Brauer Character in GAP.
$begingroup$
What is command to obtain Brauer Character in GAP? In magma, it is like
> G := Sym(5);
> I := AbsolutelyIrreducibleModules(G, GF(3));
> [BrauerCharacter(i): i in I];
[
( 1, 1, 1, 0, 1, 1, 0 ),
( 1, -1, 1, 0, -1, 1, 0 ),
( 4, 2, 0, 0, 0, -1, 0 ),
( 4, -2, 0, 0, 0, -1, 0 ),
( 6, 0, -2, 0, 0, 1, 0 )
]
Please tell me the same for GAP.
Thanks.
group-theory characters gap
$endgroup$
add a comment |
$begingroup$
What is command to obtain Brauer Character in GAP? In magma, it is like
> G := Sym(5);
> I := AbsolutelyIrreducibleModules(G, GF(3));
> [BrauerCharacter(i): i in I];
[
( 1, 1, 1, 0, 1, 1, 0 ),
( 1, -1, 1, 0, -1, 1, 0 ),
( 4, 2, 0, 0, 0, -1, 0 ),
( 4, -2, 0, 0, 0, -1, 0 ),
( 6, 0, -2, 0, 0, 1, 0 )
]
Please tell me the same for GAP.
Thanks.
group-theory characters gap
$endgroup$
1
$begingroup$
@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32
add a comment |
$begingroup$
What is command to obtain Brauer Character in GAP? In magma, it is like
> G := Sym(5);
> I := AbsolutelyIrreducibleModules(G, GF(3));
> [BrauerCharacter(i): i in I];
[
( 1, 1, 1, 0, 1, 1, 0 ),
( 1, -1, 1, 0, -1, 1, 0 ),
( 4, 2, 0, 0, 0, -1, 0 ),
( 4, -2, 0, 0, 0, -1, 0 ),
( 6, 0, -2, 0, 0, 1, 0 )
]
Please tell me the same for GAP.
Thanks.
group-theory characters gap
$endgroup$
What is command to obtain Brauer Character in GAP? In magma, it is like
> G := Sym(5);
> I := AbsolutelyIrreducibleModules(G, GF(3));
> [BrauerCharacter(i): i in I];
[
( 1, 1, 1, 0, 1, 1, 0 ),
( 1, -1, 1, 0, -1, 1, 0 ),
( 4, 2, 0, 0, 0, -1, 0 ),
( 4, -2, 0, 0, 0, -1, 0 ),
( 6, 0, -2, 0, 0, 1, 0 )
]
Please tell me the same for GAP.
Thanks.
group-theory characters gap
group-theory characters gap
edited Dec 23 '18 at 3:08
Shaun
9,338113684
9,338113684
asked Dec 22 '18 at 16:46
neelkanthneelkanth
2,28821129
2,28821129
1
$begingroup$
@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32
add a comment |
1
$begingroup$
@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32
1
1
$begingroup$
@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32
$begingroup$
@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Indeed, as in the quote from the GAP manual given by @Shaun, trying to do this immediately in GAP fails:
gap> G:=SymmetricGroup(5);
Sym( [ 1 .. 5 ] )
gap> t:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 5 ] ) )
gap> t mod 3;
fail
The GAP Character Table Library is provided by the CTblLib package (in most installations, it is loaded by default, otherwise one should load it first with LoadPackage("ctbllib");
. Then you can retrieve the character table from the library. In your example, do the following:
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
See ?AllCharacterTableNames
in GAP to search in identifiers of library tables. It could narrow the search if you are not sure which identifier to use, For example,
gap> AllCharacterTableNames(Size,120);
[ "2.A5", "2.A6M2", "2.Alt(5)", "2xA5", "A5.2", "A6.2_1M3", "D120", "L2(25)M3", "Sym(5)" ]
gap> AllCharacterTableNames(Size,7920,IsSimple,true);
[ "HSM9", "M11", "M12M2", "ONM11" ]
$endgroup$
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
|
show 1 more comment
$begingroup$
Currently GAP does not provide special functionality for computing Brauer character tables, but there is an interface to the MOC system (see [HJLP]), and the GAP Character Table Library contains many known Brauer character tables.
Found here.
See "71.3-1 CharacterTable" onwards ibid. for the capabilities.
$endgroup$
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
add a comment |
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2 Answers
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2 Answers
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$begingroup$
Indeed, as in the quote from the GAP manual given by @Shaun, trying to do this immediately in GAP fails:
gap> G:=SymmetricGroup(5);
Sym( [ 1 .. 5 ] )
gap> t:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 5 ] ) )
gap> t mod 3;
fail
The GAP Character Table Library is provided by the CTblLib package (in most installations, it is loaded by default, otherwise one should load it first with LoadPackage("ctbllib");
. Then you can retrieve the character table from the library. In your example, do the following:
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
See ?AllCharacterTableNames
in GAP to search in identifiers of library tables. It could narrow the search if you are not sure which identifier to use, For example,
gap> AllCharacterTableNames(Size,120);
[ "2.A5", "2.A6M2", "2.Alt(5)", "2xA5", "A5.2", "A6.2_1M3", "D120", "L2(25)M3", "Sym(5)" ]
gap> AllCharacterTableNames(Size,7920,IsSimple,true);
[ "HSM9", "M11", "M12M2", "ONM11" ]
$endgroup$
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
|
show 1 more comment
$begingroup$
Indeed, as in the quote from the GAP manual given by @Shaun, trying to do this immediately in GAP fails:
gap> G:=SymmetricGroup(5);
Sym( [ 1 .. 5 ] )
gap> t:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 5 ] ) )
gap> t mod 3;
fail
The GAP Character Table Library is provided by the CTblLib package (in most installations, it is loaded by default, otherwise one should load it first with LoadPackage("ctbllib");
. Then you can retrieve the character table from the library. In your example, do the following:
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
See ?AllCharacterTableNames
in GAP to search in identifiers of library tables. It could narrow the search if you are not sure which identifier to use, For example,
gap> AllCharacterTableNames(Size,120);
[ "2.A5", "2.A6M2", "2.Alt(5)", "2xA5", "A5.2", "A6.2_1M3", "D120", "L2(25)M3", "Sym(5)" ]
gap> AllCharacterTableNames(Size,7920,IsSimple,true);
[ "HSM9", "M11", "M12M2", "ONM11" ]
$endgroup$
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
|
show 1 more comment
$begingroup$
Indeed, as in the quote from the GAP manual given by @Shaun, trying to do this immediately in GAP fails:
gap> G:=SymmetricGroup(5);
Sym( [ 1 .. 5 ] )
gap> t:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 5 ] ) )
gap> t mod 3;
fail
The GAP Character Table Library is provided by the CTblLib package (in most installations, it is loaded by default, otherwise one should load it first with LoadPackage("ctbllib");
. Then you can retrieve the character table from the library. In your example, do the following:
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
See ?AllCharacterTableNames
in GAP to search in identifiers of library tables. It could narrow the search if you are not sure which identifier to use, For example,
gap> AllCharacterTableNames(Size,120);
[ "2.A5", "2.A6M2", "2.Alt(5)", "2xA5", "A5.2", "A6.2_1M3", "D120", "L2(25)M3", "Sym(5)" ]
gap> AllCharacterTableNames(Size,7920,IsSimple,true);
[ "HSM9", "M11", "M12M2", "ONM11" ]
$endgroup$
Indeed, as in the quote from the GAP manual given by @Shaun, trying to do this immediately in GAP fails:
gap> G:=SymmetricGroup(5);
Sym( [ 1 .. 5 ] )
gap> t:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 5 ] ) )
gap> t mod 3;
fail
The GAP Character Table Library is provided by the CTblLib package (in most installations, it is loaded by default, otherwise one should load it first with LoadPackage("ctbllib");
. Then you can retrieve the character table from the library. In your example, do the following:
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
See ?AllCharacterTableNames
in GAP to search in identifiers of library tables. It could narrow the search if you are not sure which identifier to use, For example,
gap> AllCharacterTableNames(Size,120);
[ "2.A5", "2.A6M2", "2.Alt(5)", "2xA5", "A5.2", "A6.2_1M3", "D120", "L2(25)M3", "Sym(5)" ]
gap> AllCharacterTableNames(Size,7920,IsSimple,true);
[ "HSM9", "M11", "M12M2", "ONM11" ]
edited Dec 27 '18 at 9:39
answered Dec 22 '18 at 21:27
Alexander KonovalovAlexander Konovalov
5,21221957
5,21221957
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
|
show 1 more comment
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Thanks ... I will try this way and will tell....
$endgroup$
– neelkanth
Dec 23 '18 at 4:31
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Yes sir it is fine and working for me ... you explained exactly that I need... thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 7:24
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
Sir can i ask one more question? If i want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks.
$endgroup$
– neelkanth
Dec 23 '18 at 7:36
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
I suggest to start with the GAP Software Carpentry lesson. It is aimed at beginners, and was taught at workshops, but should also be suitable for self-study. Then look also at my answer to the question What is the best way to self-study GAP?.
$endgroup$
– Alexander Konovalov
Dec 23 '18 at 21:50
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
$begingroup$
Thanks ....................
$endgroup$
– neelkanth
Dec 24 '18 at 4:23
|
show 1 more comment
$begingroup$
Currently GAP does not provide special functionality for computing Brauer character tables, but there is an interface to the MOC system (see [HJLP]), and the GAP Character Table Library contains many known Brauer character tables.
Found here.
See "71.3-1 CharacterTable" onwards ibid. for the capabilities.
$endgroup$
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
add a comment |
$begingroup$
Currently GAP does not provide special functionality for computing Brauer character tables, but there is an interface to the MOC system (see [HJLP]), and the GAP Character Table Library contains many known Brauer character tables.
Found here.
See "71.3-1 CharacterTable" onwards ibid. for the capabilities.
$endgroup$
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
add a comment |
$begingroup$
Currently GAP does not provide special functionality for computing Brauer character tables, but there is an interface to the MOC system (see [HJLP]), and the GAP Character Table Library contains many known Brauer character tables.
Found here.
See "71.3-1 CharacterTable" onwards ibid. for the capabilities.
$endgroup$
Currently GAP does not provide special functionality for computing Brauer character tables, but there is an interface to the MOC system (see [HJLP]), and the GAP Character Table Library contains many known Brauer character tables.
Found here.
See "71.3-1 CharacterTable" onwards ibid. for the capabilities.
edited Dec 22 '18 at 17:43
answered Dec 22 '18 at 17:37
ShaunShaun
9,338113684
9,338113684
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
add a comment |
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
1
1
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
$begingroup$
If want to learn about GAP from where to start ? I mean is there elementary level book of GAP? Please suggest me. Thanks
$endgroup$
– neelkanth
Dec 23 '18 at 10:12
1
1
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
@neelkanth Simply search online for the GAP tutorial and the GAP manual. They're free PDFs with all the information you'll ever need.
$endgroup$
– Shaun
Dec 23 '18 at 11:46
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
There's also this, @neelkanth :)
$endgroup$
– Shaun
Dec 23 '18 at 11:48
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
@ Shaun Thank you very much ...
$endgroup$
– neelkanth
Dec 23 '18 at 15:26
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
$begingroup$
please look at my problem math.stackexchange.com/questions/3051924/…
$endgroup$
– neelkanth
Dec 25 '18 at 8:39
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@Shaun thanks for edit and answer ...
$endgroup$
– neelkanth
Dec 23 '18 at 4:32