Template jEdit: spad_unittest.vm
-- Unittest .....: PQTY
-- Author .......: Kurt Pagani
-- Date .........: Sat Jul 28 16:56:04 CEST 2018
--
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)set break resume
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)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
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)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
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)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)
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v:=30.6 (%m(1)/%s(1))
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E:=m*v^2/2
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-- Test Suite
testsuite "PUSYS"
All user variables and function definitions have been cleared.
Type: Void
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-- Cases
testcase "cgs"
All user variables and function definitions have been cleared.
Type: Void
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CGS ==> PUSYS(['cm,'g,'s])
Type: Void
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[cm,g,s]:=baseUnits()$CGS
Type: List(PhysicalUnitSystem
?([cm,
g,
s]))
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erg:=g*cm^2/s^2
Type: PhysicalUnitSystem
?([cm,
g,
s])
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dyne:=g*cm/s^2
Type: PhysicalUnitSystem
?([cm,
g,
s])
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testEquals("dim cm", "[1,0,0]")
Type: Void
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testEquals("dim g", "[0,1,0]")
Type: Void
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testEquals("dim s", "[0,0,1]")
Type: Void
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testEquals("dim(cm/s*g)","[1,1,-1]")
Type: Void
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testEquals("factors(cm/g).1.exp","1")
Type: Void
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testEquals("factors(cm/g).2.exp","-1")
Type: Void
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testEquals("factors(one()$CGS)","[]")
Type: Void
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testEquals("baseSymbols()$CGS","['cm,'g,'s]")
Type: Void
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testEquals("(cm^2/s^4*g=g*s^(-4)*cm^2)$CGS","true")
Type: Void
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testEquals("(dyne * cm = erg)$CGS","true")
Type: Void
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testcase "SI"
All user variables and function definitions have been cleared.
Type: Void
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[m,kg,s,A,K,mol,cd]:=baseUnits()$SI
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force1:=%kg(1) * %m(1) * %s(-2)
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force2:=kg * m / s^2
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force3:=newton()$SI
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area1:=%m(2)
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area2:=m^2
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area3:=metre()^2
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pressure1:=force1/area1
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pressure2:=pascal()$SI
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testEquals("(force1=force2)$SI","true")
Type: Void
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testEquals("(force2=force3)$SI","true")
Type: Void
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testEquals("(pressure1=pressure2)$SI","true")
Type: Void
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testEquals("dim force1","[1,1,- 2,0,0,0,0]")
Type: Void
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testEquals("dim pressure2","[- 1,1,- 2,0,0,0,0]")
Type: Void
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-- Test Suite
testsuite "PQTY"
All user variables and function definitions have been cleared.
Type: Void
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testcase "PQTY(SI)"
All user variables and function definitions have been cleared.
Type: Void
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-- from codata.spad (package CODATA)
CT(v,e,u) ==> (interval(v-e,v+e)$Interval(Float)) u
Type: Void
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-- 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))
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-- 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))
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-- 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))
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-- 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))
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-- 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)
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-- 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))
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r1:=ival e
Type: Interval(Float)
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r2:=unit e
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r3:=magnitude e
Type: Float
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r4:=uncertainty e
Type: Float
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testEquals("(unit e = %s(1)*%A(1))$SI","true")
Type: Void
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testEquals("(unit(m_e*c^2)/joule()$SI=one()$SI)$SI","true")
Type: Void
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-- fine structure
myalpha:=(1/(4*%pi))::Float * eps_0^(-1)*e^2/hbar/c
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testEquals("abs(magnitude(myalpha-alpha))<1.0E-10","true")
Type: Void
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f:=2 newton()$SI
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l:=3.6 metre()$SI
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a:=l^2
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p:=f/a
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testEquals("test(magnitude(7.2 joule()$SI / (f*l))=1$Float)","true")
Type: Void
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testEquals("uncertainty(m_e*c^2)<1.0E-20","true")
Type: Void
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setOutputMode(1)$PQTY(SI)
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hbar
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m_e
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c
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setOutputMode(3)$PQTY(SI)
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alpha
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eps_0
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setOutputMode(2)$PQTY(SI)
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m_e
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hbar
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-- Test Suite
testsuite "DIMAN"
All user variables and function definitions have been cleared.
Type: Void
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testcase "DIMAN(SI)"
All user variables and function definitions have been cleared.
Type: Void
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-- Dimensional analysis
-- Buckingham Pi theorem
D==> DIMAN(SI)
Type: Void
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t:Table(Symbol,SI):=table()
Type: Table(Symbol,
SIunit
?)
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t.L:=%m(1)$SI ; t.M:=%kg(1)$SI; t.T:=%s(1)$SI; t.g:=%m(1)$SI/%s(2)$SI
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bt:=buckingham(t)
Type: List(Expression(Integer))
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res1:=solve(bt.1=1,'T).1
Type: Equation(Expression(Integer))
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s:Table(Symbol,SI):=table()
Type: Table(Symbol,
SIunit
?)
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s.v:=%m(1)$SI/%s(1)$SI; s.rho:=%kg(1)$SI/%m(3)$SI; s.p:=pascal()$SI
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bs:=buckingham(s)
Type: List(Expression(Integer))
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res2:=solve(bs.1=1,'v).1
Type: Equation(Expression(Integer))
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-- https://en.wikipedia.org/w/index.php?title=Dimensional_analysis
-- Example section 26
vb:Table(Symbol,SI):=table()
Type: Table(Symbol,
SIunit
?)
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vb.'l:=%m(1)$SI; vb.A:=%m(1)$SI; vb.rho:=%kg(1)$SI/%m(1)$SI;
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vb.'s:=%kg(1)$SI*%m(1)$SI/%s(2)$SI; vb.E:=%kg(1)$SI*%m(2)$SI/%s(2)$SI
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bvb:=buckingham vb
Type: List(Expression(Integer))
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testEquals("res1","T=sqrt(L/g)")
Type: Void
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testEquals("res2","v=sqrt(p/rho)")
Type: Void
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F:=operator 'F
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res3:=F(bvb.2,bvb.1)=0
Type: Equation(Expression(Integer))
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testEquals("res3","F('l*'s/'E,'A*'s/'E)=0")
Type: Void
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-- Results/Statistics
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)set output algebra on
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)version
"FriCAS 1.3.10 compiled at Wed 10 Jan 02:19:45 CET 2024"
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)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.
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)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
![\label{eq4}\left[ cm , \: g , \: s \right]](images/6819214810789007470-16.0px.png "\label{eq4}\left[ cm , \: g , \: s \right]")
![\label{eq7}\left[ m , \: kg , \: s , \: A , \: K , \: mol , \: cd \right]](images/514901753632451255-16.0px.png "\label{eq7}\left[ m , \: kg , \: s , \: A , \: K , \: mol , \: cd \right]")
![\label{eq22}\left[{0.1602176611 E - 18}, \:{0.1602176630 \_ 6 E - 18}\right]](images/5777664147495784266-16.0px.png "\label{eq22}\left[{0.1602176611 E - 18}, \:{0.1602176630 \_ 6 E - 18}\right]")
![\label{eq36}{\left[{0.0072973525 \<u> 647}, \:{0.0072973525 \</u> 681}\right]}\ 1](images/3737982492760795029-16.0px.png "\label{eq36}{\left[{0.0072973525 \<u> 647}, \:{0.0072973525 \</u> 681}\right]}\ 1")
![\label{eq37}{
\begin{array}{@{}l}
\displaystyle
\left[{0.8854187816 \_ 9999999999 E - 11}, \: \right.
\
\
\displaystyle
\left.{0.8854187817 E - 11}\right]](images/5798403772853348584-16.0px.png "\label{eq37}{
\begin{array}{@{}l}
\displaystyle
\left[{0.8854187816 \_ 9999999999 E - 11}, \: \right.
\
\
\displaystyle
\left.{0.8854187817 E - 11}\right]")
![\label{eq43}\left[{\frac{L}{{{T}^{2}}\ g}}\right]](images/8093189315368393954-16.0px.png "\label{eq43}\left[{\frac{L}{{{T}^{2}}\ g}}\right]")
![\label{eq47}\left[{\frac{rho \ {{v}^{2}}}{p}}\right]](images/2832485189473454078-16.0px.png "\label{eq47}\left[{\frac{rho \ {{v}^{2}}}{p}}\right]")
![\label{eq51}\left[{\frac{A \ s}{E}}, \:{\frac{l \ s}{E}}\right]](images/3186804600493261248-16.0px.png "\label{eq51}\left[{\frac{A \ s}{E}}, \:{\frac{l \ s}{E}}\right]")
