Meaning of ## #












12












$begingroup$


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









$endgroup$








  • 1




    $begingroup$
    FullForm[## #]
    $endgroup$
    – Kuba♦
    Dec 7 '18 at 13:30










  • $begingroup$
    Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    $endgroup$
    – Jakub Kryś
    Dec 7 '18 at 14:02






  • 1




    $begingroup$
    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...)
    $endgroup$
    – Brett Champion
    Dec 7 '18 at 14:42
















12












$begingroup$


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









$endgroup$








  • 1




    $begingroup$
    FullForm[## #]
    $endgroup$
    – Kuba♦
    Dec 7 '18 at 13:30










  • $begingroup$
    Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    $endgroup$
    – Jakub Kryś
    Dec 7 '18 at 14:02






  • 1




    $begingroup$
    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...)
    $endgroup$
    – Brett Champion
    Dec 7 '18 at 14:42














12












12








12


0



$begingroup$


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









$endgroup$




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




array slot






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Dec 7 '18 at 13:25









Jakub KryśJakub Kryś

634




634








  • 1




    $begingroup$
    FullForm[## #]
    $endgroup$
    – Kuba♦
    Dec 7 '18 at 13:30










  • $begingroup$
    Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    $endgroup$
    – Jakub Kryś
    Dec 7 '18 at 14:02






  • 1




    $begingroup$
    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...)
    $endgroup$
    – Brett Champion
    Dec 7 '18 at 14:42














  • 1




    $begingroup$
    FullForm[## #]
    $endgroup$
    – Kuba♦
    Dec 7 '18 at 13:30










  • $begingroup$
    Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
    $endgroup$
    – Jakub Kryś
    Dec 7 '18 at 14:02






  • 1




    $begingroup$
    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...)
    $endgroup$
    – Brett Champion
    Dec 7 '18 at 14:42








1




1




$begingroup$
FullForm[## #]
$endgroup$
– Kuba♦
Dec 7 '18 at 13:30




$begingroup$
FullForm[## #]
$endgroup$
– Kuba♦
Dec 7 '18 at 13:30












$begingroup$
Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
$endgroup$
– Jakub Kryś
Dec 7 '18 at 14:02




$begingroup$
Thank you, as a beginner in Mathematica, I don't use FullForm as often as I should...
$endgroup$
– Jakub Kryś
Dec 7 '18 at 14:02




1




1




$begingroup$
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...)
$endgroup$
– Brett Champion
Dec 7 '18 at 14:42




$begingroup$
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...)
$endgroup$
– Brett Champion
Dec 7 '18 at 14:42










1 Answer
1






active

oldest

votes


















11












$begingroup$

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











$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "387"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f187493%2fmeaning-of%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    11












    $begingroup$

    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











    $endgroup$


















      11












      $begingroup$

      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











      $endgroup$
















        11












        11








        11





        $begingroup$

        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











        $endgroup$



        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 '18 at 22:05

























        answered Dec 7 '18 at 13:56









        SzabolcsSzabolcs

        159k13435930




        159k13435930






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematica Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f187493%2fmeaning-of%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Probability when a professor distributes a quiz and homework assignment to a class of n students.

            Image
            0 0 $begingroup$ Need help with this problem. Suppose our lazy professor collects a quiz and a homework assignment from a class of n students one day, then distributes both the quizzes and the homework assignments back to the class in a random fashion for grading. Each student receives one quiz and one homework assignment to grade. (a) What is the probability that every student receives someone else's quiz to grade, and someone else's homework to grade? (b) What is the probability that no student receives both their own quiz and their own homework assignment to grade? In this case, some students may receive their own quiz, and others may receive their own homework assignment. (c) Compute the limiting probability as n approaches infinity in each case. ...
            Read more

            Aardman Animations

            Image
            Aardman Animations, Ltd. Aardman Animations Tipo privada Atividade Animação em stop-motion , Animação em CGI Fundação 1972 Fundador(es) Peter Lord David Sproxton Sede Bristol, Inglaterra  Reino Unido Proprietário(s) Dreamworks Pessoas-chave Peter Lord David Sproxton Nick Park Divisões Aardman Features Aardman Digital Aardman Commercials Aardman Broadcast Aardman International Aardman Rights Aardman Effects Aardman 3-D Systems Aardman Nathan Love AardBoiled Website oficial aardman.com ...
            Read more

            Are they similar matrix

            Image
            0 $begingroup$ Do $begin{bmatrix} 0&i&0\0&0&1\0&0&0 end{bmatrix} $ and $begin{bmatrix} 0&0&0\-i&0&0\0&1&0 end{bmatrix} $ are similar.Is this True/false Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector share | cite | improve this question edited Dec 10 '18 at 6:38 Vasanth Kris asked Dec 10 '18 at 6:19 ...
            Read more