From d0658531b68f9f1253eb6d617e5562d04982628d Mon Sep 17 00:00:00 2001 From: fanasina Date: Sun, 28 Jun 2026 20:23:54 +0200 Subject: [PATCH] update: finalize conditions and formulas transposition --- onedimensiontensor.synctex.gz | Bin 0 -> 240424 bytes onedimensiontensor.tex | 63 ++++++++++++++++++++++++++++++++++ 2 files changed, 63 insertions(+) create mode 100644 onedimensiontensor.synctex.gz diff --git a/onedimensiontensor.synctex.gz b/onedimensiontensor.synctex.gz new file mode 100644 index 0000000000000000000000000000000000000000..1ff8c7b43a6ff534a8763bce14adf0e0840753c3 GIT binary patch literal 240424 zcmV*CKyAMtiwFP!000006Rf>ilU}!$CHAgg(G`&o$q1^1dB|7$#Se~tu-nlNMTLW+ zD2h%=lu4@0TNVA^do3JH2OH2f4uqp;g2^z{I4J1{`LF2KfZka0r(%jy!-n9 zeEj3x&mVsO^6rn%A3y!@uRk1r;xF(yi2n*y5At z-hKM;R!-5+mfJ}(^Th0iZ#>YmsgRXAG*&Mj;0LRM$2WdD{{H@#Px#bd=W+Go;XX6^q4N9f=U&kl5BUv0 zJ25mb9QbeFeERLfXMFQ#e)%tde3?4LJbU0*ULU@^EB~2!yilya`{S?Q!QuD*%gpPA zpD9J#&zaK;NB+bKf1cXtg#v!!gdUw4y->JMjDGq&i!1Z&u`d{X{PR?!XOH#H z2#UD0(XXd&d-fRbd?;i-_g^Mn_JzZH=Joj>zyCC|dg171BYpY!5ntGUo4LJkoFANk zoh7M#;Q*hi^y}w$U;g@Y=JmoM{_&@GpML)E?(v7Wu;AW(`s3p~%IynB`JeB9fov+8 z;^*Jq{NvrHAHIBe{EwO83r9N{Lj8PrdvL>_GqV?tcrv5u@!`vdcc1y!r?;oBe6frd z4Ee|RZ$JM2`^P^fL+ zNaOSU+h5*~df|`8?}c-u^TROv;m@CcSw`FoRRg>8^FN?FfA9T?Kj+W=rm3-ExeQ|e z_ooJY3(5AI=7wPV+lQY%z4`QyUq1W>iTmznQOb+`g-xSOW57Rq&fIR~@5OlV&z?a~ za6V)v3z)gT*umIy|NQZnFMrYyT-*7@j>n$=pPxQ{`S|wZZ-V~|=iXQF`1q;*nAZ|s zIO|R_;b1lmh8J38T~N{JIGFwRrF~)erfIej@Jq{uZ<=StoW(D{Z~8iX)0~<)auy4& z-!!vku7AGy^!eQu<%WjYR|fKq$uEMMSpz$^69U)@)N#k*6s`W>+_rUazcI6gp~z+ ze*5vyccP8bKS`%H#r*|pT$J%mGgg-I1#HmHARu0wlO%rxMieMnVefRnEhda%2M8Z`tzj@E%-^PHSLT2I_E9L7{0*z2#q9g?;U}&D z{Nreo-~asn-;X`@@74FgPmW&xhSkyA1?cZ}nhW^5E2h7k9Mk*_%RzFDW#aeu7fN@l zHd?)K_dqz4(`Kdmr@N+FebZDE{UX?Y(=?OI_s1H(;QmeX>{$7#m9EQRoNB+q|N3ns zNwxYm19zRyX!lPazDn-jq#!p})(`vgk;;GbO)s2PYClh-@r5(+ zI1=#7mtRkNkXn7y#CvW#?2Qxs{IeQQji9RnzGH z3J+hu^vK9>_NO;*A5qr$O|Bkmo*?-roF#kn*Qn>SC-hrp|N7;a5x+lv`0&H$zyAEQ ztU&Xx&hUkE_1&MJG3|f;<@-M$-;Y1avdnz4=!Mg^{1-L;<-^3ZYsCAX{6s$g^{+2vgerdbzrT6^$A@1&ye;k_^|1Qxzy0w6g?#tl z|I2^<<(JRzzC5V!{_pYY|5Ez&%fom70__$2cmJus`%%B9cyiGOlfr9nwX+sJvQ;6Q zVD)R4oQf*D*Xq0bGq(PGP_OZCW26@HeIu)taK=5ZoYK{;#xr+@IR{u(8X+wiM3oi zpw4+^ydOy9G$Fsn2RZLAz{UofqkA2c^_Cy~eh2&RYoU7Oz00ao4{T7`;-5}^Rnd`E zS7zanLO|!Zg-2FsjkscA(J8N@735%S&MOZz8$R3#CN@UxZCKF`0t5qeMZ4^+7xmNL zfVHe38qZ}}!H~60vVzh0oMZ)a2stFPpp8=62dfq|29C4Y*cGi!$|>p&SCJlu%f+licVf*K#0#tDR`5_=j5ogH7jqc6k0p1ysdF4RIT;4 z;A@p%>usHl3X~P?ytB@%J#Ss|n33x^v0hnx=~{2h7MJ4Gmyea~&<{HH`IVH8gVi|^ zGX;~War7)CD5g=a+!lz_&@(sb#K@HmItV5^X zfvN@d>p=}ksUWZm_5DG`7v&rm4$(x1dADFABvOP(IAb9RQ$#nNu^2-rP%l`B1T>*p zD*>MejQv^*v`fxbudHF+pcS27zE6-V69cj5jaktvx$-vX9tZugGKm2-i7Ofd9Yv-U z4H0Bql;osyvTLhqhcCx0U(rw;F+0&z9`F=JQzfgQ_|l3_-f5J&e*8+VOwg4XQn-`v z&txC7_Sr&oK!#(4+5kb6UuS%4?kp@+gwhS$Su`?~u7iJKBFqf?8nOwWQ-?lb0a62# zxWW!)gak;_jE)Hl+m-y_f-{gt&@VQt&X!#bB{Fh%w&>TWf?C;ja-s=jD9;iGZK-q| zY^j&Bi46v}uWGwPaHGxA+Q0_-I%%7iUNXi9%s029tww@zOLuf~`)JL!!nogbhp|qR z`}%>Me6u@HTMt2}r|xL^(fwBEr`p{WeVk>xLsJDE*HJRax7*!8;bOF(+WoF3VV=g| z*9P{Or^vK6a8L?@PV`c+kl1FOOD2S30<35lbZDbhkeCGP0^hUDJVCBZ5{Hr(UERrO zrQj`83q{UrYa>MNXpod37GRfG*l6brJ&g8U>jsq(brz*9Lt=tT3#FP}Zg z8nVZLU;})EHl5mcqv;i=#so+YD2Cd~{r?Ns81_yi)=>NtTvnPimi+#YfgW2Fuj6j9n zHOeiFaza;FH)_b-@!o(v+BVevklGUZ;9FRL5* ziQ2E361X!8E{(-i~XgrhwA&(mog_@B-u7Y#co7xs}|+%Tn?}eo#X0 zU@F6yImsOdQ)H1l(1e(>4P0cJr!;~*)}8vbP+_ys6j`WH+!^y>;ea84xn>t^#K5J^ za>hmoj07=##-^eqS8VcJIa;wA1HlHB1v$afMU$R+Kz61aVW}@@=y}YzB+wbwcM!ZG zXDNYJvh~r%ur?h9kEZLm@OG5tUNA{U!{i%9J{}$0`n>flisu?mD%@mx9TBOIhzwgT z8Gkh*=!!=HUS09{;L+hQI~t;t4r=6Lo9Wa83j-d`U0AS@i!2xiXRPM30{yQu7;dn( zbfs5x=IW3jL(B!P+$~Hrjq%`CG-V>yrZZdgTLG0K+f| zJe(Sie8E3)!9;EN!1jfL5O@q43{Tnqa7`iSy~M+=g5Fy3uqqt{UJ`VOY1*kPA9O9; zFUX1IyCl8x;dIVU)Zf70wJ<9sK0EZg5qQh_Xr{4zzo&CSDn<);+fod-d9p`mnl%bz zzJT2UcC9L~jTAQv8n}9(Ovx6*&C1F&IvjH-O11TDxTbBm9Pc}>PkW>|=uP{)3OWyo zHpW;kYXGRm>m%q5pTS8=9C(}fM@k&XXSy+BW||DsRc*ct0#l_Z z>IsjWYyXoZdOYY&1@sXN5$B=TDnF6l`xs&hW0WNsE|~{PHF%cn1IRE31r4PEOcM>5 zb5IDr!<%R@TsOt=?DQs@DX_B=c*_NB;|1Pv1r3Hpr{Ax13xm~uF=wbH5xDz!*Gr)$@0v}+8Us{+Xcw76NjN`T*q~}q9baODMS~}E4?jEdYBAuFpj}cTg(mEwNX^Q6nSPm z=nyZkF1Cx4#94S0S$AAt6=qscWpiO|YqUQED=ew(vHK2M8Va)wq=Uer!&=A3IX6%3rYK>88zngp`fbiIH#L{TPeP;2B(EsDp^RvdIy4~$`2)s{ z4m;gd&=C^`&V55uIGpLQRbVFDE{3x*l2R5j=opB(q%yu{~p7;+0f zbLBqT!U7RExip@~}pZQQGXJxa*XP$&{0uOU16s5f2VPL>A zl>GT&YMvYSE8T%3yb)*}6T)^hLIT5srk`BFhkh?9jvM2$ST69T&1YfaCcXJA7_yoh z>}xd#{TbDSuNrdclU~hZ`uVYB;scarR`WVp0<+hU$v$$KjC+nNcwQ&FD-cW-Sl7Bk zN)_w_O>>?&>E!nZ*;(pnfzBD?%&h1D^;U%Q869|fBTeMHJ-IUBhAx*X&P*a_9X;+d z8a|KWsk#MCZLLCD(GX<0EZ3aT82J#1c4`zjF@9Rl?(JFJN7#mipO*mHZNXR1ym`^Z7faVKak!NG`veIf8Xg6QWl zaKF-#%~7DqC7gnTr4!0egpXou?_oZPn8}eO$z5 zn+5mpwu}J52n%IhvqBm<@yOLgeqYD|gS;$F zpV8EV#oRfgVKMWd?21m@5#h9Mm)aKm2>X1XL1 zXh)?RR~mNc-JOOFj#UAf;*F2V=F|>Qif9p z-eHy*o;-n{Io(D<|8rx(W^ao*9h^ijG6WEBRaTJX4bsT4~bXdW<6}qO%gO5bf16332_Xjz9ZZEFi zSH>9^ixxQd)I4_`1>UhsCj6^fcbLQ3r6eogGDavVBR;v<#d8ZU*|^0Ii(&16i4Gey zl;b+WtSC6D{Tw@P)K@2Olbgqb;klWX(O51JCQ)C*GiXU&WrK09OwgjfovwM

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z4?LZpr)ybXW%V>qG-e3>T%g{e?}#o?hSWeALKuKDvO;s#tYm8NbQdTxh z&I?AJ3qIA-vxSK}gVxQI#w1+aW?Rv+Ga@8yns;EP$msV|K?~xcBBeY^Iip&d z<9%s>vL#VaCRHJ36h)ndCI%&tboiN-mx3Rat{7`=P%xqSclt%jcjyLa!6K(bHaGk% f5dDTaE3<}_461TW-k_KmhBPt=GPc=XW3|5lM67N~ literal 0 HcmV?d00001 diff --git a/onedimensiontensor.tex b/onedimensiontensor.tex index 73bda4f..a69793a 100644 --- a/onedimensiontensor.tex +++ b/onedimensiontensor.tex @@ -600,6 +600,69 @@ m-\prod_{l=2}^kd_l&= -\prod_{l=2}^kd_l+ (d_3-1-i_3)\prod_{s=4}d_s+\sum_{j=4}^k(d \end{align*} +\subsection{formulas} +$$m=\sum_{j=1}^ki_j\prod_{l=j+1}^kd_l$$ +if $i_1