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Making a thicker cdot for dot product (that is thinner than bullet)

42

11

I'm trying to replicate the dot that my professor uses in his notes for the dot product between vectors but I am having a hard time doing so. This is what it looks like:

I have tried a couple of things. cdot is too thin

and bullet is too thick

and using Large with cdot gives an error. Moreover, after digging through the list of symbols I cannot find a nice medium between cdot and bullet.

How can I get a dot closest to the first picture?

math-mode symbols

share|improve this question

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I use bullet for dot products.
  
  – k-l
  Mar 22 '17 at 0:13
  

  
  
  
  

add a comment | 

42

11

I'm trying to replicate the dot that my professor uses in his notes for the dot product between vectors but I am having a hard time doing so. This is what it looks like:

I have tried a couple of things. cdot is too thin

and bullet is too thick

and using Large with cdot gives an error. Moreover, after digging through the list of symbols I cannot find a nice medium between cdot and bullet.

How can I get a dot closest to the first picture?

math-mode symbols

share|improve this question

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I use bullet for dot products.
  
  – k-l
  Mar 22 '17 at 0:13
  

  
  
  
  

add a comment | 

I'm trying to replicate the dot that my professor uses in his notes for the dot product between vectors but I am having a hard time doing so. This is what it looks like:

I have tried a couple of things. cdot is too thin

and bullet is too thick

and using Large with cdot gives an error. Moreover, after digging through the list of symbols I cannot find a nice medium between cdot and bullet.

How can I get a dot closest to the first picture?

math-mode symbols

share|improve this question

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

share|improve this question

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

share|improve this question

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

edited 11 mins ago

Svend Tveskæg

20.9k1053143

edited 11 mins ago

Svend Tveskæg

20.9k1053143

asked Mar 25 '15 at 22:09

sardojsardoj

313135

asked Mar 25 '15 at 22:09

sardojsardoj

313135

4 Answers
4

active

oldest

votes

39

May be you find a better name like dotp or something like that.

documentclass{scrartcl}

usepackage{graphicx}



makeatletter

newcommand*bigcdot{mathpalettebigcdot@{.5}}

newcommand*bigcdot@[2]{mathbin{vcenter{hbox{scalebox{#2}{$m@th#1bullet$}}}}}

makeatother



begin{document}

$a bigcdot b$

end{document}

share|improve this answer

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  @Manuel (or anyone who understands this), could you clarify a couple of points about your macros? 1. What are the two parameters to mathpalette? (I only "see" one, unless "bigcdot@" and ".5" are separate in which case I don't understand why mathpalette is called. 2. What ends up being the first parameter (#1) to bigcdot@, used right before bullet?
  
  – dedded
  Feb 3 '16 at 13:22
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  That's how mathpalette works, the #1 that is passed to bigcdot@ is the current math style (displaystyle, textstyle, scriptstyle, or scriptscriptstyle depending on the case).Basically what mathpalette does is taking two arguments, and passing the currentstyle in first place and the second argument after it, so mathpaletefoo{whatever} ends up being for instance foodisplaystyle{whatever}, so you have to define foo accordingly.
  
  – Manuel
  Feb 3 '16 at 14:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @sardoj See The mysteries of mathpalette
  
  – egreg
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  

add a comment | 

20

Here is a simple trick which needs the amsmath package.

[

a  boldsymbol{cdot} b  =  0

]

and the result is

share|improve this answer

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Interesting solution; but bf has been deprecated for 20+ years. Besides, align* serves no purpose here, where equation* would be the correct environment.
  
  – egreg
  Nov 28 '16 at 21:09
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @egreg: Yeah! I am new to LaTex! Sorry for those! :) I changed the answer a little bit. Let me know if it is OK. :)
  
  – H. R.
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  This answer has a downside that the other one has not: if used within the scope of a mathversion{bold} (or boldmath, if you prefer) declaration, the dot cannot become any bolder. I agree, nonetheless, that it is an interesting solution.
  
  – GuM
  Nov 28 '16 at 21:58
  

  
  
  
  

add a comment | 

7

The following example extends Manuel's answer in two ways:

• The vertical position is fixed to center the symbol vertically around the
  math axis as cdot and bullet do.


• The width of the symbol is not the scaled down width of the bullet
  (with scaled down side bearings), but a little larger width of cdot.

The scale and width factor can be configured by macros bigcdot@scalefactor and bigcdot@widthfactor.

documentclass{scrartcl}

usepackage{color}

usepackage{graphicx}



makeatletter

newcommand*{bigcdot}{}% Check if undefined

DeclareRobustCommand*{bigcdot}{%

  mathbin{mathpalettebigcdot@{}}%

}

newcommand*{bigcdot@scalefactor}{.5}

newcommand*{bigcdot@widthfactor}{1.15}

newcommand*{bigcdot@}[2]{%

  % #1: math style

  % #2: unused

  sbox0{$#1vcenter{}$}% math axis

  sbox2{$#1cdotm@th$}%

  hbox to bigcdot@widthfactorwd2{%

    hfil

    raiseht0hbox{%

      scalebox{bigcdot@scalefactor}{%

        lowerht0hbox{$#1bulletm@th$}%

      }%

    }%

    hfil

  }%

}

makeatother



begin{document}

[ a bigcdot b ]

%

% Comparison with cdot and bullet

[ a cdot b bigcdot c bullet d ]

%

% Different math styles

[ a bigcdot b quad

   scriptstyle a bigcdot b quad

   scriptscriptstyle a bigcdot b

]

%

% Visualization of the math axis

[

  sbox0{${-}{cdot}{bigcdot}{bullet}{-}$}

  rlap{copy0}%

  vcenter{%

    hbox{%

      textcolor{red}{%

        vrule widthwd0 height .05pt depth .05ptrelax

      }%

    }%

  }

]

end{document}

share|improve this answer

edited May 9 '18 at 16:59

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I love it! And some more words to exceed the character limit.
  
  – Simon
  Nov 13 '18 at 19:10
  
  
  

  
  
  
  

add a comment | 

-1

a text{textbullet} b = 0

How about to use a text symbol instead?

At least it is simple!

share|improve this answer

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  You should at least use a binop here.
  
  – John Dorian
  Apr 1 '18 at 9:13
  

  
  
  
  

add a comment | 

protected by Community♦ Dec 6 '17 at 16:19

Thank you for your interest in this question.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).



Would you like to answer one of these unanswered questions instead?

39

May be you find a better name like dotp or something like that.

documentclass{scrartcl}

usepackage{graphicx}



makeatletter

newcommand*bigcdot{mathpalettebigcdot@{.5}}

newcommand*bigcdot@[2]{mathbin{vcenter{hbox{scalebox{#2}{$m@th#1bullet$}}}}}

makeatother



begin{document}

$a bigcdot b$

end{document}

share|improve this answer

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  @Manuel (or anyone who understands this), could you clarify a couple of points about your macros? 1. What are the two parameters to mathpalette? (I only "see" one, unless "bigcdot@" and ".5" are separate in which case I don't understand why mathpalette is called. 2. What ends up being the first parameter (#1) to bigcdot@, used right before bullet?
  
  – dedded
  Feb 3 '16 at 13:22
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  That's how mathpalette works, the #1 that is passed to bigcdot@ is the current math style (displaystyle, textstyle, scriptstyle, or scriptscriptstyle depending on the case).Basically what mathpalette does is taking two arguments, and passing the currentstyle in first place and the second argument after it, so mathpaletefoo{whatever} ends up being for instance foodisplaystyle{whatever}, so you have to define foo accordingly.
  
  – Manuel
  Feb 3 '16 at 14:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @sardoj See The mysteries of mathpalette
  
  – egreg
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  

add a comment | 

39

May be you find a better name like dotp or something like that.

documentclass{scrartcl}

usepackage{graphicx}



makeatletter

newcommand*bigcdot{mathpalettebigcdot@{.5}}

newcommand*bigcdot@[2]{mathbin{vcenter{hbox{scalebox{#2}{$m@th#1bullet$}}}}}

makeatother



begin{document}

$a bigcdot b$

end{document}

share|improve this answer

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  @Manuel (or anyone who understands this), could you clarify a couple of points about your macros? 1. What are the two parameters to mathpalette? (I only "see" one, unless "bigcdot@" and ".5" are separate in which case I don't understand why mathpalette is called. 2. What ends up being the first parameter (#1) to bigcdot@, used right before bullet?
  
  – dedded
  Feb 3 '16 at 13:22
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  That's how mathpalette works, the #1 that is passed to bigcdot@ is the current math style (displaystyle, textstyle, scriptstyle, or scriptscriptstyle depending on the case).Basically what mathpalette does is taking two arguments, and passing the currentstyle in first place and the second argument after it, so mathpaletefoo{whatever} ends up being for instance foodisplaystyle{whatever}, so you have to define foo accordingly.
  
  – Manuel
  Feb 3 '16 at 14:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @sardoj See The mysteries of mathpalette
  
  – egreg
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  

add a comment | 

May be you find a better name like dotp or something like that.

documentclass{scrartcl}

usepackage{graphicx}



makeatletter

newcommand*bigcdot{mathpalettebigcdot@{.5}}

newcommand*bigcdot@[2]{mathbin{vcenter{hbox{scalebox{#2}{$m@th#1bullet$}}}}}

makeatother



begin{document}

$a bigcdot b$

end{document}

share|improve this answer

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

documentclass{scrartcl}

usepackage{graphicx}



makeatletter

newcommand*bigcdot{mathpalettebigcdot@{.5}}

newcommand*bigcdot@[2]{mathbin{vcenter{hbox{scalebox{#2}{$m@th#1bullet$}}}}}

makeatother



begin{document}

$a bigcdot b$

end{document}

share|improve this answer

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

answered Mar 25 '15 at 22:19

ManuelManuel

21.6k846109

20

Here is a simple trick which needs the amsmath package.

[

a  boldsymbol{cdot} b  =  0

]

and the result is

share|improve this answer

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Interesting solution; but bf has been deprecated for 20+ years. Besides, align* serves no purpose here, where equation* would be the correct environment.
  
  – egreg
  Nov 28 '16 at 21:09
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @egreg: Yeah! I am new to LaTex! Sorry for those! :) I changed the answer a little bit. Let me know if it is OK. :)
  
  – H. R.
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  This answer has a downside that the other one has not: if used within the scope of a mathversion{bold} (or boldmath, if you prefer) declaration, the dot cannot become any bolder. I agree, nonetheless, that it is an interesting solution.
  
  – GuM
  Nov 28 '16 at 21:58
  

  
  
  
  

add a comment | 

20

Here is a simple trick which needs the amsmath package.

[

a  boldsymbol{cdot} b  =  0

]

and the result is

share|improve this answer

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Interesting solution; but bf has been deprecated for 20+ years. Besides, align* serves no purpose here, where equation* would be the correct environment.
  
  – egreg
  Nov 28 '16 at 21:09
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @egreg: Yeah! I am new to LaTex! Sorry for those! :) I changed the answer a little bit. Let me know if it is OK. :)
  
  – H. R.
  Nov 28 '16 at 21:11
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  This answer has a downside that the other one has not: if used within the scope of a mathversion{bold} (or boldmath, if you prefer) declaration, the dot cannot become any bolder. I agree, nonetheless, that it is an interesting solution.
  
  – GuM
  Nov 28 '16 at 21:58
  

  
  
  
  

add a comment | 

Here is a simple trick which needs the amsmath package.

[

a  boldsymbol{cdot} b  =  0

]

and the result is

share|improve this answer

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

[

a  boldsymbol{cdot} b  =  0

]

share|improve this answer

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

edited Nov 28 '16 at 21:12

egreg

735k8919343257

edited Nov 28 '16 at 21:12

egreg

735k8919343257

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

answered Nov 28 '16 at 21:05

H. R.H. R.

441415

7

The following example extends Manuel's answer in two ways:

• The vertical position is fixed to center the symbol vertically around the
  math axis as cdot and bullet do.


• The width of the symbol is not the scaled down width of the bullet
  (with scaled down side bearings), but a little larger width of cdot.

The scale and width factor can be configured by macros bigcdot@scalefactor and bigcdot@widthfactor.

documentclass{scrartcl}

usepackage{color}

usepackage{graphicx}



makeatletter

newcommand*{bigcdot}{}% Check if undefined

DeclareRobustCommand*{bigcdot}{%

  mathbin{mathpalettebigcdot@{}}%

}

newcommand*{bigcdot@scalefactor}{.5}

newcommand*{bigcdot@widthfactor}{1.15}

newcommand*{bigcdot@}[2]{%

  % #1: math style

  % #2: unused

  sbox0{$#1vcenter{}$}% math axis

  sbox2{$#1cdotm@th$}%

  hbox to bigcdot@widthfactorwd2{%

    hfil

    raiseht0hbox{%

      scalebox{bigcdot@scalefactor}{%

        lowerht0hbox{$#1bulletm@th$}%

      }%

    }%

    hfil

  }%

}

makeatother



begin{document}

[ a bigcdot b ]

%

% Comparison with cdot and bullet

[ a cdot b bigcdot c bullet d ]

%

% Different math styles

[ a bigcdot b quad

   scriptstyle a bigcdot b quad

   scriptscriptstyle a bigcdot b

]

%

% Visualization of the math axis

[

  sbox0{${-}{cdot}{bigcdot}{bullet}{-}$}

  rlap{copy0}%

  vcenter{%

    hbox{%

      textcolor{red}{%

        vrule widthwd0 height .05pt depth .05ptrelax

      }%

    }%

  }

]

end{document}

share|improve this answer

edited May 9 '18 at 16:59

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I love it! And some more words to exceed the character limit.
  
  – Simon
  Nov 13 '18 at 19:10
  
  
  

  
  
  
  

add a comment | 

7

The following example extends Manuel's answer in two ways:

• The vertical position is fixed to center the symbol vertically around the
  math axis as cdot and bullet do.


• The width of the symbol is not the scaled down width of the bullet
  (with scaled down side bearings), but a little larger width of cdot.

The scale and width factor can be configured by macros bigcdot@scalefactor and bigcdot@widthfactor.

documentclass{scrartcl}

usepackage{color}

usepackage{graphicx}



makeatletter

newcommand*{bigcdot}{}% Check if undefined

DeclareRobustCommand*{bigcdot}{%

  mathbin{mathpalettebigcdot@{}}%

}

newcommand*{bigcdot@scalefactor}{.5}

newcommand*{bigcdot@widthfactor}{1.15}

newcommand*{bigcdot@}[2]{%

  % #1: math style

  % #2: unused

  sbox0{$#1vcenter{}$}% math axis

  sbox2{$#1cdotm@th$}%

  hbox to bigcdot@widthfactorwd2{%

    hfil

    raiseht0hbox{%

      scalebox{bigcdot@scalefactor}{%

        lowerht0hbox{$#1bulletm@th$}%

      }%

    }%

    hfil

  }%

}

makeatother



begin{document}

[ a bigcdot b ]

%

% Comparison with cdot and bullet

[ a cdot b bigcdot c bullet d ]

%

% Different math styles

[ a bigcdot b quad

   scriptstyle a bigcdot b quad

   scriptscriptstyle a bigcdot b

]

%

% Visualization of the math axis

[

  sbox0{${-}{cdot}{bigcdot}{bullet}{-}$}

  rlap{copy0}%

  vcenter{%

    hbox{%

      textcolor{red}{%

        vrule widthwd0 height .05pt depth .05ptrelax

      }%

    }%

  }

]

end{document}

share|improve this answer

edited May 9 '18 at 16:59

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I love it! And some more words to exceed the character limit.
  
  – Simon
  Nov 13 '18 at 19:10
  
  
  

  
  
  
  

add a comment | 

The following example extends Manuel's answer in two ways:

• The vertical position is fixed to center the symbol vertically around the
  math axis as cdot and bullet do.


• The width of the symbol is not the scaled down width of the bullet
  (with scaled down side bearings), but a little larger width of cdot.

The scale and width factor can be configured by macros bigcdot@scalefactor and bigcdot@widthfactor.

documentclass{scrartcl}

usepackage{color}

usepackage{graphicx}



makeatletter

newcommand*{bigcdot}{}% Check if undefined

DeclareRobustCommand*{bigcdot}{%

  mathbin{mathpalettebigcdot@{}}%

}

newcommand*{bigcdot@scalefactor}{.5}

newcommand*{bigcdot@widthfactor}{1.15}

newcommand*{bigcdot@}[2]{%

  % #1: math style

  % #2: unused

  sbox0{$#1vcenter{}$}% math axis

  sbox2{$#1cdotm@th$}%

  hbox to bigcdot@widthfactorwd2{%

    hfil

    raiseht0hbox{%

      scalebox{bigcdot@scalefactor}{%

        lowerht0hbox{$#1bulletm@th$}%

      }%

    }%

    hfil

  }%

}

makeatother



begin{document}

[ a bigcdot b ]

%

% Comparison with cdot and bullet

[ a cdot b bigcdot c bullet d ]

%

% Different math styles

[ a bigcdot b quad

   scriptstyle a bigcdot b quad

   scriptscriptstyle a bigcdot b

]

%

% Visualization of the math axis

[

  sbox0{${-}{cdot}{bigcdot}{bullet}{-}$}

  rlap{copy0}%

  vcenter{%

    hbox{%

      textcolor{red}{%

        vrule widthwd0 height .05pt depth .05ptrelax

      }%

    }%

  }

]

end{document}

share|improve this answer

edited May 9 '18 at 16:59

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

documentclass{scrartcl}

usepackage{color}

usepackage{graphicx}



makeatletter

newcommand*{bigcdot}{}% Check if undefined

DeclareRobustCommand*{bigcdot}{%

  mathbin{mathpalettebigcdot@{}}%

}

newcommand*{bigcdot@scalefactor}{.5}

newcommand*{bigcdot@widthfactor}{1.15}

newcommand*{bigcdot@}[2]{%

  % #1: math style

  % #2: unused

  sbox0{$#1vcenter{}$}% math axis

  sbox2{$#1cdotm@th$}%

  hbox to bigcdot@widthfactorwd2{%

    hfil

    raiseht0hbox{%

      scalebox{bigcdot@scalefactor}{%

        lowerht0hbox{$#1bulletm@th$}%

      }%

    }%

    hfil

  }%

}

makeatother



begin{document}

[ a bigcdot b ]

%

% Comparison with cdot and bullet

[ a cdot b bigcdot c bullet d ]

%

% Different math styles

[ a bigcdot b quad

   scriptstyle a bigcdot b quad

   scriptscriptstyle a bigcdot b

]

%

% Visualization of the math axis

[

  sbox0{${-}{cdot}{bigcdot}{bullet}{-}$}

  rlap{copy0}%

  vcenter{%

    hbox{%

      textcolor{red}{%

        vrule widthwd0 height .05pt depth .05ptrelax

      }%

    }%

  }

]

end{document}

share|improve this answer

edited May 9 '18 at 16:59

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

answered Mar 31 '18 at 23:23

Heiko OberdiekHeiko Oberdiek

232k19563913

-1

a text{textbullet} b = 0

How about to use a text symbol instead?

At least it is simple!

share|improve this answer

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  You should at least use a binop here.
  
  – John Dorian
  Apr 1 '18 at 9:13
  

  
  
  
  

add a comment | 

-1

a text{textbullet} b = 0

How about to use a text symbol instead?

At least it is simple!

share|improve this answer

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  You should at least use a binop here.
  
  – John Dorian
  Apr 1 '18 at 9:13
  

  
  
  
  

add a comment | 

a text{textbullet} b = 0

How about to use a text symbol instead?

At least it is simple!

share|improve this answer

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

a text{textbullet} b = 0

share|improve this answer

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216

answered Mar 20 '18 at 9:38

GyuHyeon ChoiGyuHyeon Choi

1216