MathAction changed pages

[MathAction Problems] reverted by Bill Page

Tue, 09 Mar 2010 13:03:10 -0800

--removed: -[[http://www.research-service.com/custom-research-paper.html research papers]] -

[#305 compBound without a well-understood valuation] fixed in FriCAS

Thu, 25 Feb 2010 06:57:30 -0800

++added: From BillPage Thu Feb 25 06:57:30 -0800 2010 From: Bill Page Date: Thu, 25 Feb 2010 06:57:30 -0800 Subject: fixed in FriCAS Message-ID: <20100225065730-0800@axiom-wiki.newsynthesis.org> Status: open => fixed somewhere The error mentioned in [SandBox Lorentz Transformations] no longer occurs in FriCAS built from source or or after "Sunday November 1, 2009 at 20:31:03 "

[SandboxPermutations] Original by Martin Baker

Wed, 24 Feb 2010 02:50:51 -0800

??changed: - \begin{axiom} PI ==> PositiveInteger LPS ==> List Permutation SetCategory PS ==> Permutation SetCategory LPSET ==> List Permutation Set Integer PSET ==> Permutation Set Integer lookup(lps2:LPS,i:PI): PS == lps2.i lookup(lps2:LPSET,i:PI): PSET == lps2.i lookup(lps2:LPS,i:PI): PS == qelt(lps2,i) lookup(lps2:LPSET,i:PI): PSET == qelt(lps2,i) leng(lps2:LPS):NNI == # lps2 leng(lps2:LPSET):NNI == # lps2 \end{axiom}

[SandBoxBen2] add \begin{axiom} ...

Mon, 22 Feb 2010 18:25:58 -0800

++added: \begin{axiom} ++added: \end{axiom}

[SandBox_pleblond]

Sun, 14 Feb 2010 13:35:22 -0800

??changed: -solve(p=log(n),n) solve(p=n*log(n),n)

[AxiomCommunity] Re: MMA is Theory System

Wed, 03 Feb 2010 17:08:44 -0800

++added: From BillPage Wed Feb 3 17:08:44 -0800 2010 From: Bill Page Date: Wed, 03 Feb 2010 17:08:44 -0800 Subject: Re: MMA is Theory System Message-ID: <20100203170844-0800@axiom-wiki.newsynthesis.org> Thanks for your comments. Since this is a wiki and editable by everyone, please feel free to make such corrections regarding Mathematica or other computer algebra systems right here.

[SandBoxF3lix] looks funny in LaTeX but is ok

Wed, 03 Feb 2010 07:53:39 -0800

++added: From BillPage Wed Feb 3 07:53:37 -0800 2010 From: Bill Page Date: Wed, 03 Feb 2010 07:53:37 -0800 Subject: looks funny in LaTeX but is ok Message-ID: <20100203075337-0800@axiom-wiki.newsynthesis.org> \begin{axiom} )set output algebra on )set output tex off \end{axiom} \begin{axiom} simplify (1-e^x)^2 - (e^(2*x)- 2*e^x + 1) unparse(%::InputForm) \end{axiom} \begin{axiom} )set output algebra off )set output tex on \end{axiom}

[BeBold] reverted by Bill Page

Wed, 13 Jan 2010 08:13:17 -0800

--removed: - -This topic is all about "essay papers":http://www.bestessays.com.au. In this topic you can see some of tips and guidelines on how to be an effective writer in research paper. If you are interested in this topic just click the link for more details and information or reply to this message.

[FormalFraction] spad version

Tue, 08 Dec 2009 17:40:47 -0800

++added: **On Sun, 01 Apr 2007 22:20:55 -0700 Tim Daly wrote:** I've attached the ffrac.spad domain. It handles "formal fractions" which do not evaluate the numerator or the denominator. Thus the formal fraction is just a data structure except that there are natural coercions to the algebra and back where they make sense. This is related to the discussion of symbolic manipulation versus algebraic manipulation. In particular, there are two books by Joel Cohen called "Computer Algebra and Symbolic Computation". I've had a discussion with Joel about his work (which he has agreed to allow Axiom to use at will). He defines MPL, a mathematical programming language, that basically does expression-tree manipulations. I'd suggested that we could create a "Cohen Algebra" category and domain set that would follow his MPL style quite closely. The main thing would be to choose a common representatin (Record or List) for all elements of the domain so they compose properly. The big difference in an axiom implementation would be to have coercions (or explicit import/export) from the Cohen domains to algebraic domains and back where they make sense. This would satisfy the apparent end-user need to manipulate the expression trees. This fits in layer 10: \begin{spad} )abbrev domain FFRAC FormalFraction +++ Author: M.G. Richardson, Timothy Daly (spad rewrite) +++ Date Created: 1996 Jan. 23 +++ Date Last Updated: 30 March 2007 +++ Basic Functions: +++ Related Constructors: Fraction +++ Also See: +++ AMS Classifications: +++ Keywords: +++ References: +++ Description: +++ This type represents formal fractions - that is, pairs displayed as +++ fractions with no simplification. +++ +++ If the elements of the pair have a type X which is an integral +++ domain, a FFRAC X can be coerced to a FRAC X, provided that this +++ is a valid type. A FRAC X can always be coerced to a FFRAC X. +++ If the type of the elements is a Field, a FFRAC X can be coerced +++ to X. +++ +++ Formal fractions are used to return results from numerical methods +++ which determine numerator and denominator separately, to enable +++ users to inspect these components and recognise, for example, +++ ratios of very small numbers as potentially indeterminate. FormalFraction(X : SetCategory) : SetCategory with _/: (X,X) -> % ++ x / y is the formal fraction of the input arguments numer : % -> X ++ numer(x) is the numerator of the formal fraction denom : % -> X ++ denom(x) is the denominator of the formal fraction if X has IntegralDomain then coerce : % -> Fraction(X) ++ coerce(x) from here to Fraction(there) coerce : Fraction(X) -> % ++ coerce(x) from Fraction(there) to here if X has Field then coerce : % -> X ++ coerce from here to Field(there) == add import Record(num : X, den : X) Rep := Record(num : X, den : X) -- representation -- (a::Symbol / b::Symbol)$FFRAC(Symbol) -- c:Symbol:=d -- e:Symbol:=f -- (c/e)$FFRAC(Symbol) (n:X / d:X):% == [n,d] -- g:=(c/e)$FFRAC(Symobl) -- h:=(c/e)$FFRAC(Symbol) -- (g=h)::Boolean -- i:=(a::Symbol / b::Symbol)$FFRAC(Symbol) -- j:=(a::Symbol / b::Symbol)$FFRAC(Symbol) -- (i=j)::Boolean _=(x:%, y:%):Boolean == (x.num = y.num) and (x.den = y.den) -- numer g -- numer i numer(r:%):X == r.num --denom g --denom i denom(r:%):X == r.den coerce(r:%):OutputForm == (r.num :: OutputForm) / (r.den :: OutputForm) -- COMPLEX(INT) has FIELD -- COMPLEX(INT) has IntegralDomain -- p:COMPLEX(INT):=2 -- p::FRAC(COMPLEX(INT))::FFRAC(COMPLEX(INT)) if X has IntegralDomain then coerce(r : %) : Fraction(X) == (r.num / r.den) @ Fraction(X) coerce(x : Fraction(X)) : % == x pretend % -- FRAC(POLY(INT)) has FIELD -- m:=(x^2)@FRAC(POLY(INT)) -- m::FFRAC(POLY(INT)) if X has Field then -- m:=(2/3)$FFRAC(INT) -- m::COMPLEX(FRAC(INT)) coerce(r : %) : X == (r.num / r.den) @ X \end{spad}

[#447 integrals of abs and sqrt]

Sun, 06 Dec 2009 20:03:09 -0800

??changed: - Elementary integrals of abs(x) fail. For instance: integrate(abs(x),x=0..1,"noPole") (7) "failed" And in the sqrt(x^2) equivalent, they may be wrong. E.g.: integrate(sqrt(x^2),x=-1..1,"noPole") (13) 0 Some more examples here: http://axiom-wiki.newsynthesis.org/SandBoxAxiom