MathAction changed pages
http://fricaswiki.math.uni.wroc.pl
MathAction changed pagesenMon, 10 Feb 2020 18:11:12 +0000[FriCAS]
http://fricaswiki.math.uni.wroc.pl/FriCAS
http://fricaswiki.math.uni.wroc.pl/FriCAS
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"FriCAS Book":http://fricas.sourceforge.net/doc/book.pdf
or read start reading FriCASTutorial.
Jenks and Sutor "Book":http://fricas.github.io/book.pdf
or read start reading FriCASTutorial. You can get list
of inplemented constructors and functions using HyperDoc or
online at "API site":http://fricas.github.io/api/genindex.html
Mon, 17 Feb 2020 16:47:33 +0000[FriCAS Library Examples]
http://fricaswiki.math.uni.wroc.pl/FriCASLibraryExamples
http://fricaswiki.math.uni.wroc.pl/FriCASLibraryExamples
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Here we collect some exaples of using FriCAS library
Here we collect some examples of using FriCAS library
Sun, 16 Feb 2020 17:55:37 +0000[ExampleSolve]
http://fricaswiki.math.uni.wroc.pl/ExampleSolve
http://fricaswiki.math.uni.wroc.pl/ExampleSolve
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This is motivated by discussion in Sage mailing list. We are given sum of ellipsis and
a strip symmetric with respect to one of the axis of the ellipsis. We want to
find circle with center on the line x = D which is tangent both to ellipsis and the strip.
More precisely, we want to find common point (x, r) and radius R of the circle.
We get equations (for convenience written as polynomials):
\begin{axiom}
)set output algebra on
)set output tex off
eq1 := (x/r1)^2 + (y/r2)^2  1
eq2 := (xD)^2+(yd/2R)^2  R^2
eq3 := (xD)/(yd/2R)  (x/y)*(r2/r1)^2
\end{axiom}
The first is equation of ellipsis, the second of the circle,
third is tangency condition.
This system can be solved, but it would take long time, the answer is large and would be hard to read. So first
we replace r, r2, D, d by sensible concrete values:
\begin{axiom}
eq1e := eval(eq1, [r1 = 11/10, r2 = 7/10, d = 15/100, D = 2])
eq2e := eval(eq2, [r1 = 11/10, r2 = 7/10, d = 15/100, D = 2])
eq3e := eval(eq3, [r1 = 11/10, r2 = 7/10, d = 15/100, D = 2])
\end{axiom}
Now we can solve
\begin{axiom}
rese := solve([eq1e, eq2e, eq3e], [x, y, R])
\end{axiom}
Not small, but we see that x and y are expressed in terms of R and
for R we get equation of degree 6. Let us see numeric solutions
for R:
\begin{axiom}
solve(rese(1)(3), 1.0e15)
\end{axiom}
So there are two real solutions, positive one solve our problem,
negative represents circle such that has interior (a disc) has intersection
with interior of the strip. This looks unnatural, but is correct
solution of the equations we gave. To exclude it we would have
to add an inequality, say y > 0.
Mon, 10 Feb 2020 18:11:11 +0000[LanguageDifferences]
http://fricaswiki.math.uni.wroc.pl/LanguageDifferences
http://fricaswiki.math.uni.wroc.pl/LanguageDifferences
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 is the same as
is the same as::
Wed, 04 Dec 2019 10:33:06 +0000[Units and Dimensions]
http://fricaswiki.math.uni.wroc.pl/UnitsAndDimensions
http://fricaswiki.math.uni.wroc.pl/UnitsAndDimensions
??changed:
Units and Dimensions converter : https://unitconverter.net/
Mon, 04 Nov 2019 15:29:55 +0000[series]
http://fricaswiki.math.uni.wroc.pl/Series
http://fricaswiki.math.uni.wroc.pl/Series
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Carl McTague asked axiom to evaluate
Currently FriCAS can not evaluate
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while he was hoping for '%pi^2/6', i.e. $\frac{\pi^2}{6}$.

Any ideas?

From wurmli Sat Sep 11 00:47:12 0500 2004
From: wurmli
Date: Sat, 11 Sep 2004 00:47:12 0500
Subject: Don't know either
MessageID: <200409110047120500@page.axiomdeveloper.org>


I have no ideas how to move axiom to spit out the answer, but considering it should
be $\zeta(2)$ I have another question:


does the zeta function exist in axiom?

It is included in FriCAS
where correct result is'%pi^2/6', i.e. $\frac{\pi^2}{6}$.
The result is $\zeta(2)$, which in FriCAS can be written as:
??changed:
It looks like in 1997, it had not been
implemented.
See
See also text from 1997:
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onto which
"AxiomDocumentationAndCommunity":AxiomDocumentationAndCommunity#WesterCritique
refers.
Sun, 11 Aug 2019 17:59:02 +0000[FriCASContributions]
http://fricaswiki.math.uni.wroc.pl/FriCASContributions
http://fricaswiki.math.uni.wroc.pl/FriCASContributions
++added:
[SeriesSolve] contributed by Martin Rubey
Fri, 02 Aug 2019 14:26:24 +0000[SeriesSolve]
http://fricaswiki.math.uni.wroc.pl/SeriesSolve
http://fricaswiki.math.uni.wroc.pl/SeriesSolve
??changed:
SeriesSolve implements a workaround to the broken package delivered with Axiom. It handles quite arbitrary functional equations, but uses a questionable algorithm. It certainly should be replaced by something better.

[ssolve.spad.pamphlet] is the pamphlet and [ssolve.spad] the source.
This package is included in FriCAS. Compared to previous series solver
it handles quite arbitrary functional equations, but uses a questionable algorithm.
It certainly should be replaced by something better.
Fri, 02 Aug 2019 14:24:04 +0000[Source Repository]
http://fricaswiki.math.uni.wroc.pl/SourceRepository
http://fricaswiki.math.uni.wroc.pl/SourceRepository
++added:
 [FriCAS Sources]
removed:
 [FriCAS Sources]

Fri, 02 Aug 2019 14:16:49 +0000[FriCAS Problems]
http://fricaswiki.math.uni.wroc.pl/FriCASProblems
http://fricaswiki.math.uni.wroc.pl/FriCASProblems
??changed:
 Expressions like 'sin(x)' appear unevaluated until a value is
 substituted for x but expressions like 'max(x,y)' return 'y'!
 Why is that? There is difference between functions and expressions:
 programming linguage functions produce values, expressions are values
There is difference between functions and expressions:
programming language functions produce values, expressions are values
??changed:
 value producing function. 'max' used order on expression to pick
function. 'max' used order on expression to pick
Fri, 02 Aug 2019 14:06:33 +0000