IndexedJetBundle (IJB)
axiom
)lib JBC JBC-
JetBundleCategory is now explicitly exposed in frame initial
JetBundleCategory will be automatically loaded when needed from
/var/zope2/var/LatexWiki/JBC.NRLIB/code
JetBundleCategory& is now explicitly exposed in frame initial
JetBundleCategory& will be automatically loaded when needed from
/var/zope2/var/LatexWiki/JBC-.NRLIB/code
spad
)abb domain IJB IndexedJetBundle
++ Description:
++ \axiomType{JetBundle} provides the standard implementation for a jet bundle
++ with a given number of dependent and independent variables.
V ==> Vector
B ==> Boolean
Sy ==> Symbol
BOP ==> BasicOperator
I ==> Integer
PI ==> PositiveInteger
NNI ==> NonNegativeInteger
L ==> List
EI ==> Expression Integer
OUT ==> OutputForm
JBC ==> JetBundleCategory
Const ==> "Const"::Sy
Indep ==> "Indep"::Sy
Dep ==> "Dep"::Sy
Deriv ==> "Deriv"::Sy
Multi ==> "Multi"::Sy
Repeated ==> "Repeated"::Sy
DerMode ==> [Multi,Repeated]@L Sy
IndexedJetBundle(x,u,p,n,m) : Cat == Def where
x,u,p : Sy
m,n : PI
Cat ==> JBC
Def ==> add
Rep := L NNI
-- The list has length 2 for independent variables, length n+2 for
-- derivatives and dependent variables. The first entry is zero for 1,
-- one for independent, two for dependent variables and three for
-- derivatives. The second entry is the upper index, the rest the
-- multi-index.
notation:Sy := Repeated
-- Global variable for notation.
setNotation(s:Sy):Sy ==
not member?(s,DerMode) => error "Unknown notation"
t := notation
notation := s
t
getNotation():Sy == notation
multiIndex(jv:$):L NNI == copy rest rest jv::Rep
index(jv:$):PI == first(rest jv)::PI
type(jv:$):Sy ==
t := first jv
zero? t => Const
one? t => Indep
t=2 => Dep
Deriv
CheckZeroIndex(il:L NNI):B ==
-- Local function; checks, whether multi-index is zero.
for i in il repeat
if not zero? i then return false
true
X(up:PI):$ ==
up>n => error errmsg2
[1,up::NNI]
U(up:PI):$ ==
up>m => error errmsg2
cons(2, cons(up::NNI, [0$NNI for i in 1..n]))
Pm(up:PI,lo:L NNI):$ ==
up>m => error errmsg2
#lo^=n => error errmsg1
CheckZeroIndex(lo) => U(up)
cons(3,cons(up::NNI,lo))
1 : $ == [0,1]
numIndVar():PI == n
numDepVar():PI == m
-- ----------- --
-- Output Form --
-- ----------- --
name(jv:$):Sy ==
(jt:=type(jv))=Const => "1"::Sy
jt=Indep =>
n>1 => superscript(x,[index(jv)::OUT])
x
jt=Dep =>
m>1 => superscript(u,[index(jv)::OUT])
u
getNotation()=Multi =>
m>1 => script(p, _
[[bracket commaSeparate [i::OUT for i in multiIndex jv]], _
[index(jv)::OUT], [], [], []])
subscript(p, _
[bracket commaSeparate [i::OUT for i in multiIndex jv]])
m>1 => script(p, _
[[blankSeparate [j::OUT for j in repeatedIndex jv]], _
[index(jv)::OUT], [], [], []])
subscript(p, [blankSeparate [j::OUT for j in repeatedIndex jv]])
-- Coerce to Symbol looses all information; therefore
-- all important data like type and indices are saved
-- as arguments of an operator
opdisp(l:L OUT):OUT == first l
coerce(jv:$):EI ==
-- Name of operator must be unique and the same as jv::Sy
-- to allow to differentiate and substitute in EI.
type(jv)=Const => 1
opname:Sy := name jv
jop := operator(opname)$BOP
display(jop,opdisp)
tmp:None := coerce(jv)$NoneFunctions1($)
jop := setProperty(jop,"%symbol",tmp)$BOP
tmp := coerce(weight(jv))$NoneFunctions1(NNI)
jop := setProperty(jop,"%weight",tmp)$BOP
tmp := coerce(type(jv))$NoneFunctions1(Sy)
jop := setProperty(jop,"%jet",tmp)$BOP
if getNotation()=Multi then
arg := [i::EI for i in multiIndex jv]
else
arg := [j::EI for j in repeatedIndex jv]
arg := concat!([opname::EI,index(jv)::EI], arg)
kernel(jop,arg)
spad
Compiling FriCAS source code from file
/var/zope2/var/LatexWiki/2771267939938826525-25px002.spad using
old system compiler.
IJB abbreviates domain IndexedJetBundle
processing macro definition V ==> Vector
processing macro definition B ==> Boolean
processing macro definition Sy ==> Symbol
processing macro definition BOP ==> BasicOperator
processing macro definition I ==> Integer
processing macro definition PI ==> PositiveInteger
processing macro definition NNI ==> NonNegativeInteger
processing macro definition L ==> List
processing macro definition EI ==> Expression Integer
processing macro definition OUT ==> OutputForm
processing macro definition JBC ==> JetBundleCategory
processing macro definition Const ==> ::(Const,Sy)
processing macro definition Indep ==> ::(Indep,Sy)
processing macro definition Dep ==> ::(Dep,Sy)
processing macro definition Deriv ==> ::(Deriv,Sy)
processing macro definition Multi ==> ::(Multi,Sy)
processing macro definition Repeated ==> ::(Repeated,Sy)
processing macro definition DerMode ==> @(construct(Multi,Repeated),L Sy)
processing macro definition Cat ==> JetBundleCategory
processing macro definition Def ==> -- the constructor capsule
------------------------------------------------------------------------
initializing NRLIB IJB for IndexedJetBundle
compiling into NRLIB IJB
compiling exported setNotation : Symbol -> Symbol
Time: 0.15 SEC.
compiling exported getNotation : () -> Symbol
Time: 0 SEC.
compiling exported multiIndex : $ -> List NonNegativeInteger
Time: 0.01 SEC.
compiling exported index : $ -> PositiveInteger
Time: 0 SEC.
compiling exported type : $ -> Symbol
Time: 0 SEC.
compiling local CheckZeroIndex : List NonNegativeInteger -> Boolean
Time: 0.01 SEC.
compiling exported X : PositiveInteger -> $
Time: 0.01 SEC.
compiling exported U : PositiveInteger -> $
Time: 0.08 SEC.
compiling exported Pm : (PositiveInteger,List NonNegativeInteger) -> $
Time: 0.04 SEC.
compiling exported One : () -> $
IJB;One;$;10 is replaced by LIST01
Time: 0.01 SEC.
compiling exported numIndVar : () -> PositiveInteger
Time: 0 SEC.
compiling exported numDepVar : () -> PositiveInteger
Time: 0 SEC.
compiling exported name : $ -> Symbol
Time: 0.09 SEC.
compiling local opdisp : List OutputForm -> OutputForm
IJB;opdisp is replaced by SPADfirst
Time: 0.01 SEC.
compiling exported coerce : $ -> Expression Integer
Time: 0.39 SEC.
(time taken in buildFunctor: 1)
;;; *** |IndexedJetBundle| REDEFINED
;;; *** |IndexedJetBundle| REDEFINED
Time: 0.01 SEC.
Cumulative Statistics for Constructor IndexedJetBundle
Time: 0.81 seconds
finalizing NRLIB IJB
Processing IndexedJetBundle for Browser database:
--->-->IndexedJetBundle(): Missing Description
------------------------------------------------------------------------
IndexedJetBundle is now explicitly exposed in frame initial
IndexedJetBundle will be automatically loaded when needed from
/var/zope2/var/LatexWiki/IJB.NRLIB/code