29:null 2a:["$","title",null,{"children":"01. Polynomial Number Method (pyPN) | Andrzej Kubaszek | Observable"}] 2f:[] 2d:{"id":"d9d7212dcbb1752f","slug":"01-polynomial-number-method-pypn","title":"01. Polynomial Number Method (pyPN)","thumbnail":"bc5ebcb690b7d172091708e79b374be1c22c6c2831ec647f10bcac1a879f9f10","access_level":"public","create_time":"$D2020-04-13T18:32:24.321Z","update_time":"$D2020-04-15T10:36:01.872Z","view_time":null,"first_public_time":"$D2020-04-15T09:05:10.729Z","has_unpublished_edits":null,"fork":{"id":"b08e18119d9f056f","slug":"polynomial-number-method","title":"01. Polynomial Number Method","owner":{"id":"12ed84ab2a5fb1d1","login":"andrzejq","name":"Andrzej Kubaszek"}},"stars":0,"starred":false,"owner":{"type":"team","id":"12ed84ab2a5fb1d1","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":"starter_2024"},"version":513,"publish_version":513,"role":null,"authored":false,"authors":[{"type":"individual","id":"a26fa75e78b968fe","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":null}],"members":[{"type":"individual","id":"a26fa75e78b968fe","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"01. Polynomial Number Method (pyPN)","cells":[{"id":168,"value":"md`# 01. Polynomial Number Method (pyPN)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"html`\n\n $\"PN-Signals\"$ \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":173,"value":"md`\nA polynomial number is generalised number. Digits of this number are elements of an arbitrary field, for example real numbers. The polynomial numbers in the transient analysis play similar role as complex numbers in AC analysis - these numbers allow to compute a solution of differential equations in the algebraic manner. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":186,"value":"md`\nThe polynomial number can correspond one to one to a function ${tex`f(t)`} or to a sequence ${tex`\\{f_k\\}`}.\n\n\n![PN-RN](https://raw.githubusercontent.com/andrzejQ/Polynomial_Numbers.ts/master/img/PN-RN_.png)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"md`\nAs well PN operations as PN functions have easy computer implementation and are analogous to the floating-point arithmetic:\n\n\n ________ R _________ ______________ PN ___________________\n \n a = 5.3 2 | a = (~-3.3~,-5.0~2.1~)\n b = 2.1 | b = (~-0.1~,1.0~)\n * ------------- | * ------------------------------\n 5 3 2 | (~-3.3~,-5.0~2.1~)\n 1 0 6 4 | (~0.33~,0.5~-0.21~)\n a * b ========= | a * b ==========================\n 1 1.1 7 2 | (~0.33~,-2.8~-5.21~2.1~)\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":159,"value":"md`\n\nThe polynomial number method refers to the computer implementation of some operational calculi. The main advantage of the PN method is unified numerical representation of transient signals; therefore, formulas and algorithms used for AC signals can be efficiently applied in the transient domain. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"html`\n\n $\"PN-calulator\"$ `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"{pyPN`\nx = PolyNum('(~-3.3~,-5.0~2.1~)') # <- Edit here\ny = PolyNum('(~-0.1~,1.0~)') # <- Edit here and press [Shift+Enter]\nxy = x * y\ny3 = y**3\n\n# window.globalVarJS\nwindow._ans = f'''\nx * y = {x} * {y} = {xy}\ny**3 = {y3}\n\nTry it (python): '''\n`; return window._ans\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":79,"value":"import {pyPN} from \"@andrzejq/pnlib-brython-python-source\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":135,"value":"import {LinksPN} from \"@andrzejq/polynomial-number-pn-class\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":480,"value":"'TO DO...'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"LinksPN","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2e:"$2d:body"