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SandBoxComplexManifold

Edit detail for SandBoxComplexManifold revision 1 of 7

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Editor: Bill Page Time: 2009/06/20 15:12:26 GMT-7
Note: new

changed:
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\begin{spad}
)abbrev domain CM ComplexManifold
ComplexManifold(R:Join(Field,RadicalCategory,OrderedSet)): Join(RadicalCategory,DirectProductCategory(2,R)) with
    elt:(%,"pos") -> R
    elt:(%,"neg") -> R
    imaginary: () -> %
    real: % -> R
    imag: % -> R
    conj: % -> %
  == DirectProduct(2,R) add
    Rep == DirectProduct(2,R)
    elt(x,"pos") == rep(x).1
    elt(x,"neg") == rep(x).2

    imaginary():% == per directProduct vector [1,-1]
    real(x:%):R == (rep(x).1 + rep(x).2)/(2::R)
    imag(x:%):R == (rep(x).1 - rep(x).2)/(2::R)
    conj(x:%):% == per directProduct vector [rep(x).2,rep(x).1]
    sqrt(x:%):% == per directProduct vector [  _
      sqrt real(x) + sqrt imag(x),  _
      ((if real(x)>=0 then sqrt real(x) else 0) - _
      (if real(x)<=0 then sqrt real(x) else 0)) + _
      ((if imag(x)<=0 then sqrt imag(x) else 0) - _
      (if imag(x)>=0 then sqrt imag(x) else 0)) ]
\end{spad}

\begin{axiom}
a:CM(EXPR INT) := 3
b:CM(EXPR INT) := -3
real(a)
s1:=sqrt(a)
real s1
imag s1
s2:=sqrt(b)
real s2
imag s2
I:CM(EXPR INT) := imaginary()
imag I
imag conj I
conj(a+b*I)
\end{axiom}

spad

)abbrev domain CM ComplexManifold
ComplexManifold(R:Join(Field,RadicalCategory,OrderedSet)): Join(RadicalCategory,DirectProductCategory(2,R)) with
    elt:(%,"pos") -> R
    elt:(%,"neg") -> R
    imaginary: () -> %
    real: % -> R
    imag: % -> R
    conj: % -> %
  == DirectProduct(2,R) add
    Rep == DirectProduct(2,R)
    elt(x,"pos") == rep(x).1
    elt(x,"neg") == rep(x).2

    imaginary():% == per directProduct vector [1,-1]
    real(x:%):R == (rep(x).1 + rep(x).2)/(2::R)
    imag(x:%):R == (rep(x).1 - rep(x).2)/(2::R)
    conj(x:%):% == per directProduct vector [rep(x).2,rep(x).1]
    sqrt(x:%):% == per directProduct vector [  _
      sqrt real(x) + sqrt imag(x),  _
      ((if real(x)>=0 then sqrt real(x) else 0) - _
      (if real(x)<=0 then sqrt real(x) else 0)) + _
      ((if imag(x)<=0 then sqrt imag(x) else 0) - _
      (if imag(x)>=0 then sqrt imag(x) else 0)) ]

spad

   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/5976774624515024081-25px001.spad using 
      Spad compiler.
   CM abbreviates domain ComplexManifold 
------------------------------------------------------------------------
   initializing NRLIB CM for ComplexManifold 
   compiling into NRLIB CM 
   Adding Integer modemaps
   Adding NonNegativeInteger modemaps
   Adding PositiveInteger modemaps
   Adding $ modemaps
   Adding R modemaps
   Adding R modemaps
   Adding R modemaps
   Adding Integer modemaps
   Adding NonNegativeInteger modemaps
   Adding PositiveInteger modemaps
   Adding Rep modemaps
   compiling exported elt : (%,pos) -> R
   Adding DirectProduct(2,R) modemaps
Time: 0.13 SEC.

   compiling exported elt : (%,neg) -> R
   Adding DirectProduct(2,R) modemaps
Time: 0 SEC.

   compiling exported imaginary : () -> %
   Adding DirectProduct(2,R) modemaps
   Adding Vector R modemaps
   Adding List R modemaps
Time: 0.04 SEC.

   compiling exported real : % -> R
   Adding DirectProduct(2,R) modemaps
Time: 0.01 SEC.

   compiling exported imag : % -> R
   Adding DirectProduct(2,R) modemaps
Time: 0.01 SEC.

   compiling exported conj : % -> %
   Adding DirectProduct(2,R) modemaps
   Adding Vector R modemaps
   Adding List R modemaps
Time: 0.01 SEC.

   compiling exported sqrt : % -> %
   Adding DirectProduct(2,R) modemaps
   Adding Vector R modemaps
   Adding List R modemaps
   Adding Boolean modemaps
Time: 0.05 SEC.

   Adding R modemaps
   augmenting R: DifferentialRing
   Adding R modemaps
   augmenting R: Evalable R
   Adding R modemaps
   augmenting R: LinearlyExplicitRingOver Integer
   Adding R modemaps
   augmenting R: PartialDifferentialRing Symbol
   Adding R modemaps
   augmenting R: RetractableTo Fraction Integer
   Adding R modemaps
   augmenting R: RetractableTo Integer
   Adding R modemaps
   augmenting R: DifferentialRing
   Adding R modemaps
   augmenting R: DifferentialRing
   Adding R modemaps
   augmenting R: RetractableTo Integer
   Adding R modemaps
   augmenting R: OrderedAbelianMonoidSup
   augmenting $: shallowlyMutable
   Adding R modemaps
   augmenting R: Finite
   Adding R modemaps
   augmenting R: OrderedAbelianMonoidSup
   Adding R modemaps
   augmenting R: OrderedRing
Predicate: 
(|has| $ (ATTRIBUTE |finiteAggregate|))   replaced by: 
T Predicate: 
(|has| $ (ATTRIBUTE |shallowlyMutable|))   replaced by: 
NIL Predicate: 
(|has| $ (ATTRIBUTE |finiteAggregate|))   replaced by: 
T (time taken in buildFunctor:  77)
Time: 0.87 SEC.

   Cumulative Statistics for Constructor ComplexManifold
      Time: 1.12 seconds

--------------non extending category----------------------
   ComplexManifold #1 of category Join(RadicalCategory,
      DirectProductCategory(2,#1)) with 
         ?.pos : (%,pos) -> #1
         ?.neg : (%,neg) -> #1
         imaginary : () -> %
         real : % -> #1
         imag : % -> #1
         conj : % -> %
    has no DirectProductCategory(NIL,#1)
   finalizing NRLIB CM 
   Processing ComplexManifold for Browser database:
--->-->ComplexManifold((elt (R % pos))): Not documented!!!!
--->-->ComplexManifold((elt (R % neg))): Not documented!!!!
--->-->ComplexManifold((imaginary (%))): Not documented!!!!
--->-->ComplexManifold((real (R %))): Not documented!!!!
--->-->ComplexManifold((imag (R %))): Not documented!!!!
--->-->ComplexManifold((conj (% %))): Not documented!!!!
--->-->ComplexManifold(constructor): Not documented!!!!
--->-->ComplexManifold: Missing Description
------------------------------------------------------------------------
   ComplexManifold is now explicitly exposed in frame initial 
   ComplexManifold will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/CM.NRLIB/code.o

axiom