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SandBoxPQTY
  
last edited 9 years ago by Kurt Pagani

Edit detail for SandBoxPQTY revision 4 of 5
1 2 3 4 5
Editor: Kurt Pagani
Time: 2015/08/02 03:22:07 GMT+0
Note: 
changed:
-solve(bpi.1=%C,T)
solve(bpi.1=1,T)

spad
++++++++++++++++++++++++
++ $Id: 01-AUG-2015$ +++
++++++++++++++++++++++++
)abbrev domain RIA Q_INTERVAL
++ Author: Kurt Pagani
++ Date Created: 2012
++ License: BSD (same as Axiom)
++ ===================================
++ Rational Interval Arithmetics (RIA)
++ ===================================
++ This is an implementation of RIA as a FriCAS domain.
++ Ref. "Guaranteed Proofs Using Interval Arithmetic"
++ by Marc Daumas, Guillaume Melquiond, and Cesar Munoz
++ See docs for more information.
++
++ 
++
Q_INTERVAL : Exports == Implementation where

    Q ==> Fraction(Integer)
    R ==> DoubleFloat
    I ==> Integer

    OF ==> OutputForm
    DF ==> DoubleFloat

    Exports == Join(CoercibleTo OutputForm, ConvertibleTo String) with

        ----------------------------
        -- Basic interval operations
        ----------------------------

        "+" : (%,%) -> %
        "-" : (%,%) -> %
        "*" : (%,%) -> %
        "/" : (%,%) -> %
        "^" : (%,I) -> %
        "-" :  % -> %
        abs :  % -> %
        elt : (Q, %) -> %
        coerce: % -> OutputForm
        coerce: List Q -> %
        coerce: Float -> %
        coerce: DF -> %

        concise : % -> OutputForm

        ----------------------------------
        -- Constructors and query functions
        -----------------------------------

        mki : (Q,Q) -> %
        lb  :  % -> Q
        ub  :  % -> Q

        mid :  % -> Q
        len :  % -> Q

        frep    : % -> OF
        tm_frep : % -> OF

    Implementation == add 

        --------------------
        -- Represent as Rec
        --------------------     
        Rep := Record(lb:Q, ub:Q)

        -----------------------
        -- Implement functions
        -----------------------
        mki(a,b) == b>=a => [a,b]$Rep

        lb(r:%) == r.lb
        ub(r:%) == r.ub

        x+y == mki(x.lb + y.lb, x.ub + y.ub)
        x-y == mki(x.lb - y.ub, x.ub - y.lb)

        x*y == 
          a:Q:=min(min(x.lb*y.lb,x.lb*y.ub),min(x.ub*y.lb,x.ub*y.ub))
          b:Q:=max(max(x.lb*y.lb,x.lb*y.ub),max(x.ub*y.lb,x.ub*y.ub))
          mki(a,b)

        x/y == if y.lb*y.ub > 0 then x*mki(1/y.ub,1/y.lb)

        -x == mki(-x.ub,-x.lb)

        abs(x) ==
          if x.lb*x.ub >= 0 then 
            mki(min(abs(x.lb), abs(x.ub)), max(abs(x.lb), abs(x.ub)))
          else
            mki(0::Q, max(abs(x.lb), abs(x.ub)))

        x^n ==
          zero? n   => mki(1,1)
          one?  n   => x
          x.lb>=0 or odd?  n => mki(x.lb^n,x.ub^n) 
          x.ub<=0 or even? n => mki(x.ub^n,x.lb^n)
          mki(0,max(x.lb^n,x.ub^n))

        coerce(r : %) : OutputForm ==
          hconcat ["[",r.lb::OF,",",r.ub::OF,"]"]

        coerce(l : List Q) : % ==
          #l ~= 2 => error "Format: [lb,ub]"
          l.1 > l.2 => error "Must have lb <= ub"
          mki(l.1,l.2)

        coerce(r:DF):% ==
          rc:Q:=retract r
          mki(rc,rc)

        coerce(r:Float):% ==
          rc:Q:=retract r
          mki(rc,rc)    

        coerceSTR(s:String):% ==
          s1 := split(s,char ".")
          s2 := split(s1.2, char "(")
          vs := concat [s1.1,".",s2.1]
          v:=float(convert vs)
          v::Rep

        elt(q:Q,x:%):% == mki(q*x.lb, q*x.ub)

        mid(x:%):Q == (x.lb + x.ub)/2::Q
        len(x:%):Q == (x.ub - x.lb)

        frep(x:%):OF ==
          pm:Character:=char(177)
          sep:=concat [" ",pm::String," "]::Symbol
          hconcat [mid(x)::DF::OF, sep::OF, (len(x)/2::Q)::DF::OF]

        tm_frep(x:%):OF ==
          sep:=" <pm> "::Symbol
          hconcat [mid(x)::DF::OF, sep::OF, (len(x)/2::Q)::DF::OF]       

        concise(x:%):OF == frep(x)  -- to do

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

)abbrev domain SI SI_UNIT 
++ Author: Kurt Pagani
++ Date Created: 2012
++ License: BSD (same as Axiom)
++ ================================
++ Physical Quantities and SI Units
++ ================================
++ This is an implementation of physical quantities and SI units as FriCAS 
++ domains.
++
++ See docs for more information.
++
++ Revision:
++ - removing outputForm, Ring
++ - added negation, elt
++
++
SI_UNIT : Exports == Implementation where

    EI  ==> Expression Integer
    VI  ==> Vector Integer
    LS  ==> List Symbol
    LEI ==> List EI
    LVI ==> List VI

    Exports == Join(PhysicalUnit,CoercibleTo OutputForm) with

        ----------------------------
        -- (de)-construct an SI unit  
        ----------------------------
        mksi: List(Integer) -> %
        si2l: % -> List(Integer)

        --------------------------------
        -- basic operation with SI units
        --------------------------------
        --"*"  : (%,%) -> %
        --"/"  : (%,%) -> %
        --"^"  : (%,Integer) -> %
        --"="  : (%,%) -> Boolean

        -----------------------------------------------------------------
        -- constructor for each base unit: e.g. %m(2)=m^2 -> square meter
        -----------------------------------------------------------------
        %m   :  Integer -> %
        %kg  :  Integer -> %  
        %s   :  Integer -> %
        %A   :  Integer -> %
        %K   :  Integer -> %  
        %mol :  Integer -> % 
        %cd  :  Integer -> %
        --%one :          -> %        

        -------------------
        -- SI derived units
        -------------------
        SI_derived : String -> %

        ----------------
        -- Buckingham Pi 
        ----------------
        buck : Table(Symbol,%) -> List(Expression(Integer))

    Implementation == add

        ---------------------------------------      
        -- Represent as 1-Array [0,0,0,0,0,0,0]
        ---------------------------------------    
        Rep := OneDimensionalArray(Integer)

        ---------------------------------
        -- Implementation of constructors
        ---------------------------------

        mksi(l) == 
          r:Rep:=new(7,0$Integer)$Rep       
          for i in 1..7 repeat r.i := l(i)
          r

        si2l(r) ==
          l:List(Integer):=[0,0,0,0,0,0,0]
          for i in 1..7 repeat l(i) := r.i
          l

        x * y ==
          z:Rep:=new(7,0$Integer)$Rep
          for i in 1..7 repeat z.i := x.i + y.i
          z

        x / y ==
          z:Rep:=new(7,0$Integer)$Rep
          for i in 1..7 repeat z.i := x.i - y.i
          z

        x ^ n ==
          z:Rep:=new(7,0$Integer)$Rep
          for i in 1..7 repeat z.i := x.i * n
          z

        x = y ==
          res:Boolean:=true 
          for i in 1..7 repeat res:=(res and test(x.i=y.i)$Boolean) 
          res

        ------------------------ 
        -- Coerce to output form
        ------------------------  
        coerce(r : %) : OutputForm ==
          SYM ==> Symbol
          OF  ==> OutputForm
          sym:List(String):=["m","kg","s","A","K","mol","cd"]
          f:OutputForm:=empty()     
          for i in 1..7 repeat 
            if not zero? r.i then 
              f:=hconcat(f,super(sym(i)::SYM::OF, r.i::OF))
          f

        ------------------------------------------
        -- Base unit constructors (implementation)
        ------------------------------------------ 

        %m(n:Integer) ==
          mksi([n,0,0,0,0,0,0]) 

        %kg(n:Integer) ==
          mksi([0,n,0,0,0,0,0]) 

        %s(n:Integer) ==
          mksi([0,0,n,0,0,0,0])          

        %A(n:Integer) ==
          mksi([0,0,0,n,0,0,0]) 

        %K(n:Integer) ==
          mksi([0,0,0,0,n,0,0]) 

        %mol(n:Integer) ==
          mksi([0,0,0,0,0,n,0])

        %cd(n:Integer) ==
          mksi([0,0,0,0,0,0,n])                   

        %one() ==
          mksi([0,0,0,0,0,0,0])  

        SI_derived(s:String):% ==
          s = "hertz"     => %s(-1)
          s = "newton"    => %kg(1)*%m(1)*%s(-2)
          s = "pascal"    => %kg(1)*%m(-1)*%s(-2)
          s = "joule"     => %kg(1)*%m(2)*%s(-2)
          s = "watt"      => %kg(1)*%m(2)*%s(-3)
          s = "coulomb"   => %s(1)*%A(1)
          s = "volt"      => %kg(1)*%m(2)*%s(-3)*%A(-1)
          s = "farad"     => %kg(-1)*%m(-2)*%s(4)*%A(2)
          s = "ohm"       => %kg(1)*%m(2)*%s(-3)*%A(2)
          s = "siemens"   => %kg(-1)*%m(-2)*%s(3)*%A(2)
          s = "weber"     => %kg(1)*%m(2)*%s(-2)*%A(-1)
          s = "tesla"     => %kg(1)*%s(-2)*%A(-1)
          s = "henry"     => %kg(1)*%m(2)*%s(-2)*%A(-2)
          s = "lumen"     => %cd(1)
          s = "lux"       => %m(-2)*%cd(1)
          s = "becquerel" => %s(-1)
          s = "gray"      => %m(2)*%s(-2)
          s = "sievert"   => %m(2)*%s(-2)
          s = "katal"     => %s(-1)*%mol(1)
          error "Expected string name of a derived SI unit."

        -- Helper function
        mkxpr(s:LS,v:VI):EI == 
          r:EI:=1
          for j in 1..#s repeat r:=r*(s.j)::EI^(v.j)
          r

        -- Buckingham Pi
        buck(t:Table(Symbol,%)):LEI ==
          M:Matrix(Integer):=matrix [si2l(t.x) for x in keys(t)]
          ns:LVI:=nullSpace transpose(M)
          r:LEI:=[]
          for j in 1..#ns repeat r:=append(r,[mkxpr(keys(t),ns.j)])
          r

-- End of SI_UNIT --        

-------------------------------------------------------------------------------
)abbrev domain PQTY PhysQty
++ Author: Kurt Pagani
++ Date Created: 2012
++ License: BSD (same as Axiom)
++
PhysQty(U): Exports == Implementation where

    Q   ==> Fraction(Integer)
    F   ==> Float
    R   ==> DoubleFloat
    I   ==> Integer
    QI  ==> Q_INTERVAL
    U:PhysicalUnit

    Exports == Join(CoercibleTo OutputForm) with

        --------------------------------------
        -- Physical quantities base operations
        --------------------------------------

        "*": (%,%) -> %
        "/": (%,%) -> %
        "+": (%,%) -> %
        "-": (%,%) -> %
        "^": (%,Integer) -> %
        "-":  % -> %
        elt: (Q, %) -> %
        elt: (QI,U) -> %
        elt: (Union(Q,F,R,I),U) -> %
        coerce : % -> OutputForm

        ---------------------------------------------------
        -- Main constructor: pqty(value, uncertainty, unit)
        ---------------------------------------------------
        pqty: (Q, Q, U) -> %    

        pqty_value: % -> Q  -- get the value
        pqty_error: % -> Q  -- get the uncertainty
        pqty_unit:  % -> U  -- get the unit

        pqty_interval: % -> QI  -- get the interval [v-delta,v+delta]
        pqty_scale: (%,Q) -> %       -- scale by rational number

        pqty_tm_toggle: U -> Boolean        

    Implementation ==  add 

        ----------------------
        -- Represent as Record
        ----------------------     
        Rep := Record(ival:QI, unit:U)

        ----------------------
        -- Implement functions
        ----------------------
        pqty(v,e,u) == [[v-e,v+e]::List(Q)::QI,u::U]$Rep

        pqty_value(r) == mid(r.ival)

        pqty_error(r) == len(r.ival)/2::Q

        pqty_unit(r) == r.unit

        pqty_interval(r) == r.ival

        ----------------------------------------------------
        -- Implement basic operations (interval arithmetic))
        ----------------------------------------------------

        x*y == [x.ival*y.ival, x.unit*y.unit]$Rep

        x/y == [x.ival/y.ival, x.unit/y.unit]$Rep

        x+y == x.unit=y.unit => [x.ival+y.ival, x.unit]$Rep

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

        x^n == [x.ival^n, x.unit^n]$Rep

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

        -----------------------------------------------------------
        -- scale
        -----------------------------------------------------------
        pqty_scale(x,s) == [s x.ival,x.unit]$Rep

        --elts
        elt(q:Q,x:%):% == pqty_scale(x,q)
        elt(qi:QI,u:U):% == [qi,u]$Rep
        elt(s:Union(Q,F,R,I),u:U):% == [[s::Q,s::Q]::List(Q)::QI,u]$Rep

        pqty_tm := false

        pqty_tm_toggle(u:U) : Boolean ==  -- bad hack
          pqty_tm := not pqty_tm
          pqty_tm

        coerce(r : %) : OutputForm ==
          OF ==> OutputForm
          pqty_tm = true =>7
          hconcat [tm_frep r.ival, " "::OF, r.unit::OF ]
          hconcat [frep r.ival, " "::OF, r.unit::OF ]

-- End of PhysQty
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8367240618814005156-25px001.spad
      using old system compiler.
   RIA abbreviates domain Q_INTERVAL 
------------------------------------------------------------------------
   initializing NRLIB RIA for Q_INTERVAL 
   compiling into NRLIB RIA 
   compiling exported mki : (Fraction Integer,Fraction Integer) -> $
Time: 0.03 SEC.

   compiling exported lb : $ -> Fraction Integer
      RIA;lb;$F;2 is replaced by QCAR 
Time: 0 SEC.

   compiling exported ub : $ -> Fraction Integer
      RIA;ub;$F;3 is replaced by QCDR 
Time: 0 SEC.

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

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

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

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

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

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

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

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

   compiling exported coerce : List Fraction Integer -> $
Time: 0.03 SEC.

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

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

   compiling local coerceSTR : String -> $
Time: 0.01 SEC.

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

   compiling exported mid : $ -> Fraction Integer
Time: 0 SEC.

   compiling exported len : $ -> Fraction Integer
Time: 0 SEC.

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

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

   compiling exported concise : $ -> OutputForm
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       Q_INTERVAL REDEFINED

;;;     ***       Q_INTERVAL REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Q_INTERVAL
      Time: 0.12 seconds

   finalizing NRLIB RIA 
   Processing Q_INTERVAL for Browser database:
--------constructor---------
--->-->Q_INTERVAL((+ (% % %))): Not documented!!!!
--->-->Q_INTERVAL((- (% % %))): Not documented!!!!
--->-->Q_INTERVAL((* (% % %))): Not documented!!!!
--->-->Q_INTERVAL((/ (% % %))): Not documented!!!!
--->-->Q_INTERVAL((^ (% % (Integer)))): Not documented!!!!
--->-->Q_INTERVAL((- (% %))): Not documented!!!!
--->-->Q_INTERVAL((abs (% %))): Not documented!!!!
--->-->Q_INTERVAL((elt (% (Fraction (Integer)) %))): Not documented!!!!
--->-->Q_INTERVAL((coerce ((OutputForm) %))): Not documented!!!!
--->-->Q_INTERVAL((coerce (% (List (Fraction (Integer)))))): Not documented!!!!
--->-->Q_INTERVAL((coerce (% (Float)))): Not documented!!!!
--->-->Q_INTERVAL((coerce (% (DoubleFloat)))): Not documented!!!!
--->-->Q_INTERVAL((concise ((OutputForm) %))): Not documented!!!!
--->-->Q_INTERVAL((mki (% (Fraction (Integer)) (Fraction (Integer))))): Not documented!!!!
--->-->Q_INTERVAL((lb ((Fraction (Integer)) %))): Not documented!!!!
--->-->Q_INTERVAL((ub ((Fraction (Integer)) %))): Not documented!!!!
--->-->Q_INTERVAL((mid ((Fraction (Integer)) %))): Not documented!!!!
--->-->Q_INTERVAL((len ((Fraction (Integer)) %))): Not documented!!!!
--->-->Q_INTERVAL((frep ((OutputForm) %))): Not documented!!!!
--->-->Q_INTERVAL((tm_frep ((OutputForm) %))): Not documented!!!!
; compiling file "/var/aw/var/LatexWiki/RIA.NRLIB/RIA.lsp" (written 02 AUG 2015 03:22:03 AM):

; /var/aw/var/LatexWiki/RIA.NRLIB/RIA.fasl written
; compilation finished in 0:00:00.102
------------------------------------------------------------------------
   Q_INTERVAL is now explicitly exposed in frame initial 
   Q_INTERVAL will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/RIA.NRLIB/RIA

   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:
--------constructor---------
--->-->PhysicalUnit((+ (% % %))): Not documented!!!!
--->-->PhysicalUnit((- (% % %))): Not documented!!!!
--->-->PhysicalUnit((* (% % %))): Not documented!!!!
--->-->PhysicalUnit((/ (% % %))): Not documented!!!!
--->-->PhysicalUnit((^ (% % (Integer)))): Not documented!!!!
--->-->PhysicalUnit((- (% %))): Not documented!!!!
--->-->PhysicalUnit((abs (% %))): Not documented!!!!
--->-->PhysicalUnit((elt (% (Fraction (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysicalUnit((coerce (% (List (Fraction (Integer)))))): Not documented!!!!
--->-->PhysicalUnit((coerce (% (Float)))): Not documented!!!!
--->-->PhysicalUnit((coerce (% (DoubleFloat)))): Not documented!!!!
--->-->PhysicalUnit((concise ((OutputForm) %))): Not documented!!!!
--->-->PhysicalUnit((mki (% (Fraction (Integer)) (Fraction (Integer))))): Not documented!!!!
--->-->PhysicalUnit((lb ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((ub ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((mid ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((len ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysicalUnit((frep ((OutputForm) %))): Not documented!!!!
--->-->PhysicalUnit((tm_frep ((OutputForm) %))): Not documented!!!!
--------constructor---------
--->-->PhysicalUnit((* (% % %))): Not documented!!!!
--->-->PhysicalUnit((/ (% % %))): Not documented!!!!
--->-->PhysicalUnit((^ (% % (Integer)))): Not documented!!!!
--->-->PhysicalUnit((= ((Boolean) % %))): Not documented!!!!
--->-->PhysicalUnit((%one (%))): Not documented!!!!
--->-->PhysicalUnit((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysicalUnit(): Spurious comments: \blankline
; compiling file "/var/aw/var/LatexWiki/PUNIT.NRLIB/PUNIT.lsp" (written 02 AUG 2015 03:22:03 AM):

; /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

   SI abbreviates domain SI_UNIT 
------------------------------------------------------------------------
   initializing NRLIB SI for SI_UNIT 
   compiling into NRLIB SI 
Local variable Rep type redefined: (Join (OneDimensionalArrayAggregate (Integer)) (CATEGORY domain (SIGNATURE oneDimensionalArray ($ (List (Integer)))) (SIGNATURE oneDimensionalArray ($ (NonNegativeInteger) (Integer))))) to (Join (SetCategory) (CATEGORY domain (SIGNATURE construct ((Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) (Fraction (Integer)) (Fraction (Integer)))) (SIGNATURE ~= ((Boolean) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))))) (SIGNATURE coerce ((OutputForm) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))))) (SIGNATURE elt ((Fraction (Integer)) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) lb)) (SIGNATURE elt ((Fraction (Integer)) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) ub)) (SIGNATURE setelt! ((Fraction (Integer)) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) lb (Fraction (Integer)))) (SIGNATURE setelt! ((Fraction (Integer)) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) ub (Fraction (Integer)))) (SIGNATURE copy ((Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer)))) (Record (: lb (Fraction (Integer))) (: ub (Fraction (Integer))))))))
   compiling exported mksi : List Integer -> $
Time: 0.01 SEC.

   compiling exported si2l : $ -> List Integer
Time: 0 SEC.

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

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

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

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

   compiling exported coerce : $ -> OutputForm
   processing macro definition SYM ==> Symbol 
   processing macro definition OF ==> OutputForm 
Time: 0.01 SEC.

   compiling exported %m : Integer -> $
Time: 0 SEC.

   compiling exported %kg : Integer -> $
Time: 0.01 SEC.

   compiling exported %s : Integer -> $
Time: 0 SEC.

   compiling exported %A : Integer -> $
Time: 0 SEC.

   compiling exported %K : Integer -> $
Time: 0 SEC.

   compiling exported %mol : Integer -> $
Time: 0 SEC.

   compiling exported %cd : Integer -> $
Time: 0 SEC.

   compiling exported %one : () -> $
Time: 0.01 SEC.

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

   compiling local mkxpr : (List Symbol,Vector Integer) -> Expression Integer
Time: 0.06 SEC.

   compiling exported buck : Table(Symbol,$) -> List Expression Integer
Time: 0.03 SEC.

(time taken in buildFunctor:  0)

;;;     ***       SI_UNIT REDEFINED

;;;     ***       SI_UNIT REDEFINED
Time: 0 SEC.

   Warnings: 
      [1] coerce:  f has no value

   Cumulative Statistics for Constructor SI_UNIT
      Time: 0.16 seconds

   finalizing NRLIB SI 
   Processing SI_UNIT for Browser database:
--------constructor---------
--->-->SI_UNIT((+ (% % %))): Not documented!!!!
--->-->SI_UNIT((- (% % %))): Not documented!!!!
--->-->SI_UNIT((* (% % %))): Not documented!!!!
--->-->SI_UNIT((/ (% % %))): Not documented!!!!
--->-->SI_UNIT((^ (% % (Integer)))): Not documented!!!!
--->-->SI_UNIT((- (% %))): Not documented!!!!
--->-->SI_UNIT((abs (% %))): Not documented!!!!
--->-->SI_UNIT((elt (% (Fraction (Integer)) %))): Not documented!!!!
--->-->SI_UNIT((coerce ((OutputForm) %))): Not documented!!!!
--->-->SI_UNIT((coerce (% (List (Fraction (Integer)))))): Not documented!!!!
--->-->SI_UNIT((coerce (% (Float)))): Not documented!!!!
--->-->SI_UNIT((coerce (% (DoubleFloat)))): Not documented!!!!
--->-->SI_UNIT((concise ((OutputForm) %))): Not documented!!!!
--->-->SI_UNIT((mki (% (Fraction (Integer)) (Fraction (Integer))))): Not documented!!!!
--->-->SI_UNIT((lb ((Fraction (Integer)) %))): Not documented!!!!
--->-->SI_UNIT((ub ((Fraction (Integer)) %))): Not documented!!!!
--->-->SI_UNIT((mid ((Fraction (Integer)) %))): Not documented!!!!
--->-->SI_UNIT((len ((Fraction (Integer)) %))): Not documented!!!!
--->-->SI_UNIT((frep ((OutputForm) %))): Not documented!!!!
--->-->SI_UNIT((tm_frep ((OutputForm) %))): Not documented!!!!
--------constructor---------
--->-->SI_UNIT((* (% % %))): Not documented!!!!
--->-->SI_UNIT((/ (% % %))): Not documented!!!!
--->-->SI_UNIT((^ (% % (Integer)))): Not documented!!!!
--->-->SI_UNIT((= ((Boolean) % %))): Not documented!!!!
--->-->SI_UNIT((%one (%))): Not documented!!!!
--->-->SI_UNIT((coerce ((OutputForm) %))): Not documented!!!!
--------constructor---------
--->-->SI_UNIT((mksi (% (List (Integer))))): Not documented!!!!
--->-->SI_UNIT((si2l ((List (Integer)) %))): Not documented!!!!
--->-->SI_UNIT(   %(Integer())()
): Not documented!!!!
--->-->SI_UNIT((%kg (% (Integer)))): Not documented!!!!
--->-->SI_UNIT(((% (|Integer|)))): Not documented!!!!
--->-->SI_UNIT((%A (% (Integer)))): Not documented!!!!
--->-->SI_UNIT((%K (% (Integer)))): Not documented!!!!
--->-->SI_UNIT((%mol (% (Integer)))): Not documented!!!!
--->-->SI_UNIT((%cd (% (Integer)))): Not documented!!!!
--->-->SI_UNIT((SI_derived (% (String)))): Not documented!!!!
--->-->SI_UNIT((buck ((List (Expression (Integer))) (Table (Symbol) %)))): Not documented!!!!
--->-->SI_UNIT(): Spurious comments: \blankline
--->-->SI_UNIT(): Spurious comments: \indented{1}{Author: Kurt Pagani} Date Created: 2012 License: \spad{BSD} (same as Axiom) ================================ Physical Quantities and SI Units ================================ This is an implementation of physical quantities and SI units as FriCAS domains. \blankline See docs for more information. \blankline Revision: - removing outputForm,{} Ring - added negation,{} elt \blankline \blankline
; compiling file "/var/aw/var/LatexWiki/SI.NRLIB/SI.lsp" (written 02 AUG 2015 03:22:03 AM):

; /var/aw/var/LatexWiki/SI.NRLIB/SI.fasl written
; compilation finished in 0:00:00.128
------------------------------------------------------------------------
   SI_UNIT is now explicitly exposed in frame initial 
   SI_UNIT will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SI.NRLIB/SI

   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 (Q_INTERVAL)) (: unit U)) (Q_INTERVAL) U)) (SIGNATURE ~= ((Boolean) (Record (: ival (Q_INTERVAL)) (: unit U)) (Record (: ival (Q_INTERVAL)) (: unit U)))) (SIGNATURE coerce ((OutputForm) (Record (: ival (Q_INTERVAL)) (: unit U)))) (SIGNATURE elt ((Q_INTERVAL) (Record (: ival (Q_INTERVAL)) (: unit U)) ival)) (SIGNATURE elt (U (Record (: ival (Q_INTERVAL)) (: unit U)) unit)) (SIGNATURE setelt! ((Q_INTERVAL) (Record (: ival (Q_INTERVAL)) (: unit U)) ival (Q_INTERVAL))) (SIGNATURE setelt! (U (Record (: ival (Q_INTERVAL)) (: unit U)) unit U)) (SIGNATURE copy ((Record (: ival (Q_INTERVAL)) (: unit U)) (Record (: ival (Q_INTERVAL)) (: unit U)))))) to (Join (OneDimensionalArrayAggregate (Integer)) (CATEGORY domain (SIGNATURE oneDimensionalArray ($ (List (Integer)))) (SIGNATURE oneDimensionalArray ($ (NonNegativeInteger) (Integer)))))
   compiling exported pqty : (Fraction Integer,Fraction Integer,U) -> $
Time: 0 SEC.

   compiling exported pqty_value : $ -> Fraction Integer
Time: 0 SEC.

   compiling exported pqty_error : $ -> Fraction Integer
Time: 0.01 SEC.

   compiling exported pqty_unit : $ -> U
      PQTY;pqty_unit;$U;4 is replaced by QCDR 
Time: 0 SEC.

   compiling exported pqty_interval : $ -> Q_INTERVAL
      PQTY;pqty_interval;$Qinterval;5 is replaced by QCAR 
Time: 0 SEC.

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

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

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

   compiling exported elt : (Q_INTERVAL,U) -> $
      PQTY;elt;QintervalU$;14 is replaced by CONS 
Time: 0 SEC.

   compiling exported elt : (Union(Fraction Integer,Float,DoubleFloat,Integer),U) -> $
Time: 0.01 SEC.

   compiling exported pqty_tm_toggle : U -> Boolean
Time: 0 SEC.

   compiling exported coerce : $ -> OutputForm
   processing macro definition OF ==> OutputForm 
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PhysQty| REDEFINED

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

   Warnings: 
      [1] pqty_value:  ival has no value
      [2] pqty_error:  ival has no value
      [3] pqty_unit:  unit has no value
      [4] pqty_interval:  ival has no value
      [5] *:  ival has no value
      [6] *:  unit has no value
      [7] /:  ival has no value
      [8] /:  unit has no value
      [9] +:  unit has no value
      [10] +:  ival has no value
      [11] -:  unit has no value
      [12] -:  ival has no value
      [13] ^:  ival has no value
      [14] ^:  unit has no value
      [15] pqty_scale:  ival has no value
      [16] pqty_scale:  unit has no value
      [17] coerce:  ival has no value
      [18] coerce:  unit has no value

   Cumulative Statistics for Constructor PhysQty
      Time: 0.02 seconds

   finalizing NRLIB PQTY 
   Processing PhysQty for Browser database:
--------constructor---------
--->-->PhysQty((+ (% % %))): Not documented!!!!
--->-->PhysQty((- (% % %))): Not documented!!!!
--->-->PhysQty((* (% % %))): Not documented!!!!
--->-->PhysQty((/ (% % %))): Not documented!!!!
--->-->PhysQty((^ (% % (Integer)))): Not documented!!!!
--->-->PhysQty((- (% %))): Not documented!!!!
--->-->PhysQty((abs (% %))): Not documented!!!!
--->-->PhysQty((elt (% (Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysQty((coerce (% (List (Fraction (Integer)))))): Not documented!!!!
--->-->PhysQty((coerce (% (Float)))): Not documented!!!!
--->-->PhysQty((coerce (% (DoubleFloat)))): Not documented!!!!
--->-->PhysQty((concise ((OutputForm) %))): Not documented!!!!
--->-->PhysQty((mki (% (Fraction (Integer)) (Fraction (Integer))))): Not documented!!!!
--->-->PhysQty((lb ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((ub ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((mid ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((len ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((frep ((OutputForm) %))): Not documented!!!!
--->-->PhysQty((tm_frep ((OutputForm) %))): Not documented!!!!
--------constructor---------
--->-->PhysQty((* (% % %))): Not documented!!!!
--->-->PhysQty((/ (% % %))): Not documented!!!!
--->-->PhysQty((^ (% % (Integer)))): Not documented!!!!
--->-->PhysQty((= ((Boolean) % %))): Not documented!!!!
--->-->PhysQty((%one (%))): Not documented!!!!
--->-->PhysQty((coerce ((OutputForm) %))): Not documented!!!!
--------constructor---------
--->-->PhysQty((mksi (% (List (Integer))))): Not documented!!!!
--->-->PhysQty((si2l ((List (Integer)) %))): Not documented!!!!
--->-->PhysQty(   %(Integer())()
): Not documented!!!!
--->-->PhysQty((%kg (% (Integer)))): Not documented!!!!
--->-->PhysQty(((% (|Integer|)))): Not documented!!!!
--->-->PhysQty((%A (% (Integer)))): Not documented!!!!
--->-->PhysQty((%K (% (Integer)))): Not documented!!!!
--->-->PhysQty((%mol (% (Integer)))): Not documented!!!!
--->-->PhysQty((%cd (% (Integer)))): Not documented!!!!
--->-->PhysQty((SI_derived (% (String)))): Not documented!!!!
--->-->PhysQty((buck ((List (Expression (Integer))) (Table (Symbol) %)))): Not documented!!!!
--------constructor---------
--->-->PhysQty((* (% % %))): Not documented!!!!
--->-->PhysQty((/ (% % %))): Not documented!!!!
--->-->PhysQty((+ (% % %))): Not documented!!!!
--->-->PhysQty((- (% % %))): Not documented!!!!
--->-->PhysQty((^ (% % (Integer)))): Not documented!!!!
--->-->PhysQty((- (% %))): Not documented!!!!
--->-->PhysQty((elt (% (Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((elt (% (Q_INTERVAL) U))): Not documented!!!!
--->-->PhysQty((elt (% (Union (Fraction (Integer)) (Float) (DoubleFloat) (Integer)) U))): Not documented!!!!
--->-->PhysQty((coerce ((OutputForm) %))): Not documented!!!!
--->-->PhysQty((pqty (% (Fraction (Integer)) (Fraction (Integer)) U))): Not documented!!!!
--->-->PhysQty((pqty_value ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((pqty_error ((Fraction (Integer)) %))): Not documented!!!!
--->-->PhysQty((pqty_unit (U %))): Not documented!!!!
--->-->PhysQty((pqty_interval ((Q_INTERVAL) %))): Not documented!!!!
--->-->PhysQty((pqty_scale (% % (Fraction (Integer))))): Not documented!!!!
--->-->PhysQty((pqty_tm_toggle ((Boolean) U))): Not documented!!!!
--->-->PhysQty(): Spurious comments: \blankline
--->-->PhysQty(): Spurious comments: \indented{1}{Author: Kurt Pagani} Date Created: 2012 License: \spad{BSD} (same as Axiom) ================================ Physical Quantities and SI Units ================================ This is an implementation of physical quantities and SI units as FriCAS domains. \blankline See docs for more information. \blankline Revision: - removing outputForm,{} Ring - added negation,{} elt \blankline \blankline
--->-->PhysQty(): Spurious comments: \indented{1}{Author: Kurt Pagani} Date Created: 2012 License: \spad{BSD} (same as Axiom) \blankline
; compiling file "/var/aw/var/LatexWiki/PQTY.NRLIB/PQTY.lsp" (written 02 AUG 2015 03:22:03 AM):

; /var/aw/var/LatexWiki/PQTY.NRLIB/PQTY.fasl written
; compilation finished in 0:00:00.062
------------------------------------------------------------------------
   PhysQty is now explicitly exposed in frame initial 
   PhysQty will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PQTY.NRLIB/PQTY

Oscillation period pendulum

fricas
t:Table(Symbol,SI_UNIT):=table()
\label{eq1} \mbox{\rm table} \left({}\right)(1)
Type: Table(Symbol,SI_UNIT)
fricas
t.L := %m(1)
\label{eq2}m_{\ }^{1}(2)
Type: SI_UNIT
fricas
t.T := %s(1)
\label{eq3}s_{\ }^{1}(3)
Type: SI_UNIT
fricas
t.M := %kg(1)
\label{eq4}kg_{\ }^{1}(4)
Type: SI_UNIT
fricas
t.g := t.L / (t.T)^2
\label{eq5}{m_{\ }^{1}}{s_{\ }^{- 2}}(5)
Type: SI_UNIT
fricas
t
\label{eq6} \mbox{\rm table} \left({{g ={{m_{\ }^{1}}{s_{\ }^{- 2}}}}, \:{M ={kg_{\ }^{1}}}, \:{T ={s_{\ }^{1}}}, \:{L ={m_{\ }^{1}}}}\right)(6)
Type: Table(Symbol,SI_UNIT)
fricas
bpi:= buck(t)
\label{eq7}\left[{L \over{{{T}^{2}}\ g}}\right](7)
Type: List(Expression(Integer))
fricas
solve(bpi.1=1,T)
\label{eq8}\left[{T ={\sqrt{L \over g}}}, \:{T = -{\sqrt{L \over g}}}\right](8)
Type: List(Equation(Expression(Integer)))

Pressure loss in a pipe

fricas
r:Table(Symbol,SI_UNIT):=table()
\label{eq9} \mbox{\rm table} \left({}\right)(9)
Type: Table(Symbol,SI_UNIT)
fricas
r.p := %kg(1)*%m(-1)*%s(-2)  -- pressure
\label{eq10}{{m_{\ }^{- 1}}{kg_{\ }^{1}}}{s_{\ }^{- 2}}(10)
Type: SI_UNIT
fricas
r.L := t.L
\label{eq11}m_{\ }^{1}(11)
Type: SI_UNIT
fricas
r.D := t.L
\label{eq12}m_{\ }^{1}(12)
Type: SI_UNIT
fricas
r.d := %kg(1) * %m(-3)
\label{eq13}{m_{\ }^{- 3}}{kg_{\ }^{1}}(13)
Type: SI_UNIT
fricas
r.m := r.p * %s(1)           -- viscosity
\label{eq14}{{m_{\ }^{- 1}}{kg_{\ }^{1}}}{s_{\ }^{- 1}}(14)
Type: SI_UNIT
fricas
r.v := t.L / t.T
\label{eq15}{m_{\ }^{1}}{s_{\ }^{- 1}}(15)
Type: SI_UNIT
fricas
r
\label{eq16} \mbox{\rm table} \left({{v ={{m_{\ }^{1}}{s_{\ }^{- 1}}}}, \:{m ={{{m_{\ }^{- 1}}{kg_{\ }^{1}}}{s_{\ }^{- 1}}}}, \:{d ={{m_{\ }^{- 3}}{kg_{\ }^{1}}}}, \:{D ={m_{\ }^{1}}}, \:{L ={m_{\ }^{1}}}, \:{p ={{{m_{\ }^{- 1}}{kg_{\ }^{1}}}{s_{\ }^{- 2}}}}}\right)(16)
Type: Table(Symbol,SI_UNIT)
fricas
buck(r)
\label{eq17}\left[{{D \ d \ v}\over m}, \:{{L \ d \ v}\over m}, \:{p \over{d \ {{v}^{2}}}}\right](17)
Type: List(Expression(Integer))