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SandBoxOpenAxiom

last edited 14 years ago by Bill Page

Edit detail for SandBoxOpenAxiom revision 24 of 25

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Editor: Bill Page Time: 2010/01/29 08:43:45 GMT-8
Note: missing \begin{axiom} ... \end{axiom}

added:
\begin{axiom}

changed:
-
\end{axiom}

What version?

axiom

)version

Value = "Tuesday October 13, 2009 at 18:38:59 "

New domain Domain:

axiom

)show Domain

 Domain  is a domain constructor
 Abbreviation for Domain is DOMAIN 
 This constructor is exposed in this frame.
 Issue )edit /usr/local/lib/open-axiom/x86_64-unknown-linux/1.4.0-2009-10-13/src/algebra/DOMAIN.spad to see algebra source code for DOMAIN 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                before? : (%,%) -> Boolean
 coerce : % -> OutputForm              hash : % -> SingleInteger
 latex : % -> String                   showSummary : % -> Void
 ?~=? : (%,%) -> Boolean              
 constructor : % -> DomainConstructor
 reflect : ConstructorCall DomainConstructor -> %
 reify : % -> ConstructorCall DomainConstructor

For example:

axiom

LD:=[Integer,Float,String]

$\label{eq1}\left[ \hbox{\axiomType{Integer}\ } , \: \hbox{\axiomType{Float}\ } , \: \hbox{\axiomType{String}\ } \right]$

(1)

Type: List Domain

New domain Syntax:

axiom

)show Syntax

 Syntax  is a domain constructor
 Abbreviation for Syntax is SYNTAX 
 This constructor is exposed in this frame.
 Issue )edit /usr/local/lib/open-axiom/x86_64-unknown-linux/1.4.0-2009-10-13/src/algebra/SYNTAX.spad to see algebra source code for SYNTAX 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                autoCoerce : % -> String
 autoCoerce : % -> Identifier          autoCoerce : % -> DoubleFloat
 autoCoerce : % -> Integer             before? : (%,%) -> Boolean
 buildSyntax : (%,List %) -> %         coerce : % -> String
 coerce : % -> Identifier              coerce : % -> DoubleFloat
 coerce : % -> Integer                 coerce : % -> InputForm
 coerce : String -> %                  coerce : Identifier -> %
 coerce : DoubleFloat -> %             coerce : Integer -> %
 coerce : % -> OutputForm              compound? : % -> Boolean
 convert : SExpression -> %            convert : % -> SExpression
 getOperands : % -> List %             hash : % -> SingleInteger
 latex : % -> String                   nil? : % -> Boolean
 retract : % -> String                 retract : % -> Identifier
 retract : % -> DoubleFloat            retract : % -> Integer
 ?~=? : (%,%) -> Boolean              
 buildSyntax : (Identifier,List %) -> %
 ?case? : (%,[|String|]) -> Boolean
 ?case? : (%,[|Identifier|]) -> Boolean
 ?case? : (%,[|DoubleFloat|]) -> Boolean
 ?case? : (%,[|Integer|]) -> Boolean
 getOperator : % -> Union(Integer,DoubleFloat,Identifier,String,%)
 retractIfCan : % -> Union(String,"failed")
 retractIfCan : % -> Union(Identifier,"failed")
 retractIfCan : % -> Union(DoubleFloat,"failed")
 retractIfCan : % -> Union(Integer,"failed")

axiom

reify(String)

$\label{eq2}\hbox{\axiomType{String}\ }$

(2)

Type: ConstructorCall? DomainConstructor?

syntax.spad.pamphlet --Bill Page, Wed, 30 Jan 2008 09:27:00 -0800 reply

[SandBoxSyntax]? describes some extensions to OpenAxiom?

move coercion to library? --page, Wed, 07 May 2008 07:29:30 -0700 reply

axiom

a := 'x :: OutputForm

$\label{eq3}x$

(3)

Type: OutputForm?

axiom

b := 'y :: OutputForm

$\label{eq4}y$

(4)

Type: OutputForm?

axiom

a and b

$\label{eq5}and \left({x , \: y}\right)$

(5)

Type: OutputForm?

... --artjcoder, Tue, 13 May 2008 02:23:40 -0700 reply

axiom

phi := operator phi

$\label{eq6}\phi$

(6)

Type: BasicOperator?

axiom

deq := 6*D(phi(x), x) + 10*phi(x) + 150*cos(phi(x)) = 0

$\label{eq7}{{6 \ {{\phi_{\ }^{,}}\left({x}\right)}}+{{150}\ {\cos \left({\phi \left({x}\right)}\right)}}+{{10}\ {\phi \left({x}\right)}}}= 0$

(7)

Type: Equation Expression Integer

axiom

solve(deq, phi, x)

$\label{eq8}{\int^{ \displaystyle {\phi \left({x}\right)}}{{6 \over{{{15}\ {\cos \left({\%H}\right)}}+ \%H}}\ {d \%H}}}+{{10}\ x}$

(8)

Type: Union(Expression Integer,...)

OpenAxiom? now displays InputForms? --Bill Page, Thu, 16 Oct 2008 18:54:56 -0700 reply

in infix (or m-expression like) notation like this:

axiom

phi := operator 'phi

$\label{eq9}\phi$

(9)

Type: BasicOperator?

axiom

(9 * D(phi(x), x, 2) + 6*D(phi(x), x) + 10 + 150*cos(phi(x)))::InputForm

$\label{eq10}9 <em> D (D (phi (x) , x : : \hbox{\axiomType{Symbol}\ }) , x : : \hbox{\axiomType{Symbol}\ }) + 6 </em> D (phi (x) , x : : \hbox{\axiomType{Symbol}\ }) + 150 <em> cos (phi (x)) + 10$

(10)

Type: InputForm?

OpenAxiom? 1.3.0 and higher now supports literal numbers expressed in a radix other than 10 (both in the interpreter and in library).

For decimal numbers, the syntax is as usual. For base other than 10, you have to specify the radix first (as a decimal number) followed by the letter r, then followed by digits expressing the number.

axiom

16rdeadbeef

$\label{eq11}3735928559$

(11)

Type: PositiveInteger?

axiom

16rcafebabe

$\label{eq12}3405691582$

(12)

Type: PositiveInteger?

axiom

2r111000101001

$\label{eq13}3625$

(13)

Type: PositiveInteger?

... --memyself, Fri, 29 Jan 2010 05:16:24 -0800 reply

axiom

y:=operator 'y

$\label{eq14}y$

(14)

Type: BasicOperator?

axiom

deq := x**3 * D(y x, x, 3) + x**2 * D(y x, x, 2) - 2 * x * D(y x, x) + 2 * y x = 2 * x**4

$\label{eq15}{{{x^3}\ {{y_{\ }^{, , ,}}\left({x}\right)}}+{{x^2}\ {{y_{\ }^{, ,}}\left({x}\right)}}-{2 \ x \ {{y_{\ }^{,}}\left({x}\right)}}+{2 \ {y \left({x}\right)}}}={2 \ {x^4}}$

(15)

Type: Equation Expression Integer

axiom

solve(deq,y,z)

$\label{eq16}\mbox{\tt "failed"}$

(16)

Type: Union("failed",...)