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SandBoxReduce

last edited 1 year ago by Bill Page

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Editor: Bill Page Time: 2009/02/13 07:26:26 GMT-8
Note: compare axiom result

added:

From BillPage Fri Feb 13 07:26:21 -0800 2009
From: Bill Page
Date: Fri, 13 Feb 2009 07:26:21 -0800
Subject: compare axiom result
Message-ID: <20090213072621-0800@axiom-wiki.newsynthesis.org>

\begin{axiom}
normalize( atan(((1+x)*sin(c+d)-sin(c-d))/((1+x)*cos(c+d)-cos(c-d))) )
\end{axiom}

Try Reduce calculations here. For example:

  \begin{reduce}
  solve({z=x*a+2},{z,x});
  int(sqrt(1-sin(x)*cos(x)),x);
  \end{reduce}

solve({z=x*a+2},{z,x});

reduce

$\displaylines{\qdd \{\{z= \[arbcomplex \(1$

int(sqrt(1-sin(x)*cos(x)),x);

reduce

$\displaylines{\qdd \int {\sqrt{ -\cos \(x$

example from my daughter's college calc --pbwagner, Mon, 10 Sep 2007 12:58:25 -0500 reply

int(log(log(x)),x);

reduce

$\displaylines{\qdd -ei \(\ln \(x$

axiom

integrate(log(log(x)),x)

$\label{eq1}{x \ {\log \left({\log \left({x}\right)}\right)}}-{li \left({x}\right)}$

(1)

Type: Union(Expression(Integer),...)

... --crashcut, Thu, 31 Jan 2008 07:57:39 -0800 reply

solve({y=-1/l*(1-(l*x+(-3*l^2-l+8)^(1/2)/4-0.5*l)^2)^(1/2)      -(-3*l^2-l+8)^(1/2)/(4*l)+2*l}, {y});

reduce

$\displaylines{\qdd \{y= \[\(- \( -8\cdot \sqrt{ -3\cdot l^{2} -l +8}\cdot l\cdot x +4\cdot \sqrt{ -3\cdot l^{2} -l +8}\cdot l -16\cdot l^{2}\cdot x^{2}\nl +16\cdot l^{2}\cdot x -l^{2} +l +8$

how to reduce this to c + atan(tan(d)*(2/x+1)) ?? --haceaton, Fri, 13 Feb 2009 05:47:13 -0800 reply

trigsimp(atan(((1+x)*sin(c+d)-sin(c-d))/((1+x)*cos(c+d)-cos(c-d))),tan);

reduce

$\displaylines{\qdd -\atan \(\frac{\tan \(c$

compare axiom result --Bill Page, Fri, 13 Feb 2009 07:26:21 -0800 reply

axiom

normalize( atan(((1+x)*sin(c+d)-sin(c-d))/((1+x)*cos(c+d)-cos(c-d))) )

$\label{eq2}\begin{array}{@{}l} \displaystyle - \ \ \displaystyle {\arctan{{\left({{{2 \ {\tan \left({{d - c}\over 2}\right)}\ {{\tan \left({{d + c}\over 2}\right)}^2}}+{{\left({{\left({2 \ x}+ 2 \right)}\ {{\tan \left({{d - c}\over 2}\right)}^2}}+{2 \ x}+ 2 \right)}\ {\tan \left({{d + c}\over 2}\right)}}+{2 \ {\tan \left({{d - c}\over 2}\right)}}}\over{{{\left({x \ {{\tan \left({{d - c}\over 2}\right)}^2}}+ x + 2 \right)}\ {{\tan \left({{d + c}\over 2}\right)}^2}}+{{\left(- x - 2 \right)}\ {{\tan \left({{d - c}\over 2}\right)}^2}}- x}}\right)}}}$

(2)

Type: Expression(Integer)