmenting R: (LinearlyExplicitRingOver (Integer))
****** Domain: R already in scope
augmenting R: (OpenMath)
****** Domain: R already in scope
augmenting R: (PartialDifferentialRing (Symbol))
****** Domain: R already in scope
augmenting R: (PatternMatchable (Float))
****** Domain: R already in scope
augmenting R: (PatternMatchable (Integer))
****** Domain: R already in scope
augmenting R: (RealConstant)
****** Domain: R already in scope
augmenting R: (RealNumberSystem)
****** Domain: R already in scope
augmenting R: (RetractableTo (Fraction (Integer)))
****** Domain: R already in scope
augmenting R: (RetractableTo (Integer))
****** Domain: R already in scope
augmenting R: (TranscendentalFunctionCategory)
(time taken in buildFunctor:  260)

;;;     ***       |MyComplex| REDEFINED

;;;     ***       |MyComplex| REDEFINED
Time: 0.30 SEC.

   Warnings: 
      [1] OMwrite: pretend(String) -- should replace by @

   Cumulative Statistics for Constructor MyComplex
      Time: 0.35 seconds

   finalizing NRLIB MYPLEX 
   Processing MyComplex for Browser database:
--------constructor---------
--->-->MyComplex(constructor): Wrong number of arguments: MyComplex(R)
; compiling file "/var/aw/var/LatexWiki/MYPLEX.NRLIB/MYPLEX.lsp" (written 14 JUL 2013 10:10:12 AM):

; /var/aw/var/LatexWiki/MYPLEX.NRLIB/MYPLEX.fasl written
; compilation finished in 0:00:00.087
------------------------------------------------------------------------
   MyComplex is now explicitly exposed in frame initial 
   MyComplex will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYPLEX.NRLIB/MYPLEX

fricas

myType := MyComplex MyComplex Integer

$\label{eq1}\hbox{\axiomType{MyComplex}\ } (\hbox{\axiomType{MyComplex}\ } (\hbox{\axiomType{Integer}\ }))$

(1)

Type: Type

fricas

m := complex(complex(1,2)$MyComplex(Integer),complex(3,4)$MyComplex(Integer))$myType

$\label{eq2}1 +{2 \ i}+{{\left(3 +{4 \ i}\right)}\ i}$

(2)

Type: MyComplex(MyComplex(Integer))

fricas

mr := real(m*m)

$\label{eq3}4 -{{20}\ i}$

(3)

Type: MyComplex(Integer)

fricas

imag(mr)

$\label{eq4}-{20}$

(4)

Type: Integer

Subject: Be Bold !!

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