Meaning of ## #











up vote
12
down vote

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While looking for an answer to a different problem, I came across the following example:



In[1]:= Array[Plus[##] &, {2,2}] 
Out[1]= {{2,3},{3,4}}


Having read through the documentation on Slot and SlotSequence, I understand the above example. If we think of it as a matrix $M_{ij}$, it takes the two indices and adds them up, $M_{ij}=i+j$. I also understand that it is equivalent to Array[Plus[#1,#2] &, {2, 2}].



I tried making the expression slightly more complicated:



In[2]:= Array[Plus[##,#] &, {2,2}] 
Out[2]= {{3,4},{5,6}}


which acts as $M_{ij}=(i+j)+i$, or if we replace the last # with #2, $M_{ij}=(i+j)+j$.



Now, I am really stuck on interpreting:



In[3]:= Array[Plus[## #] &, {2,2}]
Out[3]= {{1,2},{4,8}}


What is the corresponding expression for $M_{ij}$?










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  • 1




    FullForm[## #]
    – Kuba
    Dec 7 at 13:30










  • Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    – Jakub Kryś
    Dec 7 at 14:02






  • 1




    Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
    – Brett Champion
    Dec 7 at 14:42















up vote
12
down vote

favorite












While looking for an answer to a different problem, I came across the following example:



In[1]:= Array[Plus[##] &, {2,2}] 
Out[1]= {{2,3},{3,4}}


Having read through the documentation on Slot and SlotSequence, I understand the above example. If we think of it as a matrix $M_{ij}$, it takes the two indices and adds them up, $M_{ij}=i+j$. I also understand that it is equivalent to Array[Plus[#1,#2] &, {2, 2}].



I tried making the expression slightly more complicated:



In[2]:= Array[Plus[##,#] &, {2,2}] 
Out[2]= {{3,4},{5,6}}


which acts as $M_{ij}=(i+j)+i$, or if we replace the last # with #2, $M_{ij}=(i+j)+j$.



Now, I am really stuck on interpreting:



In[3]:= Array[Plus[## #] &, {2,2}]
Out[3]= {{1,2},{4,8}}


What is the corresponding expression for $M_{ij}$?










share|improve this question


















  • 1




    FullForm[## #]
    – Kuba
    Dec 7 at 13:30










  • Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    – Jakub Kryś
    Dec 7 at 14:02






  • 1




    Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
    – Brett Champion
    Dec 7 at 14:42













up vote
12
down vote

favorite









up vote
12
down vote

favorite











While looking for an answer to a different problem, I came across the following example:



In[1]:= Array[Plus[##] &, {2,2}] 
Out[1]= {{2,3},{3,4}}


Having read through the documentation on Slot and SlotSequence, I understand the above example. If we think of it as a matrix $M_{ij}$, it takes the two indices and adds them up, $M_{ij}=i+j$. I also understand that it is equivalent to Array[Plus[#1,#2] &, {2, 2}].



I tried making the expression slightly more complicated:



In[2]:= Array[Plus[##,#] &, {2,2}] 
Out[2]= {{3,4},{5,6}}


which acts as $M_{ij}=(i+j)+i$, or if we replace the last # with #2, $M_{ij}=(i+j)+j$.



Now, I am really stuck on interpreting:



In[3]:= Array[Plus[## #] &, {2,2}]
Out[3]= {{1,2},{4,8}}


What is the corresponding expression for $M_{ij}$?










share|improve this question













While looking for an answer to a different problem, I came across the following example:



In[1]:= Array[Plus[##] &, {2,2}] 
Out[1]= {{2,3},{3,4}}


Having read through the documentation on Slot and SlotSequence, I understand the above example. If we think of it as a matrix $M_{ij}$, it takes the two indices and adds them up, $M_{ij}=i+j$. I also understand that it is equivalent to Array[Plus[#1,#2] &, {2, 2}].



I tried making the expression slightly more complicated:



In[2]:= Array[Plus[##,#] &, {2,2}] 
Out[2]= {{3,4},{5,6}}


which acts as $M_{ij}=(i+j)+i$, or if we replace the last # with #2, $M_{ij}=(i+j)+j$.



Now, I am really stuck on interpreting:



In[3]:= Array[Plus[## #] &, {2,2}]
Out[3]= {{1,2},{4,8}}


What is the corresponding expression for $M_{ij}$?







array slot






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Dec 7 at 13:25









Jakub Kryś

634




634








  • 1




    FullForm[## #]
    – Kuba
    Dec 7 at 13:30










  • Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    – Jakub Kryś
    Dec 7 at 14:02






  • 1




    Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
    – Brett Champion
    Dec 7 at 14:42














  • 1




    FullForm[## #]
    – Kuba
    Dec 7 at 13:30










  • Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    – Jakub Kryś
    Dec 7 at 14:02






  • 1




    Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
    – Brett Champion
    Dec 7 at 14:42








1




1




FullForm[## #]
– Kuba
Dec 7 at 13:30




FullForm[## #]
– Kuba
Dec 7 at 13:30












Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
– Jakub Kryś
Dec 7 at 14:02




Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
– Jakub Kryś
Dec 7 at 14:02




1




1




Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
– Brett Champion
Dec 7 at 14:42




Hmm, I think I need to find a place to use ######& in my code. (It's perhaps less obvious what this is here than in the frontend...)
– Brett Champion
Dec 7 at 14:42










1 Answer
1






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up vote
11
down vote



accepted










Plus[## #] & is the same as Plus[Times[##, #1]], which always computes to the same as the simpler Times[##, #1] (because Plus[x] is just x).



Thus this computes the same as



Table[i^2 * j, {i, 2}, {j, 2}]





share|improve this answer























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    1 Answer
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    1 Answer
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    up vote
    11
    down vote



    accepted










    Plus[## #] & is the same as Plus[Times[##, #1]], which always computes to the same as the simpler Times[##, #1] (because Plus[x] is just x).



    Thus this computes the same as



    Table[i^2 * j, {i, 2}, {j, 2}]





    share|improve this answer



























      up vote
      11
      down vote



      accepted










      Plus[## #] & is the same as Plus[Times[##, #1]], which always computes to the same as the simpler Times[##, #1] (because Plus[x] is just x).



      Thus this computes the same as



      Table[i^2 * j, {i, 2}, {j, 2}]





      share|improve this answer

























        up vote
        11
        down vote



        accepted







        up vote
        11
        down vote



        accepted






        Plus[## #] & is the same as Plus[Times[##, #1]], which always computes to the same as the simpler Times[##, #1] (because Plus[x] is just x).



        Thus this computes the same as



        Table[i^2 * j, {i, 2}, {j, 2}]





        share|improve this answer














        Plus[## #] & is the same as Plus[Times[##, #1]], which always computes to the same as the simpler Times[##, #1] (because Plus[x] is just x).



        Thus this computes the same as



        Table[i^2 * j, {i, 2}, {j, 2}]






        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited Dec 7 at 22:05

























        answered Dec 7 at 13:56









        Szabolcs

        158k13432926




        158k13432926






























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