{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-26T00:14:02.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44263,"title":"Multivariate polynomials - emulate symbolic form","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication Problem 44262\u003e I asked you to create a class |mPoly| with overloaded multiplication, so a product of two polynomials can be expressed in the form |p = p1*p2|. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003chttps://www.mathworks.com/products/symbolic.html Symbolic Math Toolbox\u003e, one can simply define some variables,\r\n\r\n  syms x y z\r\n\r\nand then create a polynomial:\r\n\r\n  p = 2*x*y + 3*x^5*z;\r\n\r\nWe would like to do something like that here. As a start, create a class |mPolySym| with properties |exponents| and |coefficients|, and |varnames|,  where the first two properties are the same as in previous problems and |varnames| is a \u003chttps://www.mathworks.com/help/matlab/characters-and-strings.html string array\u003e. The constructor should accept a numeric, char or string input, e.g.,\r\n\r\n  x = mPolySym('x')\r\n\r\n  x = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\r\n\r\n  r = mPolySym(pi)\r\n\r\n  r = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\r\n\r\nAlso modify the method |mtimes| from the previous problem so it can multiply polynomials with different variable names.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\"\u003eProblem 44262\u003c/a\u003e I asked you to create a class \u003ctt\u003emPoly\u003c/tt\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form \u003ctt\u003ep = p1*p2\u003c/tt\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003ca href = \"https://www.mathworks.com/products/symbolic.html\"\u003eSymbolic Math Toolbox\u003c/a\u003e, one can simply define some variables,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003esyms x y z\r\n\u003c/pre\u003e\u003cp\u003eand then create a polynomial:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = 2*x*y + 3*x^5*z;\r\n\u003c/pre\u003e\u003cp\u003eWe would like to do something like that here. As a start, create a class \u003ctt\u003emPolySym\u003c/tt\u003e with properties \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and \u003ctt\u003evarnames\u003c/tt\u003e,  where the first two properties are the same as in previous problems and \u003ctt\u003evarnames\u003c/tt\u003e is a \u003ca href = \"https://www.mathworks.com/help/matlab/characters-and-strings.html\"\u003estring array\u003c/a\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = mPolySym('x')\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = mPolySym(pi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\u003c/pre\u003e\u003cp\u003eAlso modify the method \u003ctt\u003emtimes\u003c/tt\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/p\u003e","function_template":"classdef mPolySym\r\n    properties\r\n        varnames\r\n        exponents\r\n        coefficients\r\n    end\r\n    \r\n    methods\r\n        function p = mPolySym(s)\r\n        end\r\n        \r\n        function p = mtimes(p1,p2)\r\n        end            \r\n    end\r\n    \r\nend\r\n\r\n","test_suite":"%% Test mPolySym\r\nfiletext = fileread('mPolySym.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym(r);\r\nassert(isempty(x.varnames))\r\nassert(isequal(x.exponents,0))\r\nassert(isequal(x.coefficients,r))\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym('x');\r\ny = r*x;\r\nassert(isequal(y.varnames,\"x\"))\r\nassert(isequal(y.exponents,1))\r\nassert(isequal(y.coefficients,r))\r\nassert(isequal(r*x,x*r))\r\n\r\n%%\r\nx = mPolySym('x');\r\ny = mPolySym(\"y\");\r\nz = mPolySym('z');\r\nw = x*y*z;\r\nassert(isequal(w.varnames,[\"x\" \"y\" \"z\"]))\r\nassert(isequal(w.exponents,[1 1 1]))\r\nassert(isequal(w.coefficients,1))\r\n\r\n%%\r\nm = randi(5);\r\nn = randi(4);\r\nx = mPolySym(\"x\");\r\ny = mPolySym(\"y\");\r\np = [repmat(x,1,m) repmat(y,1,n)];\r\np = p(randperm(length(p)));\r\nr = randi(1000);\r\np_prod = r;\r\nfor ii=1:length(p)\r\n    p_prod = p_prod*p(ii);\r\nend\r\ns = randi(1000);\r\np_prod = p_prod*s;\r\nassert(isequal(p_prod.varnames,[\"x\" \"y\"]))\r\nassert(isequal(p_prod.exponents,[m n]))\r\nassert(isequal(p_prod.coefficients,r*s))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T23:13:17.000Z","updated_at":"2025-12-22T13:23:36.000Z","published_at":"2017-07-14T23:13:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44262\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = p1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/products/symbolic.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic Math Toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can simply define some variables,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[syms x y z]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand then create a polynomial:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = 2*x*y + 3*x^5*z;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to do something like that here. As a start, create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPolySym\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with properties\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the first two properties are the same as in previous problems and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/characters-and-strings.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estring array\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = mPolySym('x')\\n\\nx = \\n\\nmPolySym with properties:\\n\\n        varnames: \\\"x\\\"\\n       exponents: 1\\n    coefficients: 1\\n\\nr = mPolySym(pi)\\n\\nr = \\n\\nmPolySym with properties:\\n\\n        varnames: [0×0 string]\\n       exponents: 1\\n    coefficients: 3.1416]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso modify the method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44263,"title":"Multivariate polynomials - emulate symbolic form","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication Problem 44262\u003e I asked you to create a class |mPoly| with overloaded multiplication, so a product of two polynomials can be expressed in the form |p = p1*p2|. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003chttps://www.mathworks.com/products/symbolic.html Symbolic Math Toolbox\u003e, one can simply define some variables,\r\n\r\n  syms x y z\r\n\r\nand then create a polynomial:\r\n\r\n  p = 2*x*y + 3*x^5*z;\r\n\r\nWe would like to do something like that here. As a start, create a class |mPolySym| with properties |exponents| and |coefficients|, and |varnames|,  where the first two properties are the same as in previous problems and |varnames| is a \u003chttps://www.mathworks.com/help/matlab/characters-and-strings.html string array\u003e. The constructor should accept a numeric, char or string input, e.g.,\r\n\r\n  x = mPolySym('x')\r\n\r\n  x = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\r\n\r\n  r = mPolySym(pi)\r\n\r\n  r = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\r\n\r\nAlso modify the method |mtimes| from the previous problem so it can multiply polynomials with different variable names.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\"\u003eProblem 44262\u003c/a\u003e I asked you to create a class \u003ctt\u003emPoly\u003c/tt\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form \u003ctt\u003ep = p1*p2\u003c/tt\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003ca href = \"https://www.mathworks.com/products/symbolic.html\"\u003eSymbolic Math Toolbox\u003c/a\u003e, one can simply define some variables,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003esyms x y z\r\n\u003c/pre\u003e\u003cp\u003eand then create a polynomial:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = 2*x*y + 3*x^5*z;\r\n\u003c/pre\u003e\u003cp\u003eWe would like to do something like that here. As a start, create a class \u003ctt\u003emPolySym\u003c/tt\u003e with properties \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and \u003ctt\u003evarnames\u003c/tt\u003e,  where the first two properties are the same as in previous problems and \u003ctt\u003evarnames\u003c/tt\u003e is a \u003ca href = \"https://www.mathworks.com/help/matlab/characters-and-strings.html\"\u003estring array\u003c/a\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = mPolySym('x')\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = mPolySym(pi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\u003c/pre\u003e\u003cp\u003eAlso modify the method \u003ctt\u003emtimes\u003c/tt\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/p\u003e","function_template":"classdef mPolySym\r\n    properties\r\n        varnames\r\n        exponents\r\n        coefficients\r\n    end\r\n    \r\n    methods\r\n        function p = mPolySym(s)\r\n        end\r\n        \r\n        function p = mtimes(p1,p2)\r\n        end            \r\n    end\r\n    \r\nend\r\n\r\n","test_suite":"%% Test mPolySym\r\nfiletext = fileread('mPolySym.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym(r);\r\nassert(isempty(x.varnames))\r\nassert(isequal(x.exponents,0))\r\nassert(isequal(x.coefficients,r))\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym('x');\r\ny = r*x;\r\nassert(isequal(y.varnames,\"x\"))\r\nassert(isequal(y.exponents,1))\r\nassert(isequal(y.coefficients,r))\r\nassert(isequal(r*x,x*r))\r\n\r\n%%\r\nx = mPolySym('x');\r\ny = mPolySym(\"y\");\r\nz = mPolySym('z');\r\nw = x*y*z;\r\nassert(isequal(w.varnames,[\"x\" \"y\" \"z\"]))\r\nassert(isequal(w.exponents,[1 1 1]))\r\nassert(isequal(w.coefficients,1))\r\n\r\n%%\r\nm = randi(5);\r\nn = randi(4);\r\nx = mPolySym(\"x\");\r\ny = mPolySym(\"y\");\r\np = [repmat(x,1,m) repmat(y,1,n)];\r\np = p(randperm(length(p)));\r\nr = randi(1000);\r\np_prod = r;\r\nfor ii=1:length(p)\r\n    p_prod = p_prod*p(ii);\r\nend\r\ns = randi(1000);\r\np_prod = p_prod*s;\r\nassert(isequal(p_prod.varnames,[\"x\" \"y\"]))\r\nassert(isequal(p_prod.exponents,[m n]))\r\nassert(isequal(p_prod.coefficients,r*s))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T23:13:17.000Z","updated_at":"2025-12-22T13:23:36.000Z","published_at":"2017-07-14T23:13:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44262\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = p1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/products/symbolic.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic Math Toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can simply define some variables,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[syms x y z]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand then create a polynomial:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = 2*x*y + 3*x^5*z;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to do something like that here. As a start, create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPolySym\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with properties\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the first two properties are the same as in previous problems and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/characters-and-strings.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estring array\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = mPolySym('x')\\n\\nx = \\n\\nmPolySym with properties:\\n\\n        varnames: \\\"x\\\"\\n       exponents: 1\\n    coefficients: 1\\n\\nr = mPolySym(pi)\\n\\nr = \\n\\nmPolySym with properties:\\n\\n        varnames: [0×0 string]\\n       exponents: 1\\n    coefficients: 3.1416]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso modify the method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts 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