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Diffstat (limited to 'src/algebra/openmath.spad.pamphlet')
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diff --git a/src/algebra/openmath.spad.pamphlet b/src/algebra/openmath.spad.pamphlet index 24a53ae4..e69de29b 100644 --- a/src/algebra/openmath.spad.pamphlet +++ b/src/algebra/openmath.spad.pamphlet @@ -1,331 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra openmath.spad} -\author{Mike Dewar, Vilya Harvey} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{package OMEXPR ExpressionToOpenMath} -<<package OMEXPR ExpressionToOpenMath>>= -)abbrev package OMEXPR ExpressionToOpenMath -++ Author: Mike Dewar & Vilya Harvey -++ Date Created: -++ Date Last Updated: -++ Basic Functions: -++ Related Constructors: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: \spadtype{ExpressionToOpenMath} provides support for -++ converting objects of type \spadtype{Expression} into OpenMath. -ExpressionToOpenMath(R: Join(OpenMath, Ring)): with - OMwrite : Expression R -> String - OMwrite : (Expression R, Boolean) -> String - OMwrite : (OpenMathDevice, Expression R) -> Void - OMwrite : (OpenMathDevice, Expression R, Boolean) -> Void - == add - import Expression R - SymInfo ==> Record(cd:String, name:String) - import SymInfo - import Record(key: Symbol, entry: SymInfo) - import AssociationList(Symbol, SymInfo) - import OMENC - - ---------------------------- - -- Local translation tables. - ---------------------------- - - nullaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_ - [pi, ["nums1", "pi"]] ] - - unaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_ - [exp, ["transc1", "exp"]],_ - [log, ["transc1", "ln"]],_ - [sin, ["transc1", "sin"]],_ - [cos, ["transc1", "cos"]],_ - [tan, ["transc1", "tan"]],_ - [cot, ["transc1", "cot"]],_ - [sec, ["transc1", "sec"]],_ - [csc, ["transc1", "csc"]],_ - [asin, ["transc1", "arcsin"]],_ - [acos, ["transc1", "arccos"]],_ - [atan, ["transc1", "arctan"]],_ - [acot, ["transc1", "arccot"]],_ - [asec, ["transc1", "arcsec"]],_ - [acsc, ["transc1", "arccsc"]],_ - [sinh, ["transc1", "sinh"]],_ - [cosh, ["transc1", "cosh"]],_ - [tanh, ["transc1", "tanh"]],_ - [coth, ["transc1", "coth"]],_ - [sech, ["transc1", "sech"]],_ - [csch, ["transc1", "csch"]],_ - [asinh, ["transc1", "arcsinh"]],_ - [acosh, ["transc1", "arccosh"]],_ - [atanh, ["transc1", "arctanh"]],_ - [acoth, ["transc1", "arccoth"]],_ - [asech, ["transc1", "arcsech"]],_ - [acsch, ["transc1", "arccsch"]],_ - [factorial, ["integer1", "factorial"]],_ - [abs, ["arith1", "abs"]] ] - - -- Still need the following unary functions: - -- digamma - -- Gamma - -- airyAi - -- airyBi - -- erf - -- Ei - -- Si - -- Ci - -- li - -- dilog - - -- Still need the following binary functions: - -- Gamma(a, x) - -- Beta(x,y) - -- polygamma(k,x) - -- besselJ(v,x) - -- besselY(v,x) - -- besselI(v,x) - -- besselK(v,x) - -- permutation(n, m) - -- summation(x:%, n:Symbol) : as opposed to "definite" sum - -- product(x:%, n:Symbol) : ditto - - ------------------------ - -- Forward declarations. - ------------------------ - - outputOMExpr : (OpenMathDevice, Expression R) -> Void - - ------------------------- - -- Local helper functions - ------------------------- - - outputOMArith1(dev: OpenMathDevice, sym: String, args: List Expression R): Void == - OMputApp(dev) - OMputSymbol(dev, "arith1", sym) - for arg in args repeat - OMwrite(dev, arg, false) - OMputEndApp(dev) - - outputOMLambda(dev: OpenMathDevice, ex: Expression R, var: Expression R): Void == - OMputBind(dev) - OMputSymbol(dev, "fns1", "lambda") - OMputBVar(dev) - OMwrite(dev, var, false) - OMputEndBVar(dev) - OMwrite(dev, ex, false) - OMputEndBind(dev) - - outputOMInterval(dev: OpenMathDevice, lo: Expression R, hi: Expression R): Void == - OMputApp(dev) - OMputSymbol(dev, "interval1", "interval") - OMwrite(dev, lo, false) - OMwrite(dev, hi, false) - OMputEndApp(dev) - - outputOMIntInterval(dev: OpenMathDevice, lo: Expression R, hi: Expression R): Void == - OMputApp(dev) - OMputSymbol(dev, "interval1", "integer__interval") - OMwrite(dev, lo, false) - OMwrite(dev, hi, false) - OMputEndApp(dev) - - outputOMBinomial(dev: OpenMathDevice, args: List Expression R): Void == - not #args=2 => error "Wrong number of arguments to binomial" - OMputApp(dev) - OMputSymbol(dev, "combinat1", "binomial") - for arg in args repeat - OMwrite(dev, arg, false) - OMputEndApp(dev) - - outputOMPower(dev: OpenMathDevice, args: List Expression R): Void == - not #args=2 => error "Wrong number of arguments to power" - outputOMArith1(dev, "power", args) - - outputOMDefsum(dev: OpenMathDevice, args: List Expression R): Void == - #args ~= 5 => error "Unexpected number of arguments to a defsum" - OMputApp(dev) - OMputSymbol(dev, "arith1", "sum") - outputOMIntInterval(dev, args.4, args.5) - outputOMLambda(dev, eval(args.1, args.2, args.3), args.3) - OMputEndApp(dev) - - outputOMDefprod(dev: OpenMathDevice, args: List Expression R): Void == - #args ~= 5 => error "Unexpected number of arguments to a defprod" - OMputApp(dev) - OMputSymbol(dev, "arith1", "product") - outputOMIntInterval(dev, args.4, args.5) - outputOMLambda(dev, eval(args.1, args.2, args.3), args.3) - OMputEndApp(dev) - - outputOMDefint(dev: OpenMathDevice, args: List Expression R): Void == - #args ~= 5 => error "Unexpected number of arguments to a defint" - OMputApp(dev) - OMputSymbol(dev, "calculus1", "defint") - outputOMInterval(dev, args.4, args.5) - outputOMLambda(dev, eval(args.1, args.2, args.3), args.3) - OMputEndApp(dev) - - outputOMInt(dev: OpenMathDevice, args: List Expression R): Void == - #args ~= 3 => error "Unexpected number of arguments to a defint" - OMputApp(dev) - OMputSymbol(dev, "calculus1", "int") - outputOMLambda(dev, eval(args.1, args.2, args.3), args.3) - OMputEndApp(dev) - - outputOMFunction(dev: OpenMathDevice, op: Symbol, args: List Expression R): Void == - nargs := #args - zero? nargs => - omOp: Union(SymInfo, "failed") := search(op, nullaryFunctionAList) - omOp case "failed" => - msg := concat ["No OpenMath definition for nullary function ", string op] - error msg - OMputSymbol(dev, omOp.cd, omOp.name) - one? nargs => - omOp: Union(SymInfo, "failed") := search(op, unaryFunctionAList) - omOp case "failed" => - msg := concat ["No OpenMath definition for unary function ", string op] - error msg - OMputApp(dev) - OMputSymbol(dev, omOp.cd, omOp.name) - for arg in args repeat - OMwrite(dev, arg, false) - OMputEndApp(dev) - -- Most of the binary operators cannot be handled trivialy like the - -- unary ones since they have bound variables of one kind or another. - -- The special functions should be straightforward, but we don't have - -- a CD for them yet :-) - op = %defint => outputOMDefint(dev, args) - op = integral => outputOMInt(dev, args) - op = %defsum => outputOMDefsum(dev, args) - op = %defprod => outputOMDefprod(dev, args) - op = %power => outputOMPower(dev, args) - op = binomial => outputOMBinomial(dev, args) - msg := concat ["No OpenMath definition for function ", string op] - error msg - - outputOMExpr(dev: OpenMathDevice, ex: Expression R): Void == - ground? ex => OMwrite(dev, ground ex, false) - not((v := retractIfCan(ex)@Union(Symbol,"failed")) case "failed") => - OMputVariable(dev, v) - not((w := isPlus ex) case "failed") => outputOMArith1(dev, "plus", w) - not((w := isTimes ex) case "failed") => outputOMArith1(dev, "times", w) - --not((y := isMult ex) case "failed") => - -- outputOMArith("times", [OMwrite(y.coef)$Integer, - -- OMwrite(coerce y.var)]) - -- At the time of writing we don't need both isExpt and isPower - -- here but they may be relevent when we integrate this stuff into - -- the main Expression code. Note that if we don't check that - -- the exponent is non-trivial we get thrown into an infinite recursion. - not (((x := isExpt ex) case "failed") or one? x.exponent) => - not((s := symbolIfCan(x.var)@Union(Symbol,"failed")) case "failed") => - --outputOMPower(dev, [s::Expression(R), (x.exponent)::Expression(R)]) - OMputApp(dev) - OMputSymbol(dev, "arith1", "power") - OMputVariable(dev, s) - OMputInteger(dev, x.exponent) - OMputEndApp(dev) - -- TODO: add error handling code here... - not (((z := isPower ex) case "failed") or one? z.exponent) => - outputOMPower(dev, [ z.val, z.exponent::Expression R ]) - --OMputApp(dev) - --OMputSymbol(dev, "arith1", "power") - --outputOMExpr(dev, z.val) - --OMputInteger(dev, z.exponent) - --OMputEndApp(dev) - -- Must only be one top-level Kernel by this point - k : Kernel Expression R := first kernels ex - outputOMFunction(dev, name operator k, argument k) - - - ---------- - -- Exports - ---------- - - OMwrite(ex: Expression R): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - outputOMExpr(dev, ex) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(ex: Expression R, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - outputOMExpr(dev, ex) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, ex: Expression R): Void == - OMputObject(dev) - outputOMExpr(dev, ex) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, ex: Expression R, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - outputOMExpr(dev, ex) - if wholeObj then - OMputEndObject(dev) - -@ -\section{License} -<<license>>= ---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. -@ -<<*>>= -<<license>> - -<<package OMEXPR ExpressionToOpenMath>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |