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SandBoxPhysicalUnitSystem

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Editor: pagani Time: 2018/07/16 16:38:54 GMT+0
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changed:
-
\begin{spad}
)abbrev category PUNIT PhysicalUnit
PhysicalUnit() : Category == with   
    "*"  : (%,%) -> %
    "/"  : (%,%) -> %
    "^"  : (%,Integer) -> %
    "="  : (%,%) -> Boolean
    dim  : % -> List Integer
    one  : %
    coerce : % -> OutputForm


)abbrev domain PUSYS PhysicalUnitSystem 
PhysicalUnitSystem(u:List Symbol) : Exports == Implementation where
    BASU ==> OrderedVariableList(u) 
    FAGB ==> FreeModule(Integer,BASU) 
    Exports == Join(PhysicalUnit,CoercibleTo OutputForm) with
      _* : (%,%) -> %
      _/ : (%,%) -> %
      baseSymbols : List Symbol
      baseUnits : List %
      factors : % ->  List Record(gen: BASU,exp: Integer)
    Implementation == FreeGroup(BASU) add
      Rep:=FreeModule(Integer,BASU)
      sort: % -> %
      x * y == sort(x+y) 
      x / y == sort(x-y)
      x ^ n == sort(n*x) 
      one() == 0$Rep
      baseSymbols() == [convert(x)@Symbol for x in enumerate$BASU]
      baseUnits() == [x::% for x in enumerate$BASU]
      dim(x) ==
        d:=[0@Integer for j in 1..#u]
        lr:List(Record(gen:BASU,exp:Integer)):=factors(x)
        for r in lr repeat
          g:BASU:=r.gen
          k:=position(g,enumerate$BASU)$List(BASU)
          d.k:=r.exp
        d

      x = y == test(dim x = dim y)                                      
      
      coerce0(x:%):OutputForm ==
        #monomials(x) = 0 => outputForm(1)
        d:=dim(x)
        b:=baseSymbols()
        y:List OutputForm:=[]
        for j in 1..#d repeat
          if d.j=1 then y:=concat(y,outputForm(b.j))
          else
            if d.j~=0 then y:=concat(y,outputForm(b.j)^outputForm(d.j))
        blankSeparate y 

      sort(x:%):% ==
        R==>Record(gen: BASU,exp: Integer)
        f:=(a:R,b:R):Boolean+->(test(a.gen>b.gen))
        sort(f,factors x) pretend Rep 


-- SI:=PUSYS(['m,'kg,'s])
-- u:=baseUnits()$SI
-- coerce0 works as coerce, if sort then not necess.

)abbrev domain PQTY PhysQty
PhysQty(U): Exports == Implementation where
    
    Q   ==> Fraction(Integer)
    F   ==> Float
    R   ==> DoubleFloat
    I   ==> Integer
    OF  ==> OutputForm
    PI  ==> PositiveInteger
    IVF ==> Interval Float
    U:PhysicalUnit
       
    
    Exports == Join(CoercibleTo OutputForm) with
      _* : (%,%) -> %
      _/ : (%,%) -> %
      _+ : (%,%) -> %
      _- : (%,%) -> %
      _^ : (%,Integer) -> %
      _- : % -> %
      
      ival : % -> IVF
      unit : % -> U    
          
      elt : (IVF,U) -> %
      elt : (F,U) -> %
      
      setOutputMode : PI -> PI
      coerce : % -> OutputForm
    
    Implementation ==  add 
    
      Rep := Record(ival:IVF, unit:U)
      
      outputMode:PI:=1
      
      x * y == [x.ival * y.ival, x.unit * y.unit]$Rep
      x / y ==
        r:Union(IVF,"failed"):=recip(y.ival)
        r case IVF => [x.ival * r, x.unit / y.unit]$Rep
        error "failed"
      x + y == 
        x.unit=y.unit => [x.ival + y.ival, x.unit]$Rep
        error "failed"
      x - y == 
        x.unit=y.unit => [x.ival - y.ival, x.unit]$Rep
        error "failed"
      x ^ n == 
        n > 0 => [x.ival^n::PI, x.unit^n::PI]$Rep
        n = 0 => [interval(1.0,1.0)$IVF, one()]$Rep
        r:Union(IVF,"failed"):=recip(x.ival)
        m:PI:=(-n)::PI
        r case IVF => [r^m, x.unit^n]$Rep
        error "failed"
                      
      - x   == [-x.ival, x.unit]$Rep 


      ival x == x.ival
      unit x == x.unit

      elt(v:IVF,u:U):% == [v,u]$Rep
      elt(v:F,u:U):%   == [interval(v)$IVF,u]$Rep
      
      setOutputMode(s:PI):PI ==
        modes:List PI:= [1,2,3]
        if member?(s,modes) then 
            outputMode := s
            return s
        error "1: plusMinus, 2: single, 3: interval"
      
      coerce(x) ==
        pm:Character:=char(177)
        pmof:=pm::String::Symbol::OF
        val:Float:=(sup(x.ival)+inf(x.ival))/2
        err:Float:=sup(x.ival)-val
        outputMode=1 => blankSeparate [val::OF,pmof,err::OF,x.unit::OF]
        outputMode=2 => blankSeparate [val::OF,x.unit::OF]
        outputMode=3 => blankSeparate [x.ival::OF,x.unit::OF]


                                                                    
)abbrev package SI SIunits                                                
SIunits : Exports == Implementation where
  
    USY ==> ['m,'kg,'s,'A,'K,'mol,'cd]                                  
    SIU ==> PhysicalUnitSystem(USY)     
                                                  
    Exports == with
  
      %m   : Integer -> SIU
      %kg  : Integer -> SIU        
      %s   : Integer -> SIU
      %A   : Integer -> SIU
      %K   : Integer -> SIU
      %mol : Integer -> SIU
      %cd  : Integer -> SIU                       

      hertz     : SIU
      newton    : SIU
      pascal    : SIU  
      joule     : SIU 
      watt      : SIU 
      coulomb   : SIU
      volt      : SIU
      farad     : SIU
      ohm       : SIU
      siemens   : SIU
      weber     : SIU
      tesla     : SIU
      henry     : SIU
      lumen     : SIU
      lux       : SIU
      becquerel : SIU
      gray      : SIU
      sievert   : SIU
      katal     : SIU

    Implementation ==  SIU add                 
  
      u:=baseUnits()$SIU
    
      %m(n)   == u.1^n
      %kg(n)  == u.2^n
      %s(n)   == u.3^n
      %A(n)   == u.4^n
      %K(n)   == u.5^n
      %mol(n) == u.6^n
      %cd(n)  == u.7^n
                                     
      hertz      ==  %s(-1)
      newton     ==  %kg(1)*%m(1)*%s(-2)
      pascal     ==  %kg(1)*%m(-1)*%s(-2)   
      joule      ==  %kg(1)*%m(2)*%s(-2)
      watt       ==  %kg(1)*%m(2)*%s(-3)
      coulomb    ==  %s(1)*%A(1)
      volt       ==  %kg(1)*%m(2)*%s(-3)*%A(-1)
      farad      ==  %kg(-1)*%m(-2)*%s(4)*%A(2)
      ohm        ==  %kg(1)*%m(2)*%s(-3)*%A(2)
      siemens    ==  %kg(-1)*%m(-2)*%s(3)*%A(2)
      weber      ==  %kg(1)*%m(2)*%s(-2)*%A(-1)
      tesla      ==  %kg(1)*%s(-2)*%A(-1)
      henry      ==  %kg(1)*%m(2)*%s(-2)*%A(-2)
      lumen      ==  %cd(1)
      lux        ==  %m(-2)*%cd(1)
      becquerel  ==  %s(-1)
      gray       ==  %m(2)*%s(-2)
      sievert    ==  %m(2)*%s(-2)
      katal      ==  %s(-1)*%mol(1)    

\end{spad}

\begin{axiom}

SIU:=PUSYS(['m,'kg,'s,'A,'K,'mol,'cd])
u:=baseUnits()$SIU

PSI==>PQTY(SIU)

(interval(1.2)$Interval(Float)) (u.1*u.2^3)
a:=1.233 u.1
b:=2 u.2

sin(ival a) (unit a)

setOutputMode(2)$PSI
a
b
setOutputMode(3)$PSI
a
b
setOutputMode(1)$PSI

F:=4.5555 newton()$SI
A:=300.45 %m(2)$SI
unit(F/A) /pascal()$SI

)show PUNIT
)show PUSYS
)show PQTY

-- cannot show SI (reason? -> SIU)
)show SI
\end{axiom}

spad

)abbrev category PUNIT PhysicalUnit
PhysicalUnit() : Category == with   
    "*"  : (%,%) -> %
    "/"  : (%,%) -> %
    "^"  : (%,Integer) -> %
    "="  : (%,%) -> Boolean
    dim  : % -> List Integer
    one  : %
    coerce : % -> OutputForm

)abbrev domain PUSYS PhysicalUnitSystem 
PhysicalUnitSystem(u:List Symbol) : Exports == Implementation where
    BASU ==> OrderedVariableList(u) 
    FAGB ==> FreeModule(Integer,BASU) 
    Exports == Join(PhysicalUnit,CoercibleTo OutputForm) with
      _* : (%,%) -> %
      _/ : (%,%) -> %
      baseSymbols : List Symbol
      baseUnits : List %
      factors : % ->  List Record(gen: BASU,exp: Integer)
    Implementation == FreeGroup(BASU) add
      Rep:=FreeModule(Integer,BASU)
      sort: % -> %
      x * y == sort(x+y) 
      x / y == sort(x-y)
      x ^ n == sort(n*x) 
      one() == 0$Rep
      baseSymbols() == [convert(x)@Symbol for x in enumerate$BASU]
      baseUnits() == [x::% for x in enumerate$BASU]
      dim(x) ==
        d:=[0@Integer for j in 1..#u]
        lr:List(Record(gen:BASU,exp:Integer)):=factors(x)
        for r in lr repeat
          g:BASU:=r.gen
          k:=position(g,enumerate$BASU)$List(BASU)
          d.k:=r.exp
        d

      x = y == test(dim x = dim y)                                      

      coerce0(x:%):OutputForm ==
        #monomials(x) = 0 => outputForm(1)
        d:=dim(x)
        b:=baseSymbols()
        y:List OutputForm:=[]
        for j in 1..#d repeat
          if d.j=1 then y:=concat(y,outputForm(b.j))
          else
            if d.j~=0 then y:=concat(y,outputForm(b.j)^outputForm(d.j))
        blankSeparate y 

      sort(x:%):% ==
        R==>Record(gen: BASU,exp: Integer)
        f:=(a:R,b:R):Boolean+->(test(a.gen>b.gen))
        sort(f,factors x) pretend Rep 

-- SI:=PUSYS(['m,'kg,'s])
-- u:=baseUnits()$SI
-- coerce0 works as coerce, if sort then not necess.

)abbrev domain PQTY PhysQty
PhysQty(U): Exports == Implementation where

    Q   ==> Fraction(Integer)
    F   ==> Float
    R   ==> DoubleFloat
    I   ==> Integer
    OF  ==> OutputForm
    PI  ==> PositiveInteger
    IVF ==> Interval Float
    U:PhysicalUnit

    Exports == Join(CoercibleTo OutputForm) with
      _* : (%,%) -> %
      _/ : (%,%) -> %
      _+ : (%,%) -> %
      _- : (%,%) -> %
      _^ : (%,Integer) -> %
      _- : % -> %

      ival : % -> IVF
      unit : % -> U    

      elt : (IVF,U) -> %
      elt : (F,U) -> %

      setOutputMode : PI -> PI
      coerce : % -> OutputForm

    Implementation ==  add 

      Rep := Record(ival:IVF, unit:U)

      outputMode:PI:=1

      x * y == [x.ival * y.ival, x.unit * y.unit]$Rep
      x / y ==
        r:Union(IVF,"failed"):=recip(y.ival)
        r case IVF => [x.ival * r, x.unit / y.unit]$Rep
        error "failed"
      x + y == 
        x.unit=y.unit => [x.ival + y.ival, x.unit]$Rep
        error "failed"
      x - y == 
        x.unit=y.unit => [x.ival - y.ival, x.unit]$Rep
        error "failed"
      x ^ n == 
        n > 0 => [x.ival^n::PI, x.unit^n::PI]$Rep
        n = 0 => [interval(1.0,1.0)$IVF, one()]$Rep
        r:Union(IVF,"failed"):=recip(x.ival)
        m:PI:=(-n)::PI
        r case IVF => [r^m, x.unit^n]$Rep
        error "failed"

      - x   == [-x.ival, x.unit]$Rep 

      ival x == x.ival
      unit x == x.unit

      elt(v:IVF,u:U):% == [v,u]$Rep
      elt(v:F,u:U):%   == [interval(v)$IVF,u]$Rep

      setOutputMode(s:PI):PI ==
        modes:List PI:= [1,2,3]
        if member?(s,modes) then 
            outputMode := s
            return s
        error "1: plusMinus, 2: single, 3: interval"

      coerce(x) ==
        pm:Character:=char(177)
        pmof:=pm::String::Symbol::OF
        val:Float:=(sup(x.ival)+inf(x.ival))/2
        err:Float:=sup(x.ival)-val
        outputMode=1 => blankSeparate [val::OF,pmof,err::OF,x.unit::OF]
        outputMode=2 => blankSeparate [val::OF,x.unit::OF]
        outputMode=3 => blankSeparate [x.ival::OF,x.unit::OF]

)abbrev package SI SIunits                                                
SIunits : Exports == Implementation where

    USY ==> ['m,'kg,'s,'A,'K,'mol,'cd]                                  
    SIU ==> PhysicalUnitSystem(USY)     

    Exports == with

      %m   : Integer -> SIU
      %kg  : Integer -> SIU        
      %s   : Integer -> SIU
      %A   : Integer -> SIU
      %K   : Integer -> SIU
      %mol : Integer -> SIU
      %cd  : Integer -> SIU                       

      hertz     : SIU
      newton    : SIU
      pascal    : SIU  
      joule     : SIU 
      watt      : SIU 
      coulomb   : SIU
      volt      : SIU
      farad     : SIU
      ohm       : SIU
      siemens   : SIU
      weber     : SIU
      tesla     : SIU
      henry     : SIU
      lumen     : SIU
      lux       : SIU
      becquerel : SIU
      gray      : SIU
      sievert   : SIU
      katal     : SIU

    Implementation ==  SIU add                 

      u:=baseUnits()$SIU

      %m(n)   == u.1^n
      %kg(n)  == u.2^n
      %s(n)   == u.3^n
      %A(n)   == u.4^n
      %K(n)   == u.5^n
      %mol(n) == u.6^n
      %cd(n)  == u.7^n

      hertz      ==  %s(-1)
      newton     ==  %kg(1)*%m(1)*%s(-2)
      pascal     ==  %kg(1)*%m(-1)*%s(-2)   
      joule      ==  %kg(1)*%m(2)*%s(-2)
      watt       ==  %kg(1)*%m(2)*%s(-3)
      coulomb    ==  %s(1)*%A(1)
      volt       ==  %kg(1)*%m(2)*%s(-3)*%A(-1)
      farad      ==  %kg(-1)*%m(-2)*%s(4)*%A(2)
      ohm        ==  %kg(1)*%m(2)*%s(-3)*%A(2)
      siemens    ==  %kg(-1)*%m(-2)*%s(3)*%A(2)
      weber      ==  %kg(1)*%m(2)*%s(-2)*%A(-1)
      tesla      ==  %kg(1)*%s(-2)*%A(-1)
      henry      ==  %kg(1)*%m(2)*%s(-2)*%A(-2)
      lumen      ==  %cd(1)
      lux        ==  %m(-2)*%cd(1)
      becquerel  ==  %s(-1)
      gray       ==  %m(2)*%s(-2)
      sievert    ==  %m(2)*%s(-2)
      katal      ==  %s(-1)*%mol(1)

spad

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4402353047935237670-25px001.spad
      using old system compiler.
   PUNIT abbreviates category PhysicalUnit 
------------------------------------------------------------------------
   initializing NRLIB PUNIT for PhysicalUnit 
   compiling into NRLIB PUNIT 

;;;     ***       |PhysicalUnit| REDEFINED
Time: 0 SEC.

   finalizing NRLIB PUNIT 
   Processing PhysicalUnit for Browser database:
--->-->PhysicalUnit(constructor): Not documented!!!!
--->-->PhysicalUnit((* (% % %))): Not documented!!!!
--->-->PhysicalUnit((/ (% % %))): Not documented!!!!
--->-->PhysicalUnit((^ (% % (Integer)))): Not documented!!!!
--->-->PhysicalUnit((= ((Boolean) % %))): Not documented!!!!
--->-->PhysicalUnit((dim ((List (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((one (%) constant)): Not documented!!!!
--->-->PhysicalUnit((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysicalUnit(): Missing Description
; compiling file "/var/aw/var/LatexWiki/PUNIT.NRLIB/PUNIT.lsp" (written 16 JUL 2018 04:38:54 PM):

; /var/aw/var/LatexWiki/PUNIT.NRLIB/PUNIT.fasl written
; compilation finished in 0:00:00.003
------------------------------------------------------------------------
   PhysicalUnit is now explicitly exposed in frame initial 
   PhysicalUnit will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PUNIT.NRLIB/PUNIT

   PUSYS abbreviates domain PhysicalUnitSystem 
------------------------------------------------------------------------
   initializing NRLIB PUSYS for PhysicalUnitSystem 
   compiling into NRLIB PUSYS 
   compiling exported * : ($,$) -> $
Time: 0.02 SEC.

   compiling exported / : ($,$) -> $
Time: 0.01 SEC.

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

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

   compiling exported baseSymbols : () -> List Symbol
Time: 0 SEC.

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

   compiling exported dim : $ -> List Integer
Time: 0.02 SEC.

   compiling exported = : ($,$) -> Boolean
Time: 0.01 SEC.

   compiling local coerce0 : $ -> OutputForm
Time: 0.08 SEC.

   compiling local sort : $ -> $
   processing macro definition R ==> Record(gen: OrderedVariableList u,exp: Integer) 
Time: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PhysicalUnitSystem| REDEFINED

;;;     ***       |PhysicalUnitSystem| REDEFINED
Time: 0 SEC.

   Warnings: 
      [1] dim:  gen has no value
      [2] dim:  exp has no value
      [3] coerce0:  y has no value
      [4] sort:  gen has no value

   Cumulative Statistics for Constructor PhysicalUnitSystem
      Time: 0.15 seconds

--------------non extending category----------------------
.. PhysicalUnitSystem(#1) of cat 
(|Join| (|PhysicalUnit|) (|CoercibleTo| (|OutputForm|))
        (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE / ($ $ $))
         (SIGNATURE |baseSymbols| ((|List| (|Symbol|))) |constant|)
         (SIGNATURE |baseUnits| ((|List| $)) |constant|)
         (SIGNATURE |factors|
          ((|List|
            (|Record| (|:| |gen| (|OrderedVariableList| |#1|))
                      (|:| |exp| (|Integer|))))
           $))))   has no 
(|Group|)    finalizing NRLIB PUSYS 
   Processing PhysicalUnitSystem for Browser database:
--->-->PhysicalUnitSystem(constructor): Not documented!!!!
--->-->PhysicalUnitSystem((* (% % %))): Not documented!!!!
--->-->PhysicalUnitSystem((/ (% % %))): Not documented!!!!
--->-->PhysicalUnitSystem((baseSymbols ((List (Symbol))) constant)): Not documented!!!!
--->-->PhysicalUnitSystem((baseUnits ((List %)) constant)): Not documented!!!!
--->-->PhysicalUnitSystem((factors ((List (Record (: gen (OrderedVariableList u)) (: exp (Integer)))) %))): Not documented!!!!
--->-->PhysicalUnitSystem(): Missing Description
; compiling file "/var/aw/var/LatexWiki/PUSYS.NRLIB/PUSYS.lsp" (written 16 JUL 2018 04:38:55 PM):

; /var/aw/var/LatexWiki/PUSYS.NRLIB/PUSYS.fasl written
; compilation finished in 0:00:00.045
------------------------------------------------------------------------
   PhysicalUnitSystem is now explicitly exposed in frame initial 
   PhysicalUnitSystem will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PUSYS.NRLIB/PUSYS

   PQTY abbreviates domain PhysQty 
------------------------------------------------------------------------
   initializing NRLIB PQTY for PhysQty 
   compiling into NRLIB PQTY 
Local variable Rep type redefined: (Join (SetCategory) (CATEGORY domain (SIGNATURE construct ((Record (: ival (Interval (Float))) (: unit U)) (Interval (Float)) U)) (SIGNATURE ~= ((Boolean) (Record (: ival (Interval (Float))) (: unit U)) (Record (: ival (Interval (Float))) (: unit U)))) (SIGNATURE coerce ((OutputForm) (Record (: ival (Interval (Float))) (: unit U)))) (SIGNATURE elt ((Interval (Float)) (Record (: ival (Interval (Float))) (: unit U)) ival)) (SIGNATURE elt (U (Record (: ival (Interval (Float))) (: unit U)) unit)) (SIGNATURE setelt! ((Interval (Float)) (Record (: ival (Interval (Float))) (: unit U)) ival (Interval (Float)))) (SIGNATURE setelt! (U (Record (: ival (Interval (Float))) (: unit U)) unit U)) (SIGNATURE copy ((Record (: ival (Interval (Float))) (: unit U)) (Record (: ival (Interval (Float))) (: unit U)))))) to (Join (BiModule (Integer) (Integer)) (FreeModuleCategory (Integer) (OrderedVariableList u)) (CATEGORY package (IF (has (Integer) (CommutativeRing)) (ATTRIBUTE (Module (Integer))) noBranch)))
   compiling exported * : ($,$) -> $
Time: 0.02 SEC.

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

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

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

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

   compiling exported - : $ -> $
Time: 0.01 SEC.

   compiling exported ival : $ -> Interval Float
      PQTY;ival;$I;7 is replaced by QCAR 
Time: 0 SEC.

   compiling exported unit : $ -> U
      PQTY;unit;$U;8 is replaced by QCDR 
Time: 0 SEC.

   compiling exported elt : (Interval Float,U) -> $
      PQTY;elt;IU$;9 is replaced by CONS 
Time: 0 SEC.

   compiling exported elt : (Float,U) -> $
Time: 0 SEC.

   compiling exported setOutputMode : PositiveInteger -> PositiveInteger
Time: 0 SEC.

   compiling exported coerce : $ -> OutputForm
Time: 0.02 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PhysQty| REDEFINED

;;;     ***       |PhysQty| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor PhysQty
      Time: 0.05 seconds

   finalizing NRLIB PQTY 
   Processing PhysQty for Browser database:
--->-->PhysQty(constructor): Not documented!!!!
--->-->PhysQty((* (% % %))): Not documented!!!!
--->-->PhysQty((/ (% % %))): Not documented!!!!
--->-->PhysQty((+ (% % %))): Not documented!!!!
--->-->PhysQty((- (% % %))): Not documented!!!!
--->-->PhysQty((^ (% % (Integer)))): Not documented!!!!
--->-->PhysQty((- (% %))): Not documented!!!!
--->-->PhysQty((ival ((Interval (Float)) %))): Not documented!!!!
--->-->PhysQty((unit (U %))): Not documented!!!!
--->-->PhysQty((elt (% (Interval (Float)) U))): Not documented!!!!
--->-->PhysQty((elt (% (Float) U))): Not documented!!!!
--->-->PhysQty((setOutputMode ((PositiveInteger) (PositiveInteger)))): Not documented!!!!
--->-->PhysQty((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysQty(): Missing Description
; compiling file "/var/aw/var/LatexWiki/PQTY.NRLIB/PQTY.lsp" (written 16 JUL 2018 04:38:55 PM):

; /var/aw/var/LatexWiki/PQTY.NRLIB/PQTY.fasl written
; compilation finished in 0:00:00.046
------------------------------------------------------------------------
   PhysQty is now explicitly exposed in frame initial 
   PhysQty will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PQTY.NRLIB/PQTY

   SI abbreviates package SIunits 
------------------------------------------------------------------------
   initializing NRLIB SI for SIunits 
   compiling into NRLIB SI 
   compiling exported %m : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported %kg : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported %s : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported %A : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported %K : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0.01 SEC.

   compiling exported %mol : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported %cd : Integer -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported hertz : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported newton : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported pascal : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported joule : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported watt : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported coulomb : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported volt : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0.01 SEC.

   compiling exported farad : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported ohm : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported siemens : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported weber : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported tesla : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported henry : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported lumen : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported lux : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0.01 SEC.

   compiling exported becquerel : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported gray : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported sievert : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

   compiling exported katal : () -> PhysicalUnitSystem construct(QUOTE m,QUOTE kg,QUOTE s,QUOTE A,QUOTE K,QUOTE mol,QUOTE cd)
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |SIunits| REDEFINED

;;;     ***       |SIunits| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor SIunits
      Time: 0.03 seconds

--------------non extending category----------------------
.. SIunits of cat 
(CATEGORY |package|
 (SIGNATURE |%m|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE |%kg|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE |%s|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE %A
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE %K
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE |%mol|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE |%cd|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
   (|Integer|)))
 (SIGNATURE |hertz|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |newton|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |pascal|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |joule|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |watt|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |coulomb|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |volt|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |farad|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |ohm|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |siemens|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |weber|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |tesla|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |henry|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |lumen|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |lux|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |becquerel|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |gray|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |sievert|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|)
 (SIGNATURE |katal|
  ((|PhysicalUnitSystem| (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|)))
  |constant|))   has no 
(|PhysicalUnit|)    finalizing NRLIB SI 
   Processing SIunits for Browser database:
--->-->SIunits(constructor): Not documented!!!!
--->-->SIunits(   PhysicalUnitSystem(['m, 'kg, 's, 'A, 'K, 'mol, 'cd])(Integer())()
): Not documented!!!!
--->-->SIunits((%kg ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd))) (Integer)))): Not documented!!!!
--->-->SIunits((((|PhysicalUnitSystem|
                  (|construct| '|m| '|kg| '|s| 'A 'K '|mol| '|cd|))
                 (|Integer|)))): Not documented!!!!
--->-->SIunits((%A ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd))) (Integer)))): Not documented!!!!
--->-->SIunits((%K ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd))) (Integer)))): Not documented!!!!
--->-->SIunits((%mol ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd))) (Integer)))): Not documented!!!!
--->-->SIunits((%cd ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd))) (Integer)))): Not documented!!!!
--->-->SIunits((hertz ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((newton ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((pascal ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((joule ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((watt ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((coulomb ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((volt ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((farad ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((ohm ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((siemens ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((weber ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((tesla ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((henry ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((lumen ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((lux ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((becquerel ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((gray ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((sievert ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits((katal ((PhysicalUnitSystem (construct (QUOTE m) (QUOTE kg) (QUOTE s) (QUOTE A) (QUOTE K) (QUOTE mol) (QUOTE cd)))) constant)): Not documented!!!!
--->-->SIunits(): Missing Description
; compiling file "/var/aw/var/LatexWiki/SI.NRLIB/SI.lsp" (written 16 JUL 2018 04:38:55 PM):

; /var/aw/var/LatexWiki/SI.NRLIB/SI.fasl written
; compilation finished in 0:00:00.070
------------------------------------------------------------------------
   SIunits is now explicitly exposed in frame initial 
   SIunits will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SI.NRLIB/SI

fricas

SIU:=PUSYS(['m,'kg,'s,'A,'K,'mol,'cd])

$\label{eq1}\hbox{\axiomType{PhysicalUnitSystem}\ } ([ m , kg , s , A , K , mol , cd ])$

(1)

Type: Type

fricas

u:=baseUnits()$SIU

$\label{eq2}\left[ m , \: kg , \: s , \: A , \: K , \: mol , \: cd \right]$

(2)

Type: List(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

PSI==>PQTY(SIU)

Type: Void

fricas

(interval(1.2)$Interval(Float)) (u.1*u.2^3)

$\label{eq3}{1.2}\ �� \ {0.7 E - 20}\ {m \ {{kg}^{3}}}$

(3)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

a:=1.233 u.1

$\label{eq4}{1.233}\ �� \ {0.7 E - 20}\ m$

(4)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

b:=2 u.2

$\label{eq5}{2.0}\ �� \ {0.0}\ kg$

(5)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

sin(ival a) (unit a)

$\label{eq6}{0.9434872724 \_ 125741287}\ �� \ {0.7 E - 20}\ m$

(6)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

setOutputMode(2)$PSI

$\label{eq7}2$

(7)

Type: PositiveInteger?

fricas

$\label{eq8}{1.233}\ m$

(8)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

$\label{eq9}{2.0}\ kg$

(9)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

setOutputMode(3)$PSI

$\label{eq10}3$

(10)

Type: PositiveInteger?

fricas

$\label{eq11}{\left[{1.233}, \:{1.233}\right]}\ m$

(11)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

$\label{eq12}{\left[{2.0}, \:{2.0}\right]}\ kg$

(12)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

setOutputMode(1)$PSI

$\label{eq13}1$

(13)

Type: PositiveInteger?

fricas

F:=4.5555 newton()$SI

$\label{eq14}{4.5555}\ �� \ {0.3 E - 19}\ {m \ kg \ {{s}^{- 2}}}$

(14)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

A:=300.45 %m(2)$SI

$\label{eq15}{300.45}\ �� \ {0.2 E - 17}\ {{m}^{2}}$

(15)

Type: PhysQty?(PhysicalUnitSystem?([m,kg,s,A,K,mol,cd]))

fricas

unit(F/A) /pascal()$SI

$\label{eq16}1$

(16)

Type: PhysicalUnitSystem?([m,kg,s,A,K,mol,cd])

fricas

)show PUNIT

 PhysicalUnit is a category constructor
 Abbreviation for PhysicalUnit is PUNIT 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (%, %) -> %                     ?/? : (%, %) -> %
 ?=? : (%, %) -> Boolean               ?^? : (%, Integer) -> %
 coerce : % -> OutputForm              dim : % -> List(Integer)
 one : () -> %

fricas

)show PUSYS

 PhysicalUnitSystem(u: List(Symbol)) is a domain constructor
 Abbreviation for PhysicalUnitSystem is PUSYS 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (%, %) -> %                     ?/? : (%, %) -> %
 ?=? : (%, %) -> Boolean               ?^? : (%, Integer) -> %
 baseSymbols : () -> List(Symbol)      baseUnits : () -> List(%)
 coerce : % -> OutputForm              dim : % -> List(Integer)
 one : () -> %                        
 factors : % -> List(Record(gen: OrderedVariableList(u),exp: Integer))

fricas

)show PQTY

 PhysQty(U: PhysicalUnit) is a domain constructor
 Abbreviation for PhysQty is PQTY 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (%, %) -> %                     ?+? : (%, %) -> %
 -? : % -> %                           ?-? : (%, %) -> %
 ?/? : (%, %) -> %                     ?^? : (%, Integer) -> %
 coerce : % -> OutputForm              elt : (Float, U) -> %
 elt : (Interval(Float), U) -> %       ival : % -> Interval(Float)
 unit : % -> U                        
 setOutputMode : PositiveInteger -> PositiveInteger

-- cannot show SI (reason? -> SIU)

fricas

)show SI

 SIunits is a package constructor
 Abbreviation for SIunits is SI 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

   >> Error detected within library code:
   index out of range