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SandBoxPhysicalUnitSystem

Edit detail for SandBoxPhysicalUnitSystem revision 3 of 3

	1 2 3
Editor: Kurt Pagani Time: 2018/07/28 20:21:36 GMT+0
Note:

added:


removed:
-

changed:
-PhysQty(U): Exports == Implementation where
PhysQty(U:PhysicalUnit): Exports == Implementation where

changed:
-    U:PhysicalUnit
-       
-    
   

added:
      _* : (Union(F,R,I,Q,PI),%) -> %
      _/ : (%,Union(F,R,I,Q,PI)) -> %
      
      

changed:
-      unit : % -> U    
      unit : % -> U  
      
      magnitude   : % -> F
      uncertainty : % -> F

changed:
-      outputMode:PI:=1
-      
-      x * y == [x.ival * y.ival, x.unit * y.unit]$Rep
-      x / y ==
      outputMode:PI:=2
      
      x:% * y:% == [x.ival * y.ival, x.unit * y.unit]$Rep
      x:% / y:% ==

added:

      r:Union(F,R,I,Q,PI)  * x:% ==
        r case I or r case PI => [r*x.ival, x.unit]$Rep 
        mkrep(r) ==> [interval(r)$IVF * x.ival, x.unit]$Rep
        r case Q or r case F => mkrep r
        r case R => mkrep convert(r)$F
        
      x:% / r:Union(F,R,I,Q,PI) ==
        s:%:=r*[interval(1.0)$IVF, one()]$Rep
        x/s

added:
      
      magnitude x == (sup(x.ival)+inf(x.ival))/2.0
      uncertainty x == (sup(x.ival)-inf(x.ival))/2.0

changed:
-)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
)abbrev domain SI SIunit                                               
SIunit : Exports == Implementation where
                                                       
    Exports == Join(SetCategory,PhysicalUnit) with
    
      unitSystem : () -> Type
      baseUnits  : () -> List %
  
      %m   : Integer -> %
      %kg  : Integer -> %        
      %s   : Integer -> %
      %A   : Integer -> %
      %K   : Integer -> %
      %mol : Integer -> %
      %cd  : Integer -> %                       

      metre     : %
      kilogram  : %
      second    : %
      ampere    : %
      kelvin    : %
      mole      : %
      candela   : %

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

    Implementation == PhysicalUnitSystem(['m,'kg,'s,'A,'K,'mol,'cd]) add                 

      USY:=['m,'kg,'s,'A,'K,'mol,'cd]                                  
      Rep:=PhysicalUnitSystem(USY) 
      
      unitSystem() == %

      u:=baseUnits()$Rep
      baseUnits() == u

changed:
-                                     

      metre      == %m(1)
      kilogram   == %kg(1)
      second     == %s(1)
      ampere     == %A(1)
      kelvin     == %K(1)
      mole       == %mol(1)
      candela    == %cd(1)


changed:
-
      


)abbrev package DIMAN DimensionalAnalysis                                                
DimensionalAnalysis(P:PhysicalUnit) : Exports == Implementation where

    Exports == with
    
      buckingham : Table(Symbol,P) -> List(Expression(Integer))
      
    Implementation == P add
    
    
      mkxpr(s:List Symbol,v:Vector Integer):Expression Integer == 
        r:Expression Integer:=1
        for j in 1..#s repeat r:=r*(s.j)::Expression(Integer)^(v.j)
        r
        
      buckingham(t) == --[1::Expression Integer]
        M:Matrix(Integer):=matrix [dim(t.x) for x in keys(t)]
        ns:List Vector Integer:=nullSpace transpose(M)
        r:List Expression Integer:=[]
        for j in 1..#ns repeat r:=append(r,[mkxpr(keys(t),ns.j)])
        r
 

changed:
-
-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
-
-dim unit(F)
-
-setOutputMode(2)$PSI
-
-c:=a*b
-d:=a/b
-
-unit(c)/unit(d)
-
-)show PUNIT
-)show PUSYS
-)show PQTY
-
--- cannot show SI (reason? -> SIU)
-)show SI
--
-- Template jEdit: spad_unittest.vm
-- Unittest .....: PQTY
-- Author .......: Kurt Pagani
-- Date .........: Sat Jul 28 16:56:04 CEST 2018
--

)set break resume
)expose UnittestCount UnittestAux Unittest

--)lib PUSYS PQTY SI DIMAN
)expose PUSYS PQTY SI DIMAN
--)co pdim2
)sh SI

-- Usage

m:=1400.3 %kg(1)
v:=30.6 (%m(1)/%s(1))
E:=m*v^2/2


-- Test Suite
testsuite "PUSYS"

-- Cases
testcase "cgs"

CGS ==> PUSYS(['cm,'g,'s])
[cm,g,s]:=baseUnits()$CGS

erg:=g*cm^2/s^2
dyne:=g*cm/s^2

testEquals("dim cm", "[1,0,0]")
testEquals("dim g", "[0,1,0]")
testEquals("dim s", "[0,0,1]")
testEquals("dim(cm/s*g)","[1,1,-1]")
    
testEquals("factors(cm/g).1.exp","1")
testEquals("factors(cm/g).2.exp","-1")
testEquals("factors(one()$CGS)","[]")

testEquals("baseSymbols()$CGS","['cm,'g,'s]")

testEquals("(cm^2/s^4*g=g*s^(-4)*cm^2)$CGS","true")
testEquals("(dyne * cm = erg)$CGS","true")


testcase "SI"

[m,kg,s,A,K,mol,cd]:=baseUnits()$SI

force1:=%kg(1) * %m(1) * %s(-2) 
force2:=kg * m / s^2
force3:=newton()$SI

area1:=%m(2)
area2:=m^2
area3:=metre()^2

pressure1:=force1/area1
pressure2:=pascal()$SI

testEquals("(force1=force2)$SI","true")
testEquals("(force2=force3)$SI","true")
testEquals("(pressure1=pressure2)$SI","true")

testEquals("dim force1","[1,1,- 2,0,0,0,0]")
testEquals("dim pressure2","[- 1,1,- 2,0,0,0,0]")

-- Test Suite
testsuite "PQTY"

testcase "PQTY(SI)"
-- from codata.spad (package CODATA)
CT(v,e,u) ==> (interval(v-e,v+e)$Interval(Float)) u
-- speed of light in vacuum
-- Value 	 299 792 458 m s-1
-- Standard uncertainty 	 (exact)
-- Relative standard uncertainty 	 (exact)
-- Concise form 	 299 792 458 m s-1    
c  := CT(299792458.0, 0.0, %m(1)*%s(-1))

-- Planck constant over 2 pi 
-- Value 	 1.054 571 800 x 10-34 J s
-- Standard uncertainty 	 0.000 000 013 x 10-34 J s
-- Relative standard uncertainty 	  1.2 x 10-8
-- Concise form 	 1.054 571 800(13) x 10-34 J s 
hbar := CT(1.054571800E-34, 0.000000013E-34,%m(2)*%kg(1)*%s(-1))

-- elementary charge
-- $e$
-- Value 	  1.602 176 6208 x 10-19  C
-- Standard uncertainty 	 0.000 000 0098 x 10-19 C
-- Relative standard uncertainty 	  6.1 x 10-9
-- Concise form 	  1.602 176 6208(98) x 10-19 C  
e  := CT(1.6021766208E-19, 0.0000000098E-19, %A(1)*%s(1))

-- electron mass
-- $m_{\rm e}$
-- Value 	 9.109 383 56 x 10-31 kg
-- Standard uncertainty 	 0.000 000 11 x 10-31 kg
-- Relative standard uncertainty 	  1.2 x 10-8
-- Concise form 	 9.109 383 56(11) x 10-31 kg   
m_e := CT(9.10938356E-31, 0.00000011E-31, %kg(1))

-- fine-structure constant
-- Value 	 7.297 352 5664 x 10-3
-- Standard uncertainty 	 0.000 000 0017 x 10-3
-- Relative standard uncertainty 	  2.3 x 10-10
-- Concise form 	 7.297 352 5664(17) x 10-3 
alpha := CT(7.2973525664E-3, 0.0000000017E-3,%m(0)$SI)

-- electric constant
-- $\varepsilon_0$
-- Value 	 8.854 187 817... x 10-12 F m-1
-- Standard uncertainty 	 (exact)
-- Relative standard uncertainty 	 (exact)
-- Concise form 	 8.854 187 817... x 10-12 F m-1    
eps_0 := CT(8.854187817E-12,0, %m(-3)*%kg(-1)*%s(4)*%A(2))



r1:=ival e
r2:=unit e
r3:=magnitude e
r4:=uncertainty e

testEquals("(unit e = %s(1)*%A(1))$SI","true")
testEquals("(unit(m_e*c^2)/joule()$SI=one()$SI)$SI","true")

-- fine structure
myalpha:=(1/(4*%pi))::Float * eps_0^(-1)*e^2/hbar/c

testEquals("abs(magnitude(myalpha-alpha))<1.0E-10","true")

f:=2 newton()$SI
l:=3.6 metre()$SI
a:=l^2
p:=f/a

testEquals("test(magnitude(7.2 joule()$SI / (f*l))=1$Float)","true")
testEquals("uncertainty(m_e*c^2)<1.0E-20","true")

setOutputMode(1)$PQTY(SI)
hbar
m_e
c
setOutputMode(3)$PQTY(SI)
alpha
eps_0
setOutputMode(2)$PQTY(SI)
m_e
hbar

-- Test Suite
testsuite "DIMAN"

testcase "DIMAN(SI)"
-- Dimensional analysis
-- Buckingham Pi theorem

D==> DIMAN(SI)

t:Table(Symbol,SI):=table()
t.L:=%m(1)$SI ; t.M:=%kg(1)$SI; t.T:=%s(1)$SI; t.g:=%m(1)$SI/%s(2)$SI
bt:=buckingham(t)
res1:=solve(bt.1=1,'T).1


s:Table(Symbol,SI):=table()
s.v:=%m(1)$SI/%s(1)$SI; s.rho:=%kg(1)$SI/%m(3)$SI; s.p:=pascal()$SI
bs:=buckingham(s)
res2:=solve(bs.1=1,'v).1

-- https://en.wikipedia.org/w/index.php?title=Dimensional_analysis
-- Example section 26
vb:Table(Symbol,SI):=table()
vb.'l:=%m(1)$SI; vb.A:=%m(1)$SI; vb.rho:=%kg(1)$SI/%m(1)$SI; 
vb.'s:=%kg(1)$SI*%m(1)$SI/%s(2)$SI; vb.E:=%kg(1)$SI*%m(2)$SI/%s(2)$SI
bvb:=buckingham vb


testEquals("res1","T=sqrt(L/g)")
testEquals("res2","v=sqrt(p/rho)")

F:=operator 'F
res3:=F(bvb.2,bvb.1)=0
testEquals("res3","F('l*'s/'E,'A*'s/'E)=0")


-- Results/Statistics
)set output algebra on
)version
)lisp (lisp-implementation-type)
)lisp (lisp-implementation-version)

statistics()

fricas

(1) -> <spad>

fricas

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

fricas

)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)
      x * y == x+y 
      x / y == x-y
      x ^ n == n*x 
      one() == 0$Rep
      baseSymbols() == [convert(x)@Symbol for x in enumerate$BASU]
      baseUnits() == [x::% for x in enumerate$BASU]
      dim(x) == [coefficient(x,b) for b in enumerate$BASU]  
      x = y == test(dim x = dim y)

fricas

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

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

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

      _* : (Union(F,R,I,Q,PI),%) -> %
      _/ : (%,Union(F,R,I,Q,PI)) -> %

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

      magnitude   : % -> F
      uncertainty : % -> F

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

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

    Implementation ==  add 

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

      outputMode:PI:=2

      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 

      r:Union(F,R,I,Q,PI)  * x:% ==
        r case I or r case PI => [r*x.ival, x.unit]$Rep 
        mkrep(r) ==> [interval(r)$IVF * x.ival, x.unit]$Rep
        r case Q or r case F => mkrep r
        r case R => mkrep convert(r)$F

      x:% / r:Union(F,R,I,Q,PI) ==
        s:%:=r*[interval(1.0)$IVF, one()]$Rep
        x/s

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

      magnitude x == (sup(x.ival)+inf(x.ival))/2.0
      uncertainty x == (sup(x.ival)-inf(x.ival))/2.0

      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]

fricas

)abbrev domain SI SIunit                                               
SIunit : Exports == Implementation where

    Exports == Join(SetCategory,PhysicalUnit) with

      unitSystem : () -> Type
      baseUnits  : () -> List %

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

      metre     : %
      kilogram  : %
      second    : %
      ampere    : %
      kelvin    : %
      mole      : %
      candela   : %

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

    Implementation == PhysicalUnitSystem(['m,'kg,'s,'A,'K,'mol,'cd]) add                 

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

      unitSystem() == %

      u:=baseUnits()$Rep
      baseUnits() == u

      %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

      metre      == %m(1)
      kilogram   == %kg(1)
      second     == %s(1)
      ampere     == %A(1)
      kelvin     == %K(1)
      mole       == %mol(1)
      candela    == %cd(1)

      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)

fricas

)abbrev package DIMAN DimensionalAnalysis                                                
DimensionalAnalysis(P:PhysicalUnit) : Exports == Implementation where

    Exports == with

      buckingham : Table(Symbol,P) -> List(Expression(Integer))

    Implementation == P add

      mkxpr(s:List Symbol,v:Vector Integer):Expression Integer == 
        r:Expression Integer:=1
        for j in 1..#s repeat r:=r*(s.j)::Expression(Integer)^(v.j)
        r

      buckingham(t) == --[1::Expression Integer]
        M:Matrix(Integer):=matrix [dim(t.x) for x in keys(t)]
        ns:List Vector Integer:=nullSpace transpose(M)
        r:List Expression Integer:=[]
        for j in 1..#ns repeat r:=append(r,[mkxpr(keys(t),ns.j)])
        r</spad>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4318783589297783802-25px001.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 02 NOV 2024 02:51:10 AM):

; wrote /var/aw/var/LatexWiki/PUNIT.NRLIB/PUNIT.fasl
; compilation finished in 0:00:00.000
------------------------------------------------------------------------
   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 SEC.

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

   compiling exported = : (%,%) -> Boolean
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PhysicalUnitSystem| REDEFINED

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

   Cumulative Statistics for Constructor PhysicalUnitSystem
      Time: 0.02 seconds

--------------non extending category----------------------
.. PhysicalUnitSystem(#1) of cat 
(|Join| (|PhysicalUnit|) (|CoercibleTo| (|OutputForm|))
        (CATEGORY |domain|
         (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((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 02 NOV 2024 02:51:10 AM):

; wrote /var/aw/var/LatexWiki/PUSYS.NRLIB/PUSYS.fasl
; compilation finished in 0:00:00.016
------------------------------------------------------------------------
   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 domain (IF (has (Integer) (CommutativeRing)) (ATTRIBUTE (Module (Integer))) noBranch) (IF (has (Integer) (SemiRing)) (ATTRIBUTE (RetractableTo (OrderedVariableList u))) noBranch) (IF (has (Integer) (Hashable)) (IF (has (OrderedVariableList u) (Hashable)) (ATTRIBUTE (Hashable)) noBranch) noBranch) (IF (has (OrderedVariableList u) (OrderedSet)) (PROGN (IF (has (Integer) (OrderedAbelianMonoid)) (ATTRIBUTE (OrderedAbelianMonoid)) noBranch) (IF (has (Integer) (OrderedAbelianMonoidSup)) (ATTRIBUTE (OrderedAbelianMonoidSup)) noBranch)) noBranch) (SIGNATURE * (% (Integer) (OrderedVariableList u))) (SIGNATURE * (% (OrderedVariableList u) (Integer)))))
   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 * : (Union(Float,DoubleFloat,Integer,Fraction Integer,PositiveInteger),%) -> %
   processing macro definition mkrep r ==> (Sel Rep construct)(*((Sel (Interval (Float)) interval) r,x ival),x unit) 
Time: 0 SEC.

   compiling exported / : (%,Union(Float,DoubleFloat,Integer,Fraction Integer,PositiveInteger)) -> %
Time: 0 SEC.

   compiling exported ival : % -> Interval Float
      PQTY;ival;%I;9 is replaced by QCAR 
Time: 0 SEC.

   compiling exported unit : % -> U
      PQTY;unit;%U;10 is replaced by QCDR 
Time: 0 SEC.

   compiling exported magnitude : % -> Float
Time: 0 SEC.

   compiling exported uncertainty : % -> Float
Time: 0 SEC.

   compiling exported elt : (Interval Float,U) -> %
      PQTY;elt;IU%;13 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 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PhysQty| REDEFINED

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

   Cumulative Statistics for Constructor PhysQty
      Time: 0.04 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((* (% (Union (Float) (DoubleFloat) (Integer) (Fraction (Integer)) (PositiveInteger)) %))): Not documented!!!!
--->-->PhysQty((/ (% % (Union (Float) (DoubleFloat) (Integer) (Fraction (Integer)) (PositiveInteger))))): Not documented!!!!
--->-->PhysQty((ival ((Interval (Float)) %))): Not documented!!!!
--->-->PhysQty((unit (U %))): Not documented!!!!
--->-->PhysQty((magnitude ((Float) %))): Not documented!!!!
--->-->PhysQty((uncertainty ((Float) %))): 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 02 NOV 2024 02:51:10 AM):

; wrote /var/aw/var/LatexWiki/PQTY.NRLIB/PQTY.fasl
; compilation finished in 0:00:00.032
------------------------------------------------------------------------
   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 domain SIunit 
------------------------------------------------------------------------
   initializing NRLIB SI for SIunit 
   compiling into NRLIB SI 
Local variable Rep type redefined: (Join (PhysicalUnit) (CoercibleTo (OutputForm)) (CATEGORY domain (SIGNATURE baseSymbols ((List (Symbol))) constant) (SIGNATURE baseUnits ((List %)) constant) (SIGNATURE factors ((List (Record (: gen (OrderedVariableList USY)) (: exp (Integer)))) %)))) to (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))))))
   compiling exported unitSystem : () -> Type
Time: 0 SEC.

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

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

   compiling exported %kg : Integer -> %
Time: 0 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 metre : () -> %
Time: 0 SEC.

   compiling exported kilogram : () -> %
Time: 0 SEC.

   compiling exported second : () -> %
Time: 0 SEC.

   compiling exported ampere : () -> %
Time: 0 SEC.

   compiling exported kelvin : () -> %
Time: 0 SEC.

   compiling exported mole : () -> %
Time: 0 SEC.

   compiling exported candela : () -> %
Time: 0 SEC.

   compiling exported hertz : () -> %
Time: 0 SEC.

   compiling exported newton : () -> %
Time: 0 SEC.

   compiling exported pascal : () -> %
Time: 0 SEC.

   compiling exported joule : () -> %
Time: 0 SEC.

   compiling exported watt : () -> %
Time: 0 SEC.

   compiling exported coulomb : () -> %
Time: 0 SEC.

   compiling exported volt : () -> %
Time: 0 SEC.

   compiling exported farad : () -> %
Time: 0 SEC.

   compiling exported ohm : () -> %
Time: 0 SEC.

   compiling exported siemens : () -> %
Time: 0 SEC.

   compiling exported weber : () -> %
Time: 0 SEC.

   compiling exported tesla : () -> %
Time: 0 SEC.

   compiling exported henry : () -> %
Time: 0 SEC.

   compiling exported lumen : () -> %
Time: 0 SEC.

   compiling exported lux : () -> %
Time: 0 SEC.

   compiling exported becquerel : () -> %
Time: 0 SEC.

   compiling exported gray : () -> %
Time: 0 SEC.

   compiling exported sievert : () -> %
Time: 0 SEC.

   compiling exported katal : () -> %
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |SIunit| REDEFINED

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

   Cumulative Statistics for Constructor SIunit
      Time: 0.03 seconds

--------------non extending category----------------------
.. SIunit of cat 
(|Join| (|SetCategory|) (|PhysicalUnit|)
        (CATEGORY |domain| (SIGNATURE |unitSystem| ((|Type|)))
         (SIGNATURE |baseUnits| ((|List| %))) (SIGNATURE |%m| (% (|Integer|)))
         (SIGNATURE |%kg| (% (|Integer|))) (SIGNATURE |%s| (% (|Integer|)))
         (SIGNATURE %A (% (|Integer|))) (SIGNATURE %K (% (|Integer|)))
         (SIGNATURE |%mol| (% (|Integer|))) (SIGNATURE |%cd| (% (|Integer|)))
         (SIGNATURE |metre| (%) |constant|)
         (SIGNATURE |kilogram| (%) |constant|)
         (SIGNATURE |second| (%) |constant|)
         (SIGNATURE |ampere| (%) |constant|)
         (SIGNATURE |kelvin| (%) |constant|) (SIGNATURE |mole| (%) |constant|)
         (SIGNATURE |candela| (%) |constant|)
         (SIGNATURE |hertz| (%) |constant|) (SIGNATURE |newton| (%) |constant|)
         (SIGNATURE |pascal| (%) |constant|) (SIGNATURE |joule| (%) |constant|)
         (SIGNATURE |watt| (%) |constant|) (SIGNATURE |coulomb| (%) |constant|)
         (SIGNATURE |volt| (%) |constant|) (SIGNATURE |farad| (%) |constant|)
         (SIGNATURE |ohm| (%) |constant|) (SIGNATURE |siemens| (%) |constant|)
         (SIGNATURE |weber| (%) |constant|) (SIGNATURE |tesla| (%) |constant|)
         (SIGNATURE |henry| (%) |constant|) (SIGNATURE |lumen| (%) |constant|)
         (SIGNATURE |lux| (%) |constant|)
         (SIGNATURE |becquerel| (%) |constant|)
         (SIGNATURE |gray| (%) |constant|) (SIGNATURE |sievert| (%) |constant|)
         (SIGNATURE |katal| (%) |constant|)))   has no 
(SIGNATURE |baseSymbols| ((|List| (|Symbol|))) |constant|)    finalizing NRLIB SI 
   Processing SIunit for Browser database:
--->-->SIunit(constructor): Not documented!!!!
--->-->SIunit((unitSystem ((Type)))): Not documented!!!!
--->-->SIunit((baseUnits ((List %)))): Not documented!!!!
--->-->SIunit(   %(Integer())()

fricas

): Not documented!!!!
--->-->SIunit((%kg (% (Integer)))): Not documented!!!!
--->-->SIunit(((% (|Integer|)))): Not documented!!!!
--->-->SIunit((%A (% (Integer)))): Not documented!!!!
--->-->SIunit((%K (% (Integer)))): Not documented!!!!
--->-->SIunit((%mol (% (Integer)))): Not documented!!!!
--->-->SIunit((%cd (% (Integer)))): Not documented!!!!
--->-->SIunit((metre (%) constant)): Not documented!!!!
--->-->SIunit((kilogram (%) constant)): Not documented!!!!
--->-->SIunit((second (%) constant)): Not documented!!!!
--->-->SIunit((ampere (%) constant)): Not documented!!!!
--->-->SIunit((kelvin (%) constant)): Not documented!!!!
--->-->SIunit((mole (%) constant)): Not documented!!!!
--->-->SIunit((candela (%) constant)): Not documented!!!!
--->-->SIunit((hertz (%) constant)): Not documented!!!!
--->-->SIunit((newton (%) constant)): Not documented!!!!
--->-->SIunit((pascal (%) constant)): Not documented!!!!
--->-->SIunit((joule (%) constant)): Not documented!!!!
--->-->SIunit((watt (%) constant)): Not documented!!!!
--->-->SIunit((coulomb (%) constant)): Not documented!!!!
--->-->SIunit((volt (%) constant)): Not documented!!!!
--->-->SIunit((farad (%) constant)): Not documented!!!!
--->-->SIunit((ohm (%) constant)): Not documented!!!!
--->-->SIunit((siemens (%) constant)): Not documented!!!!
--->-->SIunit((weber (%) constant)): Not documented!!!!
--->-->SIunit((tesla (%) constant)): Not documented!!!!
--->-->SIunit((henry (%) constant)): Not documented!!!!
--->-->SIunit((lumen (%) constant)): Not documented!!!!
--->-->SIunit((lux (%) constant)): Not documented!!!!
--->-->SIunit((becquerel (%) constant)): Not documented!!!!
--->-->SIunit((gray (%) constant)): Not documented!!!!
--->-->SIunit((sievert (%) constant)): Not documented!!!!
--->-->SIunit((katal (%) constant)): Not documented!!!!
--->-->SIunit(): Missing Description
; compiling file "/var/aw/var/LatexWiki/SI.NRLIB/SI.lsp" (written 02 NOV 2024 02:51:11 AM):

; wrote /var/aw/var/LatexWiki/SI.NRLIB/SI.fasl
; compilation finished in 0:00:00.036
------------------------------------------------------------------------
   SIunit is now explicitly exposed in frame initial 
   SIunit will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SI.NRLIB/SI

   DIMAN abbreviates package DimensionalAnalysis 
------------------------------------------------------------------------
   initializing NRLIB DIMAN for DimensionalAnalysis 
   compiling into NRLIB DIMAN 
   compiling local mkxpr : (List Symbol,Vector Integer) -> Expression Integer
Time: 0.02 SEC.

   compiling exported buckingham : Table(Symbol,P) -> List Expression Integer
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |DimensionalAnalysis| REDEFINED

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

   Cumulative Statistics for Constructor DimensionalAnalysis
      Time: 0.03 seconds

   finalizing NRLIB DIMAN 
   Processing DimensionalAnalysis for Browser database:
--->-->DimensionalAnalysis(constructor): Not documented!!!!
--->-->DimensionalAnalysis((buckingham ((List (Expression (Integer))) (Table (Symbol) P)))): Not documented!!!!
--->-->DimensionalAnalysis(): Missing Description
; compiling file "/var/aw/var/LatexWiki/DIMAN.NRLIB/DIMAN.lsp" (written 02 NOV 2024 02:51:11 AM):

; wrote /var/aw/var/LatexWiki/DIMAN.NRLIB/DIMAN.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   DimensionalAnalysis is now explicitly exposed in frame initial 
   DimensionalAnalysis will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DIMAN.NRLIB/DIMAN

fricas --

Template jEdit: spad_unittest.vm -- Unittest .....: PQTY -- Author .......: Kurt Pagani -- Date .........: Sat Jul 28 16:56:04 CEST 2018 --

fricas

)set break resume

fricas

)expose UnittestCount UnittestAux Unittest

   UnittestCount is now explicitly exposed in frame initial 
   UnittestAux is now explicitly exposed in frame initial 
   Unittest is now explicitly exposed in frame initial 

--)lib PUSYS PQTY SI DIMAN

fricas

)expose PUSYS PQTY SI DIMAN

   PhysicalUnitSystem is already explicitly exposed in frame initial 
   PhysQty is already explicitly exposed in frame initial 
   SIunit is already explicitly exposed in frame initial 
   DimensionalAnalysis is already explicitly exposed in frame initial 
--)co pdim2

fricas

)sh SI

 SIunit is a domain constructor.
 Abbreviation for SIunit is SI 
 This constructor is exposed in this frame.
 44 Names for 44 Operations in this Domain.
------------------------------- Operations --------------------------------

 %A : Integer -> %                     %K : Integer -> %
 %cd : Integer -> %                    %kg : Integer -> %
 %m : Integer -> %                     %mol : Integer -> %
 %s : Integer -> %                     ?*? : (%, %) -> %
 ?/? : (%, %) -> %                     ?=? : (%, %) -> Boolean
 ?^? : (%, Integer) -> %               ampere : () -> %
 baseUnits : () -> List(%)             becquerel : () -> %
 candela : () -> %                     coerce : % -> OutputForm
 coulomb : () -> %                     dim : % -> List(Integer)
 farad : () -> %                       gray : () -> %
 henry : () -> %                       hertz : () -> %
 joule : () -> %                       katal : () -> %
 kelvin : () -> %                      kilogram : () -> %
 latex : % -> String                   lumen : () -> %
 lux : () -> %                         metre : () -> %
 mole : () -> %                        newton : () -> %
 ohm : () -> %                         one : () -> %
 pascal : () -> %                      second : () -> %
 siemens : () -> %                     sievert : () -> %
 tesla : () -> %                       unitSystem : () -> Type
 volt : () -> %                        watt : () -> %
 weber : () -> %                       ?~=? : (%, %) -> Boolean

-- Usage

m:=1400.3 %kg(1)

$\label{eq1}{1400.3}\ kg$

(1)

Type: PhysQty?(SIunit?)

fricas

v:=30.6 (%m(1)/%s(1))

$\label{eq2}{30.6}\ {m \ {{s}^{- 1}}}$

(2)

Type: PhysQty?(SIunit?)

fricas

E:=m*v^2/2

$\label{eq3}{655592.454}\ {{{m}^{2}}\ kg \ {{s}^{- 2}}}$

(3)

Type: PhysQty?(SIunit?)

fricas

-- Test Suite
testsuite "PUSYS"

   All user variables and function definitions have been cleared.

Type: Void

fricas

-- Cases
testcase "cgs"

   All user variables and function definitions have been cleared.

Type: Void

fricas

CGS ==> PUSYS(['cm,'g,'s])

Type: Void

fricas

[cm,g,s]:=baseUnits()$CGS

$\label{eq4}\left[ cm , \: g , \: s \right]$

(4)

Type: List(PhysicalUnitSystem?([cm,g,s]))

fricas

erg:=g*cm^2/s^2

$\label{eq5}{{cm}^{2}}\ g \ {{s}^{- 2}}$

(5)

Type: PhysicalUnitSystem?([cm,g,s])

fricas

dyne:=g*cm/s^2

$\label{eq6}cm \ g \ {{s}^{- 2}}$

(6)

Type: PhysicalUnitSystem?([cm,g,s])

fricas

testEquals("dim cm", "[1,0,0]")

Type: Void

fricas

testEquals("dim g", "[0,1,0]")

Type: Void

fricas

testEquals("dim s", "[0,0,1]")

Type: Void

fricas

testEquals("dim(cm/s*g)","[1,1,-1]")

Type: Void

fricas

testEquals("factors(cm/g).1.exp","1")

Type: Void

fricas

testEquals("factors(cm/g).2.exp","-1")

Type: Void

fricas

testEquals("factors(one()$CGS)","[]")

Type: Void

fricas

testEquals("baseSymbols()$CGS","['cm,'g,'s]")

Type: Void

fricas

testEquals("(cm^2/s^4*g=g*s^(-4)*cm^2)$CGS","true")

Type: Void

fricas

testEquals("(dyne * cm = erg)$CGS","true")

Type: Void

fricas

testcase "SI"

   All user variables and function definitions have been cleared.

Type: Void

fricas

[m,kg,s,A,K,mol,cd]:=baseUnits()$SI

$\label{eq7}\left[ m , \: kg , \: s , \: A , \: K , \: mol , \: cd \right]$

(7)

Type: List(SIunit?)

fricas

force1:=%kg(1) * %m(1) * %s(-2)

$\label{eq8}m \ kg \ {{s}^{- 2}}$

(8)

Type: SIunit?

fricas

force2:=kg * m / s^2

$\label{eq9}m \ kg \ {{s}^{- 2}}$

(9)

Type: SIunit?

fricas

force3:=newton()$SI

$\label{eq10}m \ kg \ {{s}^{- 2}}$

(10)

Type: SIunit?

fricas

area1:=%m(2)

$\label{eq11}{m}^{2}$

(11)

Type: SIunit?

fricas

area2:=m^2

$\label{eq12}{m}^{2}$

(12)

Type: SIunit?

fricas

area3:=metre()^2

$\label{eq13}{m}^{2}$

(13)

Type: SIunit?

fricas

pressure1:=force1/area1

$\label{eq14}{{m}^{- 1}}\ kg \ {{s}^{- 2}}$

(14)

Type: SIunit?

fricas

pressure2:=pascal()$SI

$\label{eq15}{{m}^{- 1}}\ kg \ {{s}^{- 2}}$

(15)

Type: SIunit?

fricas

testEquals("(force1=force2)$SI","true")

Type: Void

fricas

testEquals("(force2=force3)$SI","true")

Type: Void

fricas

testEquals("(pressure1=pressure2)$SI","true")

Type: Void

fricas

testEquals("dim force1","[1,1,- 2,0,0,0,0]")

Type: Void

fricas

testEquals("dim pressure2","[- 1,1,- 2,0,0,0,0]")

Type: Void

fricas

-- Test Suite
testsuite "PQTY"

   All user variables and function definitions have been cleared.

Type: Void

fricas

testcase "PQTY(SI)"

   All user variables and function definitions have been cleared.

Type: Void

fricas

-- from codata.spad (package CODATA)
CT(v,e,u) ==> (interval(v-e,v+e)$Interval(Float)) u

Type: Void

fricas

-- speed of light in vacuum
-- Value         299 792 458 m s-1
-- Standard uncertainty          (exact)
-- Relative standard uncertainty         (exact)
-- Concise form          299 792 458 m s-1    
c  := CT(299792458.0, 0.0, %m(1)*%s(-1))

$\label{eq16}{299792458.0}\ {m \ {{s}^{- 1}}}$

(16)

Type: PhysQty?(SIunit?)

fricas

-- Planck constant over 2 pi 
-- Value         1.054 571 800 x 10-34 J s
-- Standard uncertainty          0.000 000 013 x 10-34 J s
-- Relative standard uncertainty          1.2 x 10-8
-- Concise form          1.054 571 800(13) x 10-34 J s 
hbar := CT(1.054571800E-34, 0.000000013E-34,%m(2)*%kg(1)*%s(-1))

$\label{eq17}{0.10545718 E - 33}\ {{{m}^{2}}\ kg \ {{s}^{- 1}}}$

(17)

Type: PhysQty?(SIunit?)

fricas

-- elementary charge
-- $e$
-- Value          1.602 176 6208 x 10-19  C
-- Standard uncertainty          0.000 000 0098 x 10-19 C
-- Relative standard uncertainty          6.1 x 10-9
-- Concise form           1.602 176 6208(98) x 10-19 C  
e  := CT(1.6021766208E-19, 0.0000000098E-19, %A(1)*%s(1))

$\label{eq18}{0.1602176620 \ 8 E - 18}\ {s \ A}$

(18)

Type: PhysQty?(SIunit?)

fricas

-- electron mass
-- $m_{\rm e}$
-- Value         9.109 383 56 x 10-31 kg
-- Standard uncertainty          0.000 000 11 x 10-31 kg
-- Relative standard uncertainty          1.2 x 10-8
-- Concise form          9.109 383 56(11) x 10-31 kg   
m_e := CT(9.10938356E-31, 0.00000011E-31, %kg(1))

$\label{eq19}{0.910938356 E - 30}\ kg$

(19)

Type: PhysQty?(SIunit?)

fricas

-- fine-structure constant
-- Value         7.297 352 5664 x 10-3
-- Standard uncertainty          0.000 000 0017 x 10-3
-- Relative standard uncertainty          2.3 x 10-10
-- Concise form          7.297 352 5664(17) x 10-3 
alpha := CT(7.2973525664E-3, 0.0000000017E-3,%m(0)$SI)

$\label{eq20}{0.0072973525 \ 664}\ 1$

(20)

Type: PhysQty?(SIunit?)

fricas

-- electric constant
-- $\varepsilon_0$
-- Value         8.854 187 817... x 10-12 F m-1
-- Standard uncertainty          (exact)
-- Relative standard uncertainty         (exact)
-- Concise form          8.854 187 817... x 10-12 F m-1    
eps_0 := CT(8.854187817E-12,0, %m(-3)*%kg(-1)*%s(4)*%A(2))

$\label{eq21}{0.8854187817 E - 11}\ {{{m}^{- 3}}\ {{kg}^{- 1}}\ {{s}^{4}}\ {{A}^{2}}}$

(21)

Type: PhysQty?(SIunit?)

fricas

r1:=ival e

$\label{eq22}\left[{0.1602176611 E - 18}, \:{0.1602176630 \_ 6 E - 18}\right]$

(22)

Type: Interval(Float)

fricas

r2:=unit e

$\label{eq23}s \ A$

(23)

Type: SIunit?

fricas

r3:=magnitude e

$\label{eq24}0.1602176620 \ 8 E - 18$

(24)

Type: Float

fricas

r4:=uncertainty e

$\label{eq25}0.9800000000 \ 0067680793 E - 27$

(25)

Type: Float

fricas

testEquals("(unit e = %s(1)*%A(1))$SI","true")

Type: Void

fricas

testEquals("(unit(m_e*c^2)/joule()$SI=one()$SI)$SI","true")

Type: Void

fricas

-- fine structure
myalpha:=(1/(4*%pi))::Float * eps_0^(-1)*e^2/hbar/c

$\label{eq26}{0.0072973525 \ 6768042794 \ 47}\ 1$

(26)

Type: PhysQty?(SIunit?)

fricas

testEquals("abs(magnitude(myalpha-alpha))<1.0E-10","true")

Type: Void

fricas

f:=2 newton()$SI

$\label{eq27}{2.0}\ {m \ kg \ {{s}^{- 2}}}$

(27)

Type: PhysQty?(SIunit?)

fricas

l:=3.6 metre()$SI

$\label{eq28}{3.6}\ m$

(28)

Type: PhysQty?(SIunit?)

fricas

a:=l^2

$\label{eq29}{12.96}\ {{m}^{2}}$

(29)

Type: PhysQty?(SIunit?)

fricas

p:=f/a

$\label{eq30}{0.1543209876 \ 5432098765}\ {{{m}^{- 1}}\ kg \ {{s}^{- 2}}}$

(30)

Type: PhysQty?(SIunit?)

fricas

testEquals("test(magnitude(7.2 joule()$SI / (f*l))=1$Float)","true")

Type: Void

fricas

testEquals("uncertainty(m_e*c^2)<1.0E-20","true")

Type: Void

fricas

setOutputMode(1)$PQTY(SI)

$\label{eq31}1$

(31)

Type: PositiveInteger?

fricas

hbar

$\label{eq32}{0.10545718 E - 33}\ �� \ {0.13 E - 41}\ {{{m}^{2}}\ kg \ {{s}^{- 1}}}$

(32)

Type: PhysQty?(SIunit?)

fricas

m_e

$\label{eq33}{0.910938356 E - 30}\ �� \ {0.11 E - 37}\ kg$

(33)

Type: PhysQty?(SIunit?)

fricas

$\label{eq34}{299792458.0}\ �� \ {0.2 E - 11}\ {m \ {{s}^{- 1}}}$

(34)

Type: PhysQty?(SIunit?)

fricas

setOutputMode(3)$PQTY(SI)

$\label{eq35}3$

(35)

Type: PositiveInteger?

fricas

alpha

$\label{eq36}{\left[{0.0072973525 \ 647}, \:{0.0072973525 \ 681}\right]}\ 1$

(36)

Type: PhysQty?(SIunit?)

fricas

eps_0

$\label{eq37}{ \begin{array}{@{}l} \displaystyle \left[{0.8854187816 \_ 9999999999 E - 11}, \: \right. \ \ \displaystyle \left.{0.8854187817 E - 11}\right]$

(37)

Type: PhysQty?(SIunit?)

fricas

setOutputMode(2)$PQTY(SI)

$\label{eq38}2$

(38)

Type: PositiveInteger?

fricas

m_e

$\label{eq39}{0.910938356 E - 30}\ kg$

(39)

Type: PhysQty?(SIunit?)

fricas

hbar

$\label{eq40}{0.10545718 E - 33}\ {{{m}^{2}}\ kg \ {{s}^{- 1}}}$

(40)

Type: PhysQty?(SIunit?)

fricas

-- Test Suite
testsuite "DIMAN"

   All user variables and function definitions have been cleared.

Type: Void

fricas

testcase "DIMAN(SI)"

   All user variables and function definitions have been cleared.

Type: Void

fricas

-- Dimensional analysis
-- Buckingham Pi theorem

D==> DIMAN(SI)

Type: Void

fricas

t:Table(Symbol,SI):=table()

$\label{eq41} \mbox{\rm table} \left({}\right)$

(41)

Type: Table(Symbol,SIunit?)

fricas

t.L:=%m(1)$SI ; t.M:=%kg(1)$SI; t.T:=%s(1)$SI; t.g:=%m(1)$SI/%s(2)$SI

$\label{eq42}m \ {{s}^{- 2}}$

(42)

Type: SIunit?

fricas

bt:=buckingham(t)

$\label{eq43}\left[{\frac{L}{{{T}^{2}}\ g}}\right]$

(43)

Type: List(Expression(Integer))

fricas

res1:=solve(bt.1=1,'T).1

$\label{eq44}T ={\sqrt{\frac{L}{g}}}$

(44)

Type: Equation(Expression(Integer))

fricas

s:Table(Symbol,SI):=table()

$\label{eq45} \mbox{\rm table} \left({}\right)$

(45)

Type: Table(Symbol,SIunit?)

fricas

s.v:=%m(1)$SI/%s(1)$SI; s.rho:=%kg(1)$SI/%m(3)$SI; s.p:=pascal()$SI

$\label{eq46}{{m}^{- 1}}\ kg \ {{s}^{- 2}}$

(46)

Type: SIunit?

fricas

bs:=buckingham(s)

$\label{eq47}\left[{\frac{rho \ {{v}^{2}}}{p}}\right]$

(47)

Type: List(Expression(Integer))

fricas

res2:=solve(bs.1=1,'v).1

$\label{eq48}v ={\sqrt{\frac{p}{rho}}}$

(48)

Type: Equation(Expression(Integer))

fricas

-- https://en.wikipedia.org/w/index.php?title=Dimensional_analysis
-- Example section 26
vb:Table(Symbol,SI):=table()

$\label{eq49} \mbox{\rm table} \left({}\right)$

(49)

Type: Table(Symbol,SIunit?)

fricas

vb.'l:=%m(1)$SI; vb.A:=%m(1)$SI; vb.rho:=%kg(1)$SI/%m(1)$SI;

Type: SIunit?

fricas

vb.'s:=%kg(1)$SI*%m(1)$SI/%s(2)$SI; vb.E:=%kg(1)$SI*%m(2)$SI/%s(2)$SI

$\label{eq50}{{m}^{2}}\ kg \ {{s}^{- 2}}$

(50)

Type: SIunit?

fricas

bvb:=buckingham vb

$\label{eq51}\left[{\frac{A \ s}{E}}, \:{\frac{l \ s}{E}}\right]$

(51)

Type: List(Expression(Integer))

fricas

testEquals("res1","T=sqrt(L/g)")

Type: Void

fricas

testEquals("res2","v=sqrt(p/rho)")

Type: Void

fricas

F:=operator 'F

$\label{eq52}F$

(52)

Type: BasicOperator?

fricas

res3:=F(bvb.2,bvb.1)=0

$\label{eq53}{F \left({{\frac{l \ s}{E}}, \:{\frac{A \ s}{E}}}\right)}= 0$

(53)

Type: Equation(Expression(Integer))

fricas

testEquals("res3","F('l*'s/'E,'A*'s/'E)=0")

Type: Void

fricas

-- Results/Statistics

fricas

)set output algebra on

fricas

)version

"FriCAS 1.3.10 compiled at Wed 10 Jan 02:19:45 CET 2024"

fricas

)lisp (lisp-implementation-type)

   Your user access level is compiler and this command is therefore not
      available. See the )set userlevel command for more information.

fricas

)lisp (lisp-implementation-version)

   Your user access level is compiler and this command is therefore not
      available. See the )set userlevel command for more information.

statistics()

   =============================================================================
   General WARNINGS:
   * do not use ')clear completely' before having used 'statistics()'
     It clears the statistics without warning!
   * do not forget to pass the arguments of the testXxxx functions as Strings!
     Otherwise, the test will fail and statistics() will not notice!
   =============================================================================
   WARNINGS:
   Testsuite: PUSYS
   Testcase: cgs
   test: 7
   testing in a domain without InputForm!

   =============================================================================
   Testsuite: PUSYS
     failed (total): 0 (2)
   =============================================================================
   Testsuite: PQTY
     failed (total): 0 (1)
   =============================================================================
   Testsuite: DIMAN
     failed (total): 0 (1)

   =============================================================================
   testsuite | testcases: failed (total) | tests: failed (total)
   PUSYS                       0     (2)               0    (15)
   PQTY                        0     (1)               0     (5)
   DIMAN                       0     (1)               0     (3)
   =============================================================================
   File summary.
   unexpected failures: 0
   expected failures: 0
   unexpected passes: 0
   total tests: 23

Type: Void