RadicalPage

Some Open Problems In Radical Theory

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* [[How this page is organized]]
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Please click on a topic on the left to go to the problems.
to:
Please click on a topic on the left to go to the problems.

* [[How this page is organized]]
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The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland.
to:
The original ideas were collected during the Problem Sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland.
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In this site, you will find some open problems in the Radical Theory. There are links to comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
to:
In this site, you will find some open problems in the Radical Theory. There are links to comments and works related to the problems. History of the problems may be given, or linked to.

The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland.

We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
Changed line 3 from:
In this site, you will find some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
to:
In this site, you will find some open problems in the Radical Theory. There are links to comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
Changed line 3 from:
In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
to:
In this site, you will find some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
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Welcome to <b>RadicalPage!</b>
to:
Welcome to the <b>RadicalPage!</b>
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In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the Workshop on Radicals of Rings and Related Topics, held from August 2 to August 7, 2009, in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
to:
In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the [[http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html | Workshop on Radicals of Rings and Related Topics]], held from August 2 to August 8, 2009, at the [[http://www.impan.gov.pl/EN/ | Stefan Banach International Center]] in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
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In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the Workshop on Radicals of Rings and Related Topics, held from August 2 to August 7, 2009, in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
to:
In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the Workshop on Radicals of Rings and Related Topics, held from August 2 to August 7, 2009, in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.

Please click on a topic on the left to go to the problems
.
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Welcome to <b>RadicalWiki!</b>

This wiki uses PmWiki. More information about PmWiki is available from http://www.pmwiki.org .

The [[PmWiki/basic editing]] page describes how to create pages
in PmWiki. You can practice editing in
the [[wiki sandbox]].

Click on a topic on the left
to go to the topic.

<b>When edit, you can type in TeX formula:</b>
* [=$TeX_formula$=] for inline equations, like [=$a+b$=] or [=\(a+b\)=] in TeX
,
* [=$$TeX_formula$$=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in TeX,
* [=\%label, TeX_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on
the page as an anchor to the equation.

For example
, [=$A_B$=] produces $A_B$, [=$$A_B+C$$=] produces
$$A_B+C,$$
and [=\%eq1, A_B+C.\%=] produces
\%eq1, A_B+C.\%
Now [=EQ(eq1)=] can be used to refer to EQ(eq1)
.
to:
Welcome to <b>RadicalPage!</b>

In this site, we list some open problems in the Radical Theory. There are links to many comments and works related to the problems. History of the problems may be given, or linked to. The original ideas were collected during the problem sections in the Workshop on Radicals of Rings and Related Topics, held from August 2 to August 7, 2009, in Warsaw, Poland. We hope that this will give the new comers to the field some specific goals to work on, as well as remind those already here in the field what we have been looking for.
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Click on a topic in the side bar on the left to go to the topic.
to:
Click on a topic on the left to go to the topic.
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<b>You can type in TeX formula:</b>
to:
<b>When edit, you can type in TeX formula:</b>
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Welcome to <b>MathWiki!</b>
to:
Welcome to <b>RadicalWiki!</b>
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Click on a topic in the side bar on the left to go to the topic.
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Welcome to <b>MathWiki!</b>
to:
Welcome to <b>MathWiki!</b>

This wiki uses PmWiki. More information about PmWiki is available from http://www.pmwiki.org .
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More information about PmWiki is available from http://www.pmwiki.org .
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* [=$latex_formula$=] for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex,
* [=$$latex_formula$$=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex,
* [=\%label, latex_formula\%=], for labeled displayed equations,
to:
* [=$TeX_formula$=] for inline equations, like [=$a+b$=] or [=\(a+b\)=] in TeX,
* [=$$TeX_formula$$=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in TeX,
* [=\%label, TeX_formula\%=], for labeled displayed equations,
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Welcome to MathWiki!
to:
Welcome to <b>MathWiki!</b>
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<b>LaTeX formula usages:</b>
to:
<b>You can type in TeX formula:</b>
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LaTeX formula usages:
to:
<b>LaTeX formula usages:</b>
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Welcome to PmWiki!

A local copy of PmWiki's
documentation has been installed along with the software,
and is available via the [[PmWiki/documentation index]].

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].
to:
Welcome to MathWiki!
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Latex
formula usages:
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LaTeX formula usages:
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test
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test
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and [=\%eq1, A_B.\%=] produces
\%eq1, A_B.\%
to:
and [=\%eq1, A_B+C.\%=] produces
\%eq1, A_B+C.\%
Changed line 21 from:
For example, [=$A_B$=] produces $A_B$, [=$$A_B$$=] produces
to:
For example, [=$A_B$=] produces $A_B$, [=$$A_B+C$$=] produces
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For example, [=$A_B+C$=] produces $A_B+C$, [=$$A_B$$=] produces
$$A_B,$$
to:
For example, [=$A_B$=] produces $A_B$, [=$$A_B$$=] produces
$$A_B+C,$$
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For example, [=$A_B+C$=] produces $A_B+C$, [=\[A_B\]=] produces
\[A_B,\]
to:
For example, [=$A_B+C$=] produces $A_B+C$, [=$$A_B$$=] produces
$$A_B,$$
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中文也可。
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* [=\[latex_formula\]=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex,
to:
* [=$$latex_formula$$=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex,
Changed lines 21-22 from:
For example, [=\(A_B+C\)=] produces $A_B+C$, [=\[A_B\]=] produces
$$A_B,$$
to:
For example, [=$A_B+C$=] produces $A_B+C$, [=\[A_B\]=] produces
\[A_B,\]
Changed lines 16-17 from:
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
*
[=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
to:
* [=$latex_formula$=] for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex,
*
[=\[latex_formula\]=] for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex,
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* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
to:
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation.
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&#20013;&#25991;&#20063;&#21487;&#12290;
to:
中文也可。
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&#20013;&#25991;&#20063;&#21487;&#12290;
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\%eq1, A_B.\%
to:
Deleted lines 20-57:
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
Changed lines 22-24 from:
$$A_B,$$ and [=\%eq1, A_B.\%=] produces
to:
$$A_B,$$
and [=\%eq1, A_B.\%=] produces
\%eq1, A_B.\%
Deleted line 25:
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to:
\%eq1, A_B.\%
Added lines 22-59:
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
* [=\%label, latex_formula\%=], for labeled displayed equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation
Deleted line 61:
\%eq1, A_B.\%
Changed lines 16-17 from:
* [=\( latex_formula \)=], for inline equations, like $ a+b $ or [=\( a+b \)=] in latex
* [=\[ latex_formula \]=], for displayed equations, like $$ a+b $$ or [=\[ a+b \]=] in latex
to:
* [=$latex_formula$=] or [=\(latex_formula\)=], for inline equations, like [=$a+b$=] or [=\(a+b\)=] in latex
* [=$$latex_formula$$=] or [=\[latex_formula\]=], for displayed equations, like [=$$a+b$$=] or [=\[a+b\]=] in latex
Changed lines 21-22 from:
For example, [=\(A_B\)=] produces \(A_B\), [=\[A_B\]=] produces
\[A_B,\] and [=\%eq1, A_B.\%=] produces
to:
For example, [=\(A_B+C\)=] produces $A_B+C$, [=\[A_B\]=] produces
$$A_B,$$ and [=\%eq1, A_B.\%=] produces
Changed lines 21-22 from:
For example,
[=\[A_B\]=] produces \[A_B,\] and [=\%eq1, A_B.\%=] produces
to:
For example, [=\(A_B\)=] produces \(A_B\), [=\[A_B\]=] produces
\[A_B,\] and [=\%eq1, A_B.\%=] produces
October 10, 2008, at 10:43 PM EST by 125.229.167.180 -
Changed line 18 from:
* [=\%label, latex_formula%\=], for labeled displayed equations,
to:
* [=\%label, latex_formula\%=], for labeled displayed equations,
October 10, 2008, at 10:43 PM EST by 125.229.167.180 -
Changed lines 16-18 from:
* [=\( latex formula \)=], for inline equations, like $ a+b $ or [=\( a+b \)=] in latex
* [=\[ latex formula \]=], for displayed equations, like $$ a+b $$ or [=\[ a+b \]=] in latex
* [=\%label, latex formula%\=], for labeled displayed equations,
to:
* [=\( latex_formula \)=], for inline equations, like $ a+b $ or [=\( a+b \)=] in latex
* [=\[ latex_formula \]=], for displayed equations, like $$ a+b $$ or [=\[ a+b \]=] in latex
* [=\%label, latex_formula%\=], for labeled displayed equations,
October 10, 2008, at 10:41 PM EST by 125.229.167.180 -
Changed line 22 from:
[=\[A_B\]=] produces \[A_B,\] and [={%eq1, A_B.%}=] produces
to:
[=\[A_B\]=] produces \[A_B,\] and [=\%eq1, A_B.\%=] produces
October 10, 2008, at 10:41 PM EST by 125.229.167.180 -
Changed lines 16-17 from:
* [={$ latex formula $}=], for inline equations, like \( a+b \) in latex
*
[={%label, latex formula%}=], for \begin{math} like equations,
to:
* [=\( latex formula \)=], for inline equations, like $ a+b $ or [=\( a+b \)=] in latex
* [=
\[ latex formula \]=], for displayed equations, like $$ a+b $$ or [=\[ a+b \]=] in latex
* [=\%label, latex formula%\=], for labeled displayed
equations,
Changed lines 22-23 from:
[={$A_B$}=] produces {$A_B$}, and [={%eq1, A_B.%}=] produces
{%eq1, A_B.%}
to:
[=\[A_B\]=] produces \[A_B,\] and [={%eq1, A_B.%}=] produces
\%eq1, A_B.\%
October 10, 2008, at 09:00 PM EST by 125.229.167.180 -
Changed line 21 from:
[={$A_B$}=] produces {$A_B$}, and [={%eq1, A_B%}=] produces
to:
[={$A_B$}=] produces {$A_B$}, and [={%eq1, A_B.%}=] produces
October 10, 2008, at 06:02 PM EST by 125.229.167.180 -
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Latex formula use:
to:
Latex formula usages:
October 10, 2008, at 05:55 PM EST by 125.229.167.180 -
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{%eq1, A_B%}.
to:
{%eq1, A_B.%}
October 10, 2008, at 05:54 PM EST by 125.229.167.180 -
Changed lines 14-24 from:
{$A_B$}
to:
Latex formula use:
* [=
{$ latex formula $}=], for inline equations, like \( a+b \) in latex
* [={%label, latex formula%}=], for \begin{math} like equations,
* [=EQ(label)=] can be used anywhere on the page as an anchor to the equation

For example,
[={$A_B$}=] produces {$A_B$}, and [={%eq1, A_B%}=] produces
{%eq1, A_B%}.
Now [=EQ(eq1)=] can be used to refer to EQ(eq1).
October 10, 2008, at 05:46 PM EST by 125.229.167.180 -
Added lines 13-14:

{$A_B$}

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