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Conjugate opertors

spad
)abbrev domain BOP BasicOperator
++ Basic system operators
++ Author: Manuel Bronstein
++ Date Created: 22 March 1988
++ Date Last Updated: 11 October 1993
++ Description:
++   A basic operator is an object that can be applied to a list of
++   arguments from a set, the result being a kernel over that set.
++ Keywords: operator, kernel.
BasicOperator() : Exports == Implementation where
  O   ==> OutputForm
  P   ==> AssociationList(Symbol, None)
  L   ==> List Record(key : Symbol, entry : None)
  SEX ==> InputForm
Exports ==> OrderedSet with name : % -> Symbol ++ name(op) returns the name of op. properties : % -> P ++ properties(op) returns the list of all the properties ++ currently attached to op. copy : % -> % ++ copy(op) returns a copy of op. conjugate : % -> % ++ conjugate(op) returns the conjugate of op operator : Symbol -> % ++ operator(f) makes f into an operator with arbitrary arity. operator : (Symbol, NonNegativeInteger) -> % ++ operator(f, n) makes f into an n-ary operator. arity : % -> Union(NonNegativeInteger, "failed") ++ arity(op) returns n if op is n-ary, and ++ "failed" if op has arbitrary arity. nullary? : % -> Boolean ++ nullary?(op) tests if op is nullary. unary? : % -> Boolean ++ unary?(op) tests if op is unary. nary? : % -> Boolean ++ nary?(op) tests if op has arbitrary arity. weight : % -> NonNegativeInteger ++ weight(op) returns the weight attached to op. weight : (%, NonNegativeInteger) -> % ++ weight(op, n) attaches the weight n to op. equality : (%, (%, %) -> Boolean) -> % ++ equality(op, foo?) attaches foo? as the "%equal?" property ++ to op. If op1 and op2 have the same name, and one of them ++ has an "%equal?" property f, then \spad{f(op1, op2)} is called to ++ decide whether op1 and op2 should be considered equal. comparison : (%, (%, %) -> Boolean) -> % ++ comparison(op, foo?) attaches foo? as the "%less?" property ++ to op. If op1 and op2 have the same name, and one of them ++ has a "%less?" property f, then \spad{f(op1, op2)} is called to ++ decide whether \spad{op1 < op2}. display : % -> Union(List O -> O, "failed") ++ display(op) returns the "%display" property of op if ++ it has one attached, and "failed" otherwise. display : (%, List O -> O) -> % ++ display(op, foo) attaches foo as the "%display" property ++ of op. If op has a "%display" property f, then \spad{op(a1,...,an)} ++ gets converted to OutputForm as \spad{f(a1, ..., an)}. display : (%, O -> O) -> % ++ display(op, foo) attaches foo as the "%display" property ++ of op. If op has a "%display" property f, then \spad{op(a)} ++ gets converted to OutputForm as \spad{f(a)}. ++ Argument op must be unary. input : (%, List SEX -> SEX) -> % ++ input(op, foo) attaches foo as the "%input" property ++ of op. If op has a "%input" property f, then \spad{op(a1,...,an)} ++ gets converted to InputForm as \spad{f(a1, ..., an)}. input : % -> Union(List SEX -> SEX, "failed") ++ input(op) returns the "%input" property of op if ++ it has one attached, "failed" otherwise. is? : (%, Symbol) -> Boolean ++ is?(op, s) tests if the name of op is s. has? : (%, Symbol) -> Boolean ++ has?(op, s) tests if property s is attached to op. assert : (%, Symbol) -> % ++ assert(op, s) attaches property s to op. ++ Argument op is modified "in place", i.e. no copy is made. deleteProperty! : (%, Symbol) -> % ++ deleteProperty!(op, s) unattaches property s from op. ++ Argument op is modified "in place", i.e. no copy is made. property : (%, Symbol) -> Union(None, "failed") ++ property(op, s) returns the value of property s if ++ it is attached to op, and "failed" otherwise. setProperty : (%, Symbol, None) -> % ++ setProperty(op, s, v) attaches property s to op, ++ and sets its value to v. ++ Argument op is modified "in place", i.e. no copy is made. setProperties : (%, P) -> % ++ setProperties(op, l) sets the property list of op to l. ++ Argument op is modified "in place", i.e. no copy is made.
Implementation ==> add -- if narg < 0 then the operator has variable arity. Rep := Record(opname : Symbol, narg : SingleInteger, props : P)
import from P import from SingleInteger import from NonNegativeInteger import from Set(Symbol)
-- some internal properties LESS? := "%less?"::Symbol EQUAL? := "%equal?"::Symbol WEIGHT := '%weight DISPLAY := '%display SEXPR := '%input CONJ := '%conjugate DIFFDISP:= '%diffDisp
oper : (Symbol, SingleInteger, P) -> %
is?(op, s) == name(op) = s name op == op.opname properties op == op.props setProperties(op, l) == (op.props := l; op) operator s == oper(s, -1::SingleInteger, table()) operator(s, n) == oper(s, n::Integer::SingleInteger, table()) property(op, name) == search(name, op.props) assert(op, s) == setProperty(op, s, NIL$Lisp) has?(op, name) == key?(name, op.props) oper(se, n, prop) == [se, n, prop] weight(op, n) == setProperty(op, WEIGHT, n pretend None) nullary? op == zero?(op.narg) -- unary? op == one?(op.narg) unary? op == ((op.narg) = 1) nary? op == negative?(op.narg) equality(op, func) == setProperty(op, EQUAL?, func pretend None) comparison(op, func) == setProperty(op, LESS?, func pretend None) display(op : %, f : O -> O) == display(op, (l1 : List(O)) : O +-> f first l1) deleteProperty!(op, name) == (remove!(name, properties op); op) setProperty(op, name, valu) == (op.props.name := valu; op) coerce(op : %) : OutputForm == name(op)::OutputForm input(op : %, f : List SEX -> SEX) == setProperty(op, SEXPR, f pretend None) display(op : %, f : List O -> O) == setProperty(op, DISPLAY, f pretend None) diffDisp(op : %, f : List O -> O):% == setProperty(op, DIFFDISP, f pretend None)
display op == (u := property(op, DISPLAY)) case "failed" => "failed" (u::None) pretend (List O -> O)
input op == (u := property(op, SEXPR)) case "failed" => "failed" (u::None) pretend (List SEX -> SEX)
arity op == negative?(n := op.narg) => "failed" convert(n)@Integer :: NonNegativeInteger
copy op == oper(name op, op.narg, table([[r.key, r.entry] for r in entries(properties op)@L]$L))
conjugate op == (op?:=property(op,CONJ)) case None => op?::None pretend % --op' := copy op op' := oper(superscript(name op,["*"::Symbol::O]), op.narg, table([[r.key, r.entry] for r in entries(properties op)@L]$L)) setProperty(op, CONJ, op' pretend None) setProperty(op', CONJ, op pretend None) deleteProperty!(op','%eval) deleteProperty!(op','%diff) --display(op',(a:List O):O+->prefix(overbar(op::O),a)) --diffDisp(op',(a:List O):O+->prefix(overbar(first a),rest a)) op'
-- property EQUAL? contains a function f: (BOP, BOP) -> Boolean -- such that f(o1, o2) is true iff o1 = o2 op1 = op2 == (EQ$Lisp)(op1, op2) => true name(op1) ~= name(op2) => false op1.narg ~= op2.narg => false brace(keys properties op1) ~=$Set(Symbol) brace(keys properties op2) => false (func := property(op1, EQUAL?)) case None => ((func::None) pretend ((%, %) -> Boolean)) (op1, op2) true
-- property WEIGHT allows one to change the ordering around -- by default, every operator has weigth 1 weight op == (w := property(op, WEIGHT)) case "failed" => 1 (w::None) pretend NonNegativeInteger
-- property LESS? contains a function f: (BOP, BOP) -> Boolean -- such that f(o1, o2) is true iff o1 < o2 op1 < op2 == (w1 := weight op1) ~= (w2 := weight op2) => w1 < w2 op1.narg ~= op2.narg => op1.narg < op2.narg name(op1) ~= name(op2) => name(op1) < name(op2) n1 := #(k1 := brace(keys(properties op1))$Set(Symbol)) n2 := #(k2 := brace(keys(properties op2))$Set(Symbol)) n1 ~= n2 => n1 < n2 not zero?(n1 := #(d1 := difference(k1, k2))) => n1 ~= (n2 := #(d2 := difference(k2, k1))) => n1 < n2 inspect(d1) < inspect(d2) (func := property(op1, LESS?)) case None => ((func::None) pretend ((%, %) -> Boolean)) (op1, op2) (func := property(op1, EQUAL?)) case None => not(((func::None) pretend ((%, %) -> Boolean)) (op1, op2)) false
)abbrev package BOP1 BasicOperatorFunctions1 ++ Tools to set/get common properties of operators ++ Author: Manuel Bronstein ++ Date Created: 28 Mar 1988 ++ Date Last Updated: 15 May 1990 ++ Description: ++ This package exports functions to set some commonly used properties ++ of operators, including properties which contain functions. ++ Keywords: operator. BasicOperatorFunctions1(A : SetCategory) : Exports == Implementation where OP ==> BasicOperator
Exports ==> with evaluate : (OP, List A) -> Union(A, "failed") ++ evaluate(op, [a1,...,an]) checks if op has an "%eval" ++ property f. If it has, then \spad{f(a1, ..., an)} is returned, and ++ "failed" otherwise. evaluate : (OP, List A -> A) -> OP ++ evaluate(op, foo) attaches foo as the "%eval" property ++ of op. If op has an "%eval" property f, then applying op ++ to \spad{(a1, ..., an)} returns the result of \spad{f(a1, ..., an)}. evaluate : (OP, A -> A) -> OP ++ evaluate(op, foo) attaches foo as the "%eval" property ++ of op. If op has an "%eval" property f, then applying op ++ to a returns the result of \spad{f(a)}. Argument op must be unary. evaluate : OP -> Union(List A -> A, "failed") ++ evaluate(op) returns the value of the "%eval" property of ++ op if it has one, and "failed" otherwise. derivative : (OP, List (List A -> A)) -> OP ++ derivative(op, [foo1, ..., foon]) attaches [foo1, ..., foon] as ++ the "%diff" property of op. If op has an "%diff" property ++ \spad{[f1, ..., fn]} then applying a derivation D to \spad{op(a1, ..., an)} ++ returns \spad{f1(a1, ..., an) * D(a1) + ... + fn(a1, ..., an) * D(an)}. derivative : (OP, A -> A) -> OP ++ derivative(op, foo) attaches foo as the "%diff" property ++ of op. If op has an "%diff" property f, then applying a ++ derivation D to op(a) returns \spad{f(a) * D(a)}. Argument op must be unary. derivative : OP -> Union(List(List A -> A), "failed") ++ derivative(op) returns the value of the "%diff" property of ++ op if it has one, and "failed" otherwise. constantOperator : A -> OP ++ constantOperator(a) returns a nullary operator op ++ such that \spad{op()} always evaluate to \spad{a}. constantOpIfCan : OP -> Union(A, "failed") ++ constantOpIfCan(op) returns \spad{a} if op is the constant ++ nullary operator always returning \spad{a}, "failed" otherwise.
Implementation ==> add
EVAL := '%eval CONST := '%constant DIFF := '%diff
evaluate(op : OP, func : A -> A) == evaluate(op, (l1 : List(A)) : A +-> func first l1)
evaluate op == (func := property(op, EVAL)) case "failed" => "failed" (func::None) pretend (List A -> A)
evaluate(op : OP, args : List A) == (func := property(op, EVAL)) case "failed" => "failed" ((func::None) pretend (List A -> A)) args
evaluate(op : OP, func : List A -> A) == setProperty(op, EVAL, func pretend None)
derivative op == (func := property(op, DIFF)) case "failed" => "failed" ((func::None) pretend List(List A -> A))
derivative(op : OP, grad : List(List A -> A)) == setProperty(op, DIFF, grad pretend None)
derivative(op : OP, f : A -> A) == unary? op or nary? op => derivative(op, [(l1 : List(A)) : A +-> f first l1]$List(List A -> A)) error "Operator is not unary"
cdisp : (OutputForm, List OutputForm) -> OutputForm csex : (InputForm, List InputForm) -> InputForm eqconst? : (OP, OP) -> Boolean constOp : A -> OP
cdisp(a, l) == a csex(a, l) == a
eqconst?(a, b) == (va := property(a, CONST)) case "failed" => not has?(b, CONST) ((vb := property(b, CONST)) case None) and ((va::None) pretend A) = ((vb::None) pretend A) opconst : OP if A has Comparable then ltconst? : (OP, OP) -> Boolean ltconst?(a, b) == (va := property(a, CONST)) case "failed" => has?(b, CONST) ((vb := property(b, CONST)) case None) and smaller?((va::None) pretend A, (vb::None) pretend A) opconst := comparison(equality(operator('constant, 0), eqconst?), ltconst?) else opconst := equality(operator('constant, 0), eqconst?)
constOp a == setProperty(display(copy opconst, (l1 : List(OutputForm)) : OutputForm +-> cdisp(a::OutputForm, l1)), CONST, a pretend None)
constantOpIfCan op == is?(op, 'constant) and ((u := property(op, CONST)) case None) => (u::None) pretend A "failed"
if A has ConvertibleTo InputForm then constantOperator a == input(constOp a, (l1 : List(InputForm)) : InputForm +-> csex(convert a, l1)) else constantOperator a == constOp a
)abbrev package COMMONOP CommonOperators ++ Provides commonly used operators ++ Author: Manuel Bronstein ++ Date Created: 25 Mar 1988 ++ Date Last Updated: 2 December 1994 ++ Description: ++ This package exports the elementary operators, with some semantics ++ already attached to them. The semantics that is attached here is not ++ dependent on the set in which the operators will be applied. ++ Keywords: operator. CommonOperators() : Exports == Implementation where OP ==> BasicOperator O ==> OutputForm POWER ==> '%power ALGOP ==> '%alg EVEN ==> 'even ODD ==> 'odd DUMMYVAR ==> '%dummyVar
Exports ==> with operator : Symbol -> OP ++ operator(s) returns an operator with name s, with the ++ appropriate semantics if s is known. If s is not known, ++ the result has no semantics.
Implementation ==> add dpi : List O -> O dgamma : List O -> O dquote : List O -> O dexp : O -> O dfact : O -> O startUp : Boolean -> Void setDummyVar : (OP, NonNegativeInteger) -> OP
brandNew? : Reference(Boolean) := ref true
opalg := operator('rootOf, 2)$OP oproot := operator('nthRoot, 2) oppi := operator('pi, 0) oplog := operator('log, 1) opexp := operator('exp, 1) opabs := operator('abs, 1) opsin := operator('sin, 1) opcos := operator('cos, 1) optan := operator('tan, 1) opcot := operator('cot, 1) opsec := operator('sec, 1) opcsc := operator('csc, 1) opasin := operator('asin, 1) opacos := operator('acos, 1) opatan := operator('atan, 1) opacot := operator('acot, 1) opasec := operator('asec, 1) opacsc := operator('acsc, 1) opsinh := operator('sinh, 1) opcosh := operator('cosh, 1) optanh := operator('tanh, 1) opcoth := operator('coth, 1) opsech := operator('sech, 1) opcsch := operator('csch, 1) opasinh := operator('asinh, 1) opacosh := operator('acosh, 1) opatanh := operator('atanh, 1) opacoth := operator('acoth, 1) opasech := operator('asech, 1) opacsch := operator('acsch, 1) opbox := operator('%box)$OP oppren := operator('%paren)$OP opquote := operator('%quote)$OP opdiff := operator('%diff, 3) opsi := operator('Si, 1) opci := operator('Ci, 1) opshi := operator('Shi, 1) opchi := operator('Chi, 1) opei := operator('Ei, 1) opli := operator('li, 1) operf := operator('erf, 1) operfi := operator('erfi, 1) opli2 := operator('dilog, 1) opfis := operator('fresnelS, 1) opfic := operator('fresnelC, 1) opGamma := operator('Gamma, 1) opGamma2 := operator('Gamma2, 2) opBeta := operator('Beta, 2) opdigamma := operator('digamma, 1) oppolygamma := operator('polygamma, 2) opBesselJ := operator('besselJ, 2) opBesselY := operator('besselY, 2) opBesselI := operator('besselI, 2) opBesselK := operator('besselK, 2) opAiryAi := operator('airyAi, 1) opAiryAiPrime := operator('airyAiPrime, 1) opAiryBi := operator('airyBi , 1) opAiryBiPrime := operator('airyBiPrime, 1) opLambertW := operator('lambertW, 1) opPolylog := operator('polylog, 2) opWeierstrassP := operator('weierstrassP, 3) opWeierstrassPPrime := operator('weierstrassPPrime, 3) opWeierstrassSigma := operator('weierstrassSigma, 3) opWeierstrassZeta := operator('weierstrassZeta, 3) -- arbitrary arity opHypergeometricF := operator('hypergeometricF)$BasicOperator opMeijerG := operator('meijerG)$BasicOperator
opWhittakerM := operator('whittakerM, 3)$OP opWhittakerW := operator('whittakerW, 3)$OP opAngerJ := operator('angerJ, 2)$OP opWeberE := operator('weberE, 2)$OP opStruveH := operator('struveH, 2)$OP opStruveL := operator('struveL, 2)$OP opHankelH1 := operator('hankelH1, 2)$OP opHankelH2 := operator('hankelH2, 2)$OP opLommelS1 := operator('lommelS1, 3)$OP opLommelS2 := operator('lommelS2, 3)$OP opKummerM := operator('kummerM, 3)$OP opKummerU := operator('kummerU, 3)$OP opLegendreP := operator('legendreP, 3)$OP opLegendreQ := operator('legendreQ, 3)$OP opKelvinBei := operator('kelvinBei, 2)$OP opKelvinBer := operator('kelvinBer, 2)$OP opKelvinKei := operator('kelvinKei, 2)$OP opKelvinKer := operator('kelvinKer, 2)$OP opEllipticK := operator('ellipticK, 1)$OP opEllipticE := operator('ellipticE, 1)$OP opEllipticE2 := operator('ellipticE2, 2)$OP opEllipticF := operator('ellipticF, 2)$OP opEllipticPi := operator('ellipticPi, 3)$OP opJacobiSn := operator('jacobiSn, 2)$OP opJacobiCn := operator('jacobiCn, 2)$OP opJacobiDn := operator('jacobiDn, 2)$OP opJacobiZeta := operator('jacobiZeta, 2)$OP opJacobiTheta := operator('jacobiTheta, 2)$OP opWeierstrassPInverse := operator('weierstrassPInverse, 3)$OP opLerchPhi := operator('lerchPhi, 3)$OP opRiemannZeta := operator('riemannZeta, 1)$OP
-- orthogonal polynomials opCharlierC := operator('charlierC, 3)$OP opHermiteH := operator('hermiteH, 2)$OP opJacobiP := operator('jacobiP, 4)$OP opLaguerreL := operator('laguerreL, 3)$OP opMeixnerM := operator('meixnerM, 4)$OP
op_log_gamma := operator('%logGamma, 1)$OP op_eis := operator('%eis, 1)$OP op_erfs := operator('%erfs, 1)$OP op_erfis := operator('%erfis, 1)$OP
opint := operator('integral, 3) -- arbitrary arity opiint := operator('%iint)$BasicOperator opdint := operator('%defint, 5) opfact := operator('factorial, 1) opperm := operator('permutation, 2) opbinom := operator('binomial, 2) oppow := operator(POWER, 2) opsum := operator('summation, 3) opdsum := operator('%defsum, 5) opprod := operator('product, 3) opdprod := operator('%defprod, 5)
oprootsum := operator('%root_sum, 3) opfloor := operator('floor, 1) opceil := operator('ceil, 1) opreal := operator('real, 1) opimag := operator('imag, 1) opconjugate := operator('conjugate, 1) oparg := operator('arg, 1) opsign := operator('sign, 1) opDiracDelta := operator('diracDelta, 1) -- arbitrary arity opmax := operator('max)$BasicOperator opmin := operator('min)$BasicOperator
algop := [oproot, opalg]$List(OP) rtrigop := [opsin, opcos, optan, opcot, opsec, opcsc, opasin, opacos, opatan, opacot, opasec, opacsc] htrigop := [opsinh, opcosh, optanh, opcoth, opsech, opcsch, opasinh, opacosh, opatanh, opacoth, opasech, opacsch] trigop := concat(rtrigop, htrigop) elemop := concat(trigop, [oppi, oplog, opexp]) primop := [opei, opli, opsi, opci, opshi, opchi, operf, operfi, opli2, opint, opdint, opfis, opfic, opiint] combop := [opfact, opperm, opbinom, oppow, opsum, opdsum, opprod, opdprod] specop := [opGamma, opGamma2, opBeta, opdigamma, oppolygamma, opabs, _ opconjugate, opfloor, opceil, opreal, opimag, opsign, opmax, _ opmin,opDiracDelta, oparg, opconjugate, op_log_gamma, _ op_eis, op_erfs, op_erfis, _ opBesselJ, opBesselY, opBesselI, opBesselK, opAiryAi, opAiryBi, _ opAiryAiPrime, opAiryBiPrime, opLambertW, opPolylog, _ opWeierstrassP, opWeierstrassPPrime, opWeierstrassZeta, _ opWeierstrassSigma, opHypergeometricF, opMeijerG, _ opWhittakerM, _ opWhittakerW, _ opAngerJ, _ opWeberE, _ opStruveH, _ opStruveL, _ opHankelH1, _ opHankelH2, _ opLommelS1, _ opLommelS2, _ opKummerM, _ opKummerU, _ opLegendreP, _ opLegendreQ, _ opKelvinBei, _ opKelvinBer, _ opKelvinKei, _ opKelvinKer, _ opEllipticK, _ opEllipticE, _ opEllipticE2, _ opEllipticF, _ opEllipticPi, _ opJacobiSn, _ opJacobiCn, _ opJacobiDn, _ opJacobiZeta, _ opJacobiTheta, _ opLerchPhi, _ opRiemannZeta, _ opCharlierC, _ opHermiteH, _ opJacobiP, _ opLaguerreL, _ opMeixnerM _ ] -- opWeierstrassPInverse, _
anyop := [oppren, opdiff, opbox, opquote] allop := concat(concat(concat(concat(concat( algop, elemop), primop), combop), specop), anyop)
-- odd and even single argument operators, must be maintained current! evenop := [opcos, opsec, opcosh, opsech, opabs, opDiracDelta] oddop := [opsin, opcsc, optan, opcot, opasin, opacsc, opatan, opsinh, opcsch, optanh, opcoth, opasinh, opacsch, opatanh, opacoth, opsi, opshi, operf, operfi, opsign, opreal, opimag]
-- operators whose second argument is a dummy variable dummyvarop1 := [opdiff, opalg, opint, oprootsum, opsum, opprod] -- operators whose second and third arguments are dummy variables dummyvarop2 := [opdint, opdsum, opdprod]
operator s == if (deref brandNew?) then startUp false for op in allop repeat is?(op, s) => return copy op operator(s)$OP
dpi l == '%pi::O dfact x == postfix("!"::Symbol::O, (ATOM(x)$Lisp => x; paren x)) dquote l == prefix(quote(first(l)::O), rest l) dgamma l == prefix('Gamma::O, l) dEllipticE2(l : List O) : O == prefix('ellipticE::O, l)
setDummyVar(op, n) == setProperty(op, DUMMYVAR, n pretend None)
dexp x == e := '%e::O x = 1::O => e e ^ x
startUp b == brandNew?() := b display(oppren, paren) display(opbox, commaSeparate) display(oppi, dpi) display(opexp, dexp) display(opGamma2, dgamma) display(opEllipticE2, dEllipticE2) display(opfact, dfact) display(opquote, dquote) display(opperm, (z1 : List O) : O +-> supersub('A::O, z1)) display(opbinom, (z1 : List O) : O +-> binomial(first z1, second z1)) display(oppow, (z1 : List O) : O +-> first(z1) ^ second(z1)) display(opsum, (z1 : List O) : O +-> sum(first z1, second z1, third z1)) display(opprod, (z1 : List O) : O +-> prod(first z1, second z1, third z1)) display(opint, (z1 : List O) : O +-> int(first z1 * hconcat('d::O, second z1), empty(), third z1)) input(oppren, (z1 : List InputForm) : InputForm +-> convert concat(convert("("::Symbol)@InputForm, concat(z1, convert(")"::Symbol)@InputForm))) input(oppow, (z1 : List InputForm) : InputForm +-> convert concat(convert("^"::Symbol)@InputForm, z1)) input(oproot, (z1 : List InputForm) : InputForm +-> convert [convert("^"::Symbol)@InputForm, first z1, 1 / second z1]) for op in algop repeat assert(op, ALGOP) for op in rtrigop repeat assert(op, 'rtrig) for op in htrigop repeat assert(op, 'htrig) for op in trigop repeat assert(op, 'trig) for op in elemop repeat assert(op, 'elem) for op in primop repeat assert(op, 'prim) for op in combop repeat assert(op, 'comb) for op in specop repeat assert(op, 'special) for op in anyop repeat assert(op, 'any) for op in evenop repeat assert(op, EVEN) for op in oddop repeat assert(op, ODD) for op in dummyvarop1 repeat setDummyVar(op, 1) for op in dummyvarop2 repeat setDummyVar(op, 2) assert(oppren, 'linear) void
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. -- --Redistribution and use in source and binary forms, with or without --modification, are permitted provided that the following conditions are --met: -- -- - Redistributions of source code must retain the above copyright -- notice, this list of conditions and the following disclaimer. -- -- - Redistributions in binary form must reproduce the above copyright -- notice, this list of conditions and the following disclaimer in -- the documentation and/or other materials provided with the -- distribution. -- -- - Neither the name of The Numerical ALgorithms Group Ltd. nor the -- names of its contributors may be used to endorse or promote products -- derived from this software without specific prior written permission. -- --THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS --IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED --TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A --PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER --OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, --EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, --PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR --PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF --LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING --NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS --SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-- SPAD files for the functional world should be compiled in the -- following order: -- -- OP kl expr function
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1350830317830994170-25px001.spad
      using old system compiler.
   BOP abbreviates domain BasicOperator 
------------------------------------------------------------------------
   initializing NRLIB BOP for BasicOperator 
   compiling into NRLIB BOP 
   importing AssociationList(Symbol,None)
   importing SingleInteger
   importing NonNegativeInteger
   importing Set Symbol
   compiling exported is? : ($,Symbol) -> Boolean
Time: 0.01 SEC.
compiling exported name : $ -> Symbol BOP;name;$S;2 is replaced by QVELTop0 Time: 0.01 SEC.
compiling exported properties : $ -> AssociationList(Symbol,None) BOP;properties;$Al;3 is replaced by QVELTop2 Time: 0 SEC.
compiling exported setProperties : ($,AssociationList(Symbol,None)) -> $ Time: 0 SEC.
compiling exported operator : Symbol -> $ Time: 0 SEC.
compiling exported operator : (Symbol,NonNegativeInteger) -> $ Time: 0 SEC.
compiling exported property : ($,Symbol) -> Union(None,failed) Time: 0 SEC.
compiling exported assert : ($,Symbol) -> $ Time: 0 SEC.
compiling exported has? : ($,Symbol) -> Boolean Time: 0 SEC.
compiling local oper : (Symbol,SingleInteger,AssociationList(Symbol,None)) -> $ BOP;oper is replaced by VECTOR Time: 0 SEC.
compiling exported weight : ($,NonNegativeInteger) -> $ Time: 0 SEC.
compiling exported nullary? : $ -> Boolean Time: 0 SEC.
compiling exported unary? : $ -> Boolean Time: 0 SEC.
compiling exported nary? : $ -> Boolean Time: 0 SEC.
compiling exported equality : ($,($,$) -> Boolean) -> $ Time: 0 SEC.
compiling exported comparison : ($,($,$) -> Boolean) -> $ Time: 0 SEC.
compiling exported display : ($,OutputForm -> OutputForm) -> $ Time: 0.01 SEC.
compiling exported deleteProperty! : ($,Symbol) -> $ Time: 0 SEC.
compiling exported setProperty : ($,Symbol,None) -> $ Time: 0 SEC.
compiling exported coerce : $ -> OutputForm Time: 0 SEC.
compiling exported input : ($,List InputForm -> InputForm) -> $ Time: 0 SEC.
compiling exported display : ($,List OutputForm -> OutputForm) -> $ Time: 0 SEC.
compiling local diffDisp : ($,List OutputForm -> OutputForm) -> $ Time: 0 SEC.
compiling exported display : $ -> Union(List OutputForm -> OutputForm,failed) Time: 0.01 SEC.
compiling exported input : $ -> Union(List InputForm -> InputForm,failed) Time: 0 SEC.
compiling exported arity : $ -> Union(NonNegativeInteger,failed) Time: 0 SEC.
compiling exported copy : $ -> $ Time: 0.01 SEC.
compiling exported conjugate : $ -> $ Time: 0 SEC.
compiling exported = : ($,$) -> Boolean Time: 0.02 SEC.
compiling exported weight : $ -> NonNegativeInteger Time: 0 SEC.
compiling exported < : ($,$) -> Boolean Time: 0.02 SEC.
(time taken in buildFunctor: 0)
;;; *** |BasicOperator| REDEFINED
;;; *** |BasicOperator| REDEFINED Time: 0 SEC.
Warnings: [1] name: opname has no value [2] properties: props has no value [3] setProperties: props has no value [4] property: props has no value [5] has?: props has no value [6] nullary?: narg has no value [7] unary?: narg has no value [8] nary?: narg has no value [9] setProperty: props has no value [10] arity: narg has no value [11] copy: narg has no value [12] copy: key has no value [13] copy: entry has no value [14] conjugate: narg has no value [15] conjugate: key has no value [16] conjugate: entry has no value [17] =: narg has no value [18] <: narg has no value
Cumulative Statistics for Constructor BasicOperator Time: 0.09 seconds
finalizing NRLIB BOP Processing BasicOperator for Browser database: --------constructor--------- --------(name ((Symbol) %))--------- --------(properties ((AssociationList (Symbol) (None)) %))--------- --------(copy (% %))--------- --------(conjugate (% %))--------- --------(operator (% (Symbol)))--------- --------(operator (% (Symbol) (NonNegativeInteger)))--------- --------(arity ((Union (NonNegativeInteger) failed) %))--------- --------(nullary? ((Boolean) %))--------- --------(unary? ((Boolean) %))--------- --------(nary? ((Boolean) %))--------- --------(weight ((NonNegativeInteger) %))--------- --------(weight (% % (NonNegativeInteger)))--------- --------(equality (% % (Mapping (Boolean) % %)))--------- --------(comparison (% % (Mapping (Boolean) % %)))--------- --------(display ((Union (Mapping (OutputForm) (List (OutputForm))) failed) %))--------- --------(display (% % (Mapping (OutputForm) (List (OutputForm)))))--------- --------(display (% % (Mapping (OutputForm) (OutputForm))))--------- --------(input (% % (Mapping (InputForm) (List (InputForm)))))--------- --------(input ((Union (Mapping (InputForm) (List (InputForm))) failed) %))--------- --------(is? ((Boolean) % (Symbol)))--------- --------(has? ((Boolean) % (Symbol)))--------- --------(assert (% % (Symbol)))--------- --------(deleteProperty! (% % (Symbol)))--------- --------(property ((Union (None) failed) % (Symbol)))--------- --------(setProperty (% % (Symbol) (None)))--------- --------(setProperties (% % (AssociationList (Symbol) (None))))--------- ; compiling file "/var/aw/var/LatexWiki/BOP.NRLIB/BOP.lsp" (written 06 MAR 2015 05:32:40 PM):
; /var/aw/var/LatexWiki/BOP.NRLIB/BOP.fasl written ; compilation finished in 0:00:00.104 ------------------------------------------------------------------------ BasicOperator is now explicitly exposed in frame initial BasicOperator will be automatically loaded when needed from /var/aw/var/LatexWiki/BOP.NRLIB/BOP
BOP1 abbreviates package BasicOperatorFunctions1 ------------------------------------------------------------------------ initializing NRLIB BOP1 for BasicOperatorFunctions1 compiling into NRLIB BOP1 compiling exported evaluate : (BasicOperator,A -> A) -> BasicOperator Time: 0 SEC.
compiling exported evaluate : BasicOperator -> Union(List A -> A,failed) Time: 0 SEC.
compiling exported evaluate : (BasicOperator,List A) -> Union(A,failed) Time: 0.01 SEC.
compiling exported evaluate : (BasicOperator,List A -> A) -> BasicOperator Time: 0 SEC.
compiling exported derivative : BasicOperator -> Union(List List A -> A,failed) Time: 0 SEC.
compiling exported derivative : (BasicOperator,List List A -> A) -> BasicOperator Time: 0 SEC.
compiling exported derivative : (BasicOperator,A -> A) -> BasicOperator Time: 0.01 SEC.
compiling local cdisp : (OutputForm,List OutputForm) -> OutputForm BOP1;cdisp is replaced by a Time: 0.01 SEC.
compiling local csex : (InputForm,List InputForm) -> InputForm BOP1;csex is replaced by a Time: 0 SEC.
compiling local eqconst? : (BasicOperator,BasicOperator) -> Boolean Time: 0 SEC.
****** Domain: A already in scope augmenting A: (Comparable) compiling local ltconst? : (BasicOperator,BasicOperator) -> Boolean Time: 0 SEC.
compiling local constOp : A -> BasicOperator Time: 0 SEC.
compiling exported constantOpIfCan : BasicOperator -> Union(A,failed) Time: 0 SEC.
****** Domain: A already in scope augmenting A: (ConvertibleTo (InputForm)) compiling exported constantOperator : A -> BasicOperator Time: 0.01 SEC.
compiling exported constantOperator : A -> BasicOperator Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |BasicOperatorFunctions1| REDEFINED
;;; *** |BasicOperatorFunctions1| REDEFINED Time: 0 SEC.
Warnings: [1] constOp: opconst has no value
Cumulative Statistics for Constructor BasicOperatorFunctions1 Time: 0.04 seconds
finalizing NRLIB BOP1 Processing BasicOperatorFunctions1 for Browser database: --------constructor--------- --------(name ((Symbol) %))--------- --------(properties ((AssociationList (Symbol) (None)) %))--------- --------(copy (% %))--------- --------(conjugate (% %))--------- --------(operator (% (Symbol)))--------- --------(operator (% (Symbol) (NonNegativeInteger)))--------- --------(arity ((Union (NonNegativeInteger) failed) %))--------- --------(nullary? ((Boolean) %))--------- --------(unary? ((Boolean) %))--------- --------(nary? ((Boolean) %))--------- --------(weight ((NonNegativeInteger) %))--------- --------(weight (% % (NonNegativeInteger)))--------- --------(equality (% % (Mapping (Boolean) % %)))--------- --------(comparison (% % (Mapping (Boolean) % %)))--------- --------(display ((Union (Mapping (OutputForm) (List (OutputForm))) failed) %))--------- --------(display (% % (Mapping (OutputForm) (List (OutputForm)))))--------- --------(display (% % (Mapping (OutputForm) (OutputForm))))--------- --------(input (% % (Mapping (InputForm) (List (InputForm)))))--------- --------(input ((Union (Mapping (InputForm) (List (InputForm))) failed) %))--------- --------(is? ((Boolean) % (Symbol)))--------- --------(has? ((Boolean) % (Symbol)))--------- --------(assert (% % (Symbol)))--------- --------(deleteProperty! (% % (Symbol)))--------- --------(property ((Union (None) failed) % (Symbol)))--------- --------(setProperty (% % (Symbol) (None)))--------- --------(setProperties (% % (AssociationList (Symbol) (None))))--------- --------constructor--------- --------(evaluate ((Union A failed) (BasicOperator) (List A)))--------- --------(evaluate ((BasicOperator) (BasicOperator) (Mapping A (List A))))--------- --------(evaluate ((BasicOperator) (BasicOperator) (Mapping A A)))--------- --------(evaluate ((Union (Mapping A (List A)) failed) (BasicOperator)))--------- --------(derivative ((BasicOperator) (BasicOperator) (List (Mapping A (List A)))))--------- --------(derivative ((BasicOperator) (BasicOperator) (Mapping A A)))--------- --------(derivative ((Union (List (Mapping A (List A))) failed) (BasicOperator)))--------- --------(constantOperator ((BasicOperator) A))--------- --------(constantOpIfCan ((Union A failed) (BasicOperator)))--------- --->/usr/local/lib/fricas/target/x86_64-unknown-linux/../../src/algebra/BOP1.spad-->BasicOperatorFunctions1(): Spurious comments: This package exports functions to set some commonly used properties of operators,{} including properties which contain functions. ; compiling file "/var/aw/var/LatexWiki/BOP1.NRLIB/BOP1.lsp" (written 06 MAR 2015 05:32:40 PM):
; /var/aw/var/LatexWiki/BOP1.NRLIB/BOP1.fasl written ; compilation finished in 0:00:00.055 ------------------------------------------------------------------------ BasicOperatorFunctions1 is now explicitly exposed in frame initial BasicOperatorFunctions1 will be automatically loaded when needed from /var/aw/var/LatexWiki/BOP1.NRLIB/BOP1
COMMONOP abbreviates package CommonOperators ------------------------------------------------------------------------ initializing NRLIB COMMONOP for CommonOperators compiling into NRLIB COMMONOP compiling exported operator : Symbol -> BasicOperator Time: 0.03 SEC.
compiling local dpi : List OutputForm -> OutputForm Time: 0 SEC.
compiling local dfact : OutputForm -> OutputForm Time: 0 SEC.
compiling local dquote : List OutputForm -> OutputForm Time: 0 SEC.
compiling local dgamma : List OutputForm -> OutputForm Time: 0.01 SEC.
compiling local dEllipticE2 : List OutputForm -> OutputForm Time: 0 SEC.
compiling local setDummyVar : (BasicOperator,NonNegativeInteger) -> BasicOperator Time: 0 SEC.
compiling local dexp : OutputForm -> OutputForm Time: 0 SEC.
compiling local startUp : Boolean -> Void Time: 0.07 SEC.
(time taken in buildFunctor: 0)
;;; *** |CommonOperators| REDEFINED
;;; *** |CommonOperators| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor CommonOperators Time: 0.12 seconds
finalizing NRLIB COMMONOP Processing CommonOperators for Browser database: --------constructor--------- --------(name ((Symbol) %))--------- --------(properties ((AssociationList (Symbol) (None)) %))--------- --------(copy (% %))--------- --------(conjugate (% %))--------- --------(operator (% (Symbol)))--------- --------(operator (% (Symbol) (NonNegativeInteger)))--------- --------(arity ((Union (NonNegativeInteger) failed) %))--------- --------(nullary? ((Boolean) %))--------- --------(unary? ((Boolean) %))--------- --------(nary? ((Boolean) %))--------- --------(weight ((NonNegativeInteger) %))--------- --------(weight (% % (NonNegativeInteger)))--------- --------(equality (% % (Mapping (Boolean) % %)))--------- --------(comparison (% % (Mapping (Boolean) % %)))--------- --------(display ((Union (Mapping (OutputForm) (List (OutputForm))) failed) %))--------- --------(display (% % (Mapping (OutputForm) (List (OutputForm)))))--------- --------(display (% % (Mapping (OutputForm) (OutputForm))))--------- --------(input (% % (Mapping (InputForm) (List (InputForm)))))--------- --------(input ((Union (Mapping (InputForm) (List (InputForm))) failed) %))--------- --------(is? ((Boolean) % (Symbol)))--------- --------(has? ((Boolean) % (Symbol)))--------- --------(assert (% % (Symbol)))--------- --------(deleteProperty! (% % (Symbol)))--------- --------(property ((Union (None) failed) % (Symbol)))--------- --------(setProperty (% % (Symbol) (None)))--------- --------(setProperties (% % (AssociationList (Symbol) (None))))--------- --------constructor--------- --------(evaluate ((Union A failed) (BasicOperator) (List A)))--------- --------(evaluate ((BasicOperator) (BasicOperator) (Mapping A (List A))))--------- --------(evaluate ((BasicOperator) (BasicOperator) (Mapping A A)))--------- --------(evaluate ((Union (Mapping A (List A)) failed) (BasicOperator)))--------- --------(derivative ((BasicOperator) (BasicOperator) (List (Mapping A (List A)))))--------- --------(derivative ((BasicOperator) (BasicOperator) (Mapping A A)))--------- --------(derivative ((Union (List (Mapping A (List A))) failed) (BasicOperator)))--------- --------(constantOperator ((BasicOperator) A))--------- --------(constantOpIfCan ((Union A failed) (BasicOperator)))--------- --------constructor--------- --------(operator ((BasicOperator) (Symbol)))--------- --->/usr/local/lib/fricas/target/x86_64-unknown-linux/../../src/algebra/COMMONOP.spad-->CommonOperators(): Spurious comments: This package exports functions to set some commonly used properties of operators,{} including properties which contain functions. --->/usr/local/lib/fricas/target/x86_64-unknown-linux/../../src/algebra/COMMONOP.spad-->CommonOperators(): Spurious comments: This package exports the elementary operators,{} with some semantics already attached to them. The semantics that is attached here is not dependent on the set in which the operators will be applied. ; compiling file "/var/aw/var/LatexWiki/COMMONOP.NRLIB/COMMONOP.lsp" (written 06 MAR 2015 05:32:40 PM):
; /var/aw/var/LatexWiki/COMMONOP.NRLIB/COMMONOP.fasl written ; compilation finished in 0:00:07.518 ------------------------------------------------------------------------ CommonOperators is now explicitly exposed in frame initial CommonOperators will be automatically loaded when needed from /var/aw/var/LatexWiki/COMMONOP.NRLIB/COMMONOP




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