Attachment 'quickref-linalg-tr.tex'
Downloadlatex error! exitcode was 1 (signal 0), transscript follows: This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=latex) entering extended mode (./latex_196db71385b281e88596f68b95fb50851f88d04e_p.tex LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 2 languages loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty (/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def (/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu))) No file latex_196db71385b281e88596f68b95fb50851f88d04e_p.aux. ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.18 \documentclass {article} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.19 \usepackage {graphicx} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.20 \usepackage [landscape]{geometry} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.21 \usepackage [pdftex]{color} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.22 \usepackage {url} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.23 \usepackage {multicol} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.24 \usepackage {amsmath} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.25 \usepackage {amsfonts} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.44 \usepackage [utf8]{inputenc} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.46 \usepackage [T1]{fontenc} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.48 \begin{document} ! LaTeX Error: Environment multicols* undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.49 \begin{multicols*} {3} ! Undefined control sequence. <recently read> \url l.56 \url {http://wiki.sagemath.org/quickref}\\ ! Undefined control sequence. \warn ->\bf \color {red} l.68 {\warn Uyarı}: Bir vektörün ilk indisi $0$'dır.\\ ! Undefined control sequence. \ex ->\color {blue} l.70 {\ex \verb!u = vector(QQ, [1, 3/2, -1])!} $= (1,\frac{3}{2},-1) \in \mat... ! Undefined control sequence. l.70 ..., -1])!} $= (1,\frac{3}{2},-1) \in \mathbb {Q}^3$ \\ ! Undefined control sequence. \ex ->\color {blue} l.71 {\ex \verb!v = vector(QQ, {2:4, 95:4, 210:0})!}\\ ! Undefined control sequence. \ex ->\color {blue} l.78 {\ex \verb!u = vector(QQ, [1, 3/2, -1])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.79 {\ex \verb!v = vector(ZZ, [1, 8, -2])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.81 {\ex \verb!2*u - 3*v!} doÄŸrusal bileÅŸim\\ ! Undefined control sequence. \ex ->\color {blue} l.82 {\ex \verb!u.dot_product(v)!} \\ ! Undefined control sequence. \ex ->\color {blue} l.83 {\ex \verb!u.dot_product(v)!} iç çarpım\\ ! Undefined control sequence. \ex ->\color {blue} l.85 {\ex \verb!u.cross_product(v)!} sıralama: \verb!u!$\times$\verb!v!\\ ! Undefined control sequence. \ex ->\color {blue} l.87 {\ex \verb!u.inner_product(v)!} u'nun anasından gelen iç çarpım\\ ! Undefined control sequence. \ex ->\color {blue} l.89 {\ex \verb!u.pairwise_product(v)!} $=(u_0v_0, u_1v_1, u_2v_2, \ldots)$ \\ ! Undefined control sequence. \ex ->\color {blue} l.91 {\ex \verb!u.norm() == u.norm(2)!} Öklid normu\\ ! Undefined control sequence. \ex ->\color {blue} l.93 {\ex \verb!u.norm(1)!} kutu içeriklerinin toplamı\\ ! Undefined control sequence. \ex ->\color {blue} l.95 {\ex \verb!u.norm(Infinity)!} en büyük kutu içeriÄŸi\\ ! Undefined control sequence. \ex ->\color {blue} l.97 {\ex \verb!A.gram_schmidt()!} \verb!A! matrisinin satırlarını dönüÅ... ! Undefined control sequence. \warn ->\bf \color {red} l.103 {\warn Uyarı}: Satır ve sütunların isimlendirilmesi 0'dan baÅŸlar\\ ! Undefined control sequence. \ex ->\color {blue} l.104 {\ex \verb!A = matrix(ZZ, [[1,2],[3,4],[5,6]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.107 {\ex \verb!B = matrix(QQ, 2, [1,2,3,4,5,6])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.110 {\ex \verb!C = matrix(CDF, 2, 2, [[5*I, 4*I], [I, 6]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.114 {\ex \verb!Z = matrix(QQ, 2, 2, 0)!} sıfır matris\\ ! Undefined control sequence. \ex ->\color {blue} l.115 {\ex \verb!D = matrix(QQ, 2, 2, 8)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.119 {\ex \verb!I = identity_matrix(5)!} $5\times 5$-lik birim matris\\ ! Undefined control sequence. \ex ->\color {blue} l.120 {\ex \verb!J = jordan_block(-2,3)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.123 {\ex \verb!var('x y z'); K = matrix(SR, [[x,y+z],[0,x^2*z]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.126 {\ex \verb!L=matrix(ZZ, 20, 80, {(5,9):30, (15,77):-6})!}\\ Overfull \hbox (211.33492pt too wide) in paragraph at lines 103--129 | $\OT1/cmr/m/n/12 3 \OMS/cmsy/m/n/12 ^^B \OT1/cmr/m/n/12 3$-l^^?uk ma-tris, k^ ^?o^^Xsegende $\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 2$, k^^?o^^Xsegen^^?ust^^?un de $1$'ler blue[]\OT1/cmtt/m/n/12 var('x y z'); K = matrix(SR, [[x,y+z],[0,x^2* z]]) [1] ! Undefined control sequence. \ex ->\color {blue} l.133 {\ex \verb!u = vector(QQ, [1,2,3])!},\quad{\ex\verb!v = vector(QQ, [1,2... ! Undefined control sequence. \ex ->\color {blue} l.133 ...\verb!u = vector(QQ, [1,2,3])!},\quad{\ex \verb!v = vector(QQ, [1,2]... ! Undefined control sequence. \ex ->\color {blue} l.134 {\ex \verb!A = matrix(QQ, [[1,2,3],[4,5,6]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.135 {\ex \verb!B = matrix(QQ, [[1,2],[3,4]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.136 {\ex \verb!u*A!},\quad ! Undefined control sequence. \ex ->\color {blue} l.137 {\ex \verb!A*v!},\quad ! Undefined control sequence. \ex ->\color {blue} l.138 {\ex \verb!B*A!},\quad ! Undefined control sequence. \ex ->\color {blue} l.139 {\ex \verb!B^6!},\quad ! Undefined control sequence. \ex ->\color {blue} l.141 {\ex \verb!B^(-3)!}'nün tümü geçerlidir.\\ ! Undefined control sequence. \ex ->\color {blue} l.143 {\ex \verb!B.iterates(v, 6)!} $vB^0, vB^1,\dots, vB^5$'u üretir\\ ! Undefined control sequence. \ex ->\color {blue} l.146 {\ex \verb!f(x)=x^2+5*x+3!} tanımlıysa, {\ex\verb!f(B)!} geçerlidir\\ ! Undefined control sequence. \ex ->\color {blue} l.146 ...\verb!f(x)=x^2+5*x+3!} tanımlıysa, {\ex \verb!f(B)!} geçerlidir\\ ! Undefined control sequence. \ex ->\color {blue} l.148 {\ex \verb!B.exp()!} $= e^B = \sum_{k=0}^{\infty}\frac{B^k}{k!}$ ! Undefined control sequence. \ex ->\color {blue} l.153 {\ex \verb!M = MatrixSpace(QQ, 3, 4)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.156 {\ex \verb!A = M([1,2,3,4,5,6,7,8,9,10,11,12])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.162 {\ex \verb!M.basis()!} \verb!M!'nin tabanı \\ ! Undefined control sequence. \ex ->\color {blue} l.163 {\ex \verb!M.dimension()!} \verb!M!'nin boyutu\\ ! Undefined control sequence. \ex ->\color {blue} l.164 {\ex \verb!M.zero_matrix()!} \verb!M!'nin sıfır matrisi ! Undefined control sequence. \ex ->\color {blue} l.170 {\ex \verb!5*A+2*B!} doÄŸrusal bileÅŸim\\ ! Undefined control sequence. \ex ->\color {blue} l.172 {\ex \verb!A.inverse()!}, {\ex\verb!A^(-1)!}, {\ex\verb!~A!} = \verb!A!... ! Undefined control sequence. \ex ->\color {blue} l.172 {\ex\verb!A.inverse()!}, {\ex \verb!A^(-1)!}, {\ex\verb!~A!} = \verb!A!... ! Undefined control sequence. \ex ->\color {blue} l.172 ...b!A.inverse()!}, {\ex\verb!A^(-1)!}, {\ex \verb!~A!} = \verb!A!'nın... ! Undefined control sequence. \ex ->\color {blue} l.176 {\ex \verb!A.transpose()!} $=\verb!A!^t=$ \verb!A!'nın devriÄŸi \\ ! Undefined control sequence. \ex ->\color {blue} l.178 {\ex \verb!A.antitranspose()!} $\verb!A!^t$'nin satır ve sütunları t... ! Undefined control sequence. \ex ->\color {blue} l.180 {\ex \verb!A.adjoint()!} Kofaktörler matrisi\\ ! Undefined control sequence. \ex ->\color {blue} l.182 {\ex \verb!A.conjugate()!} kutu kutu karmaşık eÅŸlenikler\\ ! Undefined control sequence. \ex ->\color {blue} l.184 {\ex \verb!A.restrict(V)!} \verb!A!'nın korunan \verb!V! altuzayına k... ! Undefined control sequence. \warn ->\bf \color {red} l.192 {\warn Uyarı}: İlk satırın indisi 0'dır\\ ! Undefined control sequence. \ex ->\color {blue} l.194 {\ex \verb!A.rescale_row(i,a)!} \verb!a*!(\verb!i! satırı)\\ ! Undefined control sequence. \ex ->\color {blue} l.196 {\ex \verb!A.add_multiple_of_row(i,j,a)!} \verb!a*!(\verb!j! satırı) ... ! Undefined control sequence. \ex ->\color {blue} l.198 {\ex \verb!A.swap_rows(i,j)!} \verb!i! satırıyla \verb!j! satırı y... ! Undefined control sequence. \ex ->\color {blue} l.202 Yeni bir matris için, örn. \ {\ex \verb!B = A.with_rescaled_row(i,a)!} [2] ! Undefined control sequence. \ex ->\color {blue} l.207 {\ex \verb!A.echelon_form()!}, ! Undefined control sequence. \ex ->\color {blue} l.208 {\ex \verb!A.echelonize()!}, ! Undefined control sequence. \ex ->\color {blue} l.209 {\ex \verb!A.hermite_form()!}\\ ! Undefined control sequence. \warn ->\bf \color {red} l.211 {\warn Uyarı}: Sonuçlar, tanım halkasına baÄŸlıdır \\ ! Undefined control sequence. \ex ->\color {blue} l.212 {\ex \verb!A = matrix(ZZ,[[4,2,1],[6,3,2]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.213 {\ex \verb!B = matrix(QQ,[[4,2,1],[6,3,2]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.215 {\ex \verb!A.echelon_form()!} & {\ex\verb!B.echelon_form()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.215 {\ex\verb!A.echelon_form()!} & {\ex \verb!B.echelon_form()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.228 {\ex \verb!A.pivots()!} sütun uzayını geren sütunların indisleri\\ ! Undefined control sequence. \ex ->\color {blue} l.229 {\ex \verb!A.pivot_rows()!} satır uzayını geren satırların indisleri ! Undefined control sequence. \warn ->\bf \color {red} l.235 {\warn Uyarı}: Satır ve sütunların isimlendirilmesi 0'dan baÅŸlar\\ ! Undefined control sequence. \ex ->\color {blue} l.236 {\ex \verb!A.nrows()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.237 {\ex \verb!A.ncols()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.239 {\ex \verb!A[i,j]!} \verb!i!-nci satır ve \verb!j!-nci sütundaki kutu... ! Undefined control sequence. \warn ->\bf \color {red} l.241 \skipin{\warn Uyarı}: DoÄŸru: \verb!A[2,3] = 8!, Yanlış: \verb!A[2]... ! Undefined control sequence. \ex ->\color {blue} l.243 {\ex \verb!A[i]!} \verb!i! satırı (deÄŸiÅŸtirilemez bir Python destes... ! Undefined control sequence. \ex ->\color {blue} l.245 {\ex \verb!A.row(i)!} \verb!i! satırı (Sage vektörü)\\ ! Undefined control sequence. \ex ->\color {blue} l.247 {\ex \verb!A.column(j)!} \verb!j! sütunu (Sage vektörü)\\ ! Undefined control sequence. \ex ->\color {blue} l.249 {\ex \verb!A.list()!} Matris, satır öncelikli dizilmiÅŸ (Python liste... ! Undefined control sequence. \ex ->\color {blue} l.250 {\ex \verb!A.matrix_from_columns([8,2,8])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.253 {\ex \verb!A.matrix_from_rows([2,5,1])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.256 {\ex \verb!A.matrix_from_rows_and_columns([2,4,2],[3,1])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.260 {\ex \verb!A.rows()!} tüm satırlar (destelerden bir liste halinde)\\ ! Undefined control sequence. \ex ->\color {blue} l.262 {\ex \verb!A.columns()!} tüm sütunlar (destelerden bir liste halinde)\\ ! Undefined control sequence. \ex ->\color {blue} l.263 {\ex \verb!A.submatrix(i,j,nr,nc)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.267 {\ex \verb!A[2:4,1:7]!}, {\ex\verb!A[0:8:2,3::-1]!} Python tarzı liste... ! Undefined control sequence. \ex ->\color {blue} l.267 {\ex\verb!A[2:4,1:7]!}, {\ex \verb!A[0:8:2,3::-1]!} Python tarzı liste... ! Undefined control sequence. \ex ->\color {blue} l.273 {\ex \verb!A.augment(B)!} $=[\verb!A|B!]$, \verb!A! matrisi \verb!B!'n... ! Undefined control sequence. \ex ->\color {blue} l.275 {\ex \verb!A.stack(B)!} \verb!A! matrisi \verb!B!'nin üzerine konur\\ ! Undefined control sequence. \ex ->\color {blue} l.277 {\ex \verb!A.block_sum(B)!} \verb!A! solüstte, \verb!B! saÄŸaltta blok... ! Undefined control sequence. \ex ->\color {blue} l.279 {\ex \verb!A.tensor_product(B)!} \verb!B!'nin katları \verb!A!'ya uygu... ! Undefined control sequence. \ex ->\color {blue} l.284 {\ex \verb!A.rank()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.285 {\ex \verb!A.nullity() == A.left_nullity()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.286 {\ex \verb!A.right_nullity()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.287 {\ex \verb!A.determinant() == A.det()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.288 {\ex \verb!A.permanent()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.289 {\ex \verb!A.trace()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.294 {\ex \verb!A.norm() == A.norm(2)!} Öklid normu\\ ! Undefined control sequence. \ex ->\color {blue} l.295 {\ex \verb!A.norm(1)!} en büyük sütun toplamı\\ ! Undefined control sequence. \ex ->\color {blue} l.296 {\ex \verb!A.norm(Infinity)!} en büyük satır toplamı\\ ! Undefined control sequence. \ex ->\color {blue} l.297 {\ex \verb!A.norm('frob')!} Frobenius normu [3] ! Undefined control sequence. \ex ->\color {blue} l.309 {\ex \verb!.is_zero()!} (sıfır mı?), ! Undefined control sequence. \ex ->\color {blue} l.310 {\ex \verb!.is_one()!} (birim matris mi?),\\ ! Undefined control sequence. \ex ->\color {blue} l.311 {\ex \verb!.is_scalar()!} (birimin katı mı?), ! Undefined control sequence. \ex ->\color {blue} l.312 {\ex \verb!.is_square()!},\\ ! Undefined control sequence. \ex ->\color {blue} l.313 {\ex \verb!.is_symmetric()!}, ! Undefined control sequence. \ex ->\color {blue} l.314 {\ex \verb!.is_invertible()!}, ! Undefined control sequence. \ex ->\color {blue} l.315 {\ex \verb!.is_nilpotent()!} ! Undefined control sequence. \ex ->\color {blue} l.321 {\ex \verb!A.charpoly('t')!} $=\det(\verb!t! - \verb!A!)$ (varsayılan ... ! Undefined control sequence. \ex ->\color {blue} l.322 {\ex \verb! A.characteristic_polynomial() == A.charpoly()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.324 {\ex \verb!A.fcp('t')!} çarpanlarına ayrılmış karakteristik polinom\\ ! Undefined control sequence. \ex ->\color {blue} l.326 {\ex \verb!A.minpoly()!} minimum polinom\\ ! Undefined control sequence. \ex ->\color {blue} l.327 {\ex \verb! A.minimal_polynomial() == A.minpoly()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.329 {\ex \verb!A.eigenvalues()!} ÖzdeÄŸerlerin listesi (sırasız, katlıl... ! Undefined control sequence. \ex ->\color {blue} l.337 {\ex \verb!A.eigenvectors_left()!} vektörler solda (saÄŸ $\to $\verb!_... ! Undefined control sequence. \ex ->\color {blue} l.349 {\ex \verb!A.eigenmatrix_right()!} vektörler saÄŸda \verb!_left! too\\ ! Undefined control sequence. \warn ->\bf \color {red} l.359 {\warn Önemli}: Bu yöntemler, uygun halkalarda tanımlıdır.\\ ! Undefined control sequence. \ex ->\color {blue} l.366 {\ex \verb!A.jordan_form(transformation=True)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.377 {\ex \verb!A.smith_form()!} üç matris verir:\\ ! Undefined control sequence. \ex ->\color {blue} l.388 {\ex \verb!A.LU()!} üç matris verir:\\ ! Undefined control sequence. \ex ->\color {blue} l.399 {\ex \verb!A.QR()!} iki matris verir:\\ ! Undefined control sequence. \ex ->\color {blue} l.410 {\ex \verb!A.SVD()!} üç matris verir:\\ ! Undefined control sequence. \ex ->\color {blue} l.416 {\ex \verb!A.symplectic_form()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.417 {\ex \verb!A.hessenberg_form()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.418 {\ex \verb!A.cholesky()!}\par [4] ! Undefined control sequence. \ex ->\color {blue} l.427 {\ex \verb!A.solve_right(B)!}, {\ex\verb!A.solve_left(B)!} sırasıyla ... ! Undefined control sequence. \ex ->\color {blue} l.427 {\ex\verb!A.solve_right(B)!}, {\ex \verb!A.solve_left(B)!} sırasıyla ... ! Undefined control sequence. \ex ->\color {blue} l.429 {\ex \verb!A = matrix(QQ, [[1,2],[3,4]])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.430 {\ex \verb!b = vector(QQ, [3,4])!}\\ ! Undefined control sequence. \ex ->\color {blue} l.431 ...için \verb!A*x = b!'nin çözümü {\ex \verb!A\b!}$=\verb!A!^{-1}... ! Undefined control sequence. \ex ->\color {blue} l.431 ...x\verb!A\b!}$=\verb!A!^{-1}\verb!b!=${\ex \verb!(-2, 5/2)!}'tir. Overfull \hbox (11.95332pt too wide) in paragraph at lines 427--432 []\OT1/cmr/m/n/12 blue[]\OT1/cmtt/m/n/12 A.solve_right(B)\OT1/cmr/m/n/12 , blue []\OT1/cmtt/m/n/12 A.solve_left(B) \OT1/cmr/m/n/12 s^^Pras^^Pyla []\OT1/cmtt/m/ n/12 A*X = B | \OT1/cmr/m/n/12 ve []\OT1/cmtt/m/n/12 X*A = B ! Undefined control sequence. \ex ->\color {blue} l.444 {\ex \verb!U = VectorSpace(QQ, 4)!} kesirler üstünde 4 boyutlu uzay\\ ! Undefined control sequence. \ex ->\color {blue} l.445 {\ex \verb!V = VectorSpace(RR, 4)!} ``cisim'' 53-bit hassas gerçeller\\ ! Undefined control sequence. \ex ->\color {blue} l.446 {\ex \verb!W = VectorSpace(RealField(200), 4)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.448 {\ex \verb!X = CC^4!} 4-boyutlu, 53-bit hassas karmaşıklar\\ ! Undefined control sequence. \ex ->\color {blue} l.449 {\ex \verb!Y = VectorSpace(GF(7), 4)!} sonlu doÄŸrusal uzay\\ ! Undefined control sequence. \ex ->\color {blue} l.450 \skipin{\ex \verb!Y.finite()!} sorusu DoÄŸru (\verb!True!) yanıtı ver... ! Undefined control sequence. \ex ->\color {blue} l.451 \skipin{\ex \verb!len(Y.list())!} $=7^4=2401=$ \verb!Y!'nin üye sayısı ! Undefined control sequence. \ex ->\color {blue} l.465 {\ex \verb!V.dimension()!} \verb!V!'nin boyutu\\ ! Undefined control sequence. \ex ->\color {blue} l.466 {\ex \verb!V.basis()!} \verb!V!'nin tabanı\\ ! Undefined control sequence. \ex ->\color {blue} l.467 {\ex \verb!V.echelonized_basis()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.468 {\ex \verb!V.has_user_basis()!} kullanıcı \verb!V! için bir taban v... ! Undefined control sequence. \ex ->\color {blue} l.469 {\ex \verb!V.is_subspace(W)!} \verb!W!, \verb!V!'nin altuzayı mı?\\ ! Undefined control sequence. \ex ->\color {blue} l.470 {\ex \verb!V.is_full()!} modül olarak, rank mertebeye eÅŸit mi?\\ ! Undefined control sequence. \ex ->\color {blue} l.471 {\ex \verb!Y = GF(7)^4!},\quad{\ex\verb!T = Y.subspaces(2)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.471 {\ex\verb!Y = GF(7)^4!},\quad{\ex \verb!T = Y.subspaces(2)!}\\ ! Undefined control sequence. \ex ->\color {blue} l.494 {\ex \verb!span([v1,v2,v3], QQ)!} \verb!v1,v2,v3!'ün gerdiÄŸi altuzay... ! Undefined control sequence. \ex ->\color {blue} l.499 {\ex \verb!A.left_kernel() == A.kernel()!} saÄŸ yan için \verb!right_!\\ ! Undefined control sequence. \ex ->\color {blue} l.500 {\ex \verb!A.row_space() == A.row_module()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.501 {\ex \verb!A.column_space() == A.column_module()!}\\ ! Undefined control sequence. \ex ->\color {blue} l.502 {\ex \verb!A.eigenspaces_right()!} vektörler saÄŸda, sol için \verb!_... [5] ! Undefined control sequence. \ex ->\color {blue} l.506 {\ex \verb!V.quotient(W)!} $= \verb!V!/ \verb!W! =$ \verb!V!'nin \verb... ! Undefined control sequence. \ex ->\color {blue} l.507 {\ex \verb!V.intersection(W)!} $= \verb!V! \cap \verb!W! =$ \verb!V!'ni... ! Undefined control sequence. \ex ->\color {blue} l.508 {\ex \verb!V.direct_sum(W)!} $= \verb!V! \oplus \verb!W! =$ \verb!V! il... ! Undefined control sequence. \ex ->\color {blue} l.509 {\ex \verb!V.subspace([v1,v2,v3])!} %% BURAYA ! Undefined control sequence. \warn ->\bf \color {red} l.522 {\warn Not:} Algoritmalar, nesnelerin temsil ÅŸekline göre deÄŸiÅŸir\\ ! Undefined control sequence. \ex ->\color {blue} l.526 {\ex \verb!.is_dense()!} yoÄŸun mu?, {\ex\verb!.is_sparse()!} seyrek mi?\\ ! Undefined control sequence. \ex ->\color {blue} l.526 {\ex\verb!.is_dense()!} yoÄŸun mu?, {\ex \verb!.is_sparse()!} seyrek mi?\\ ! Undefined control sequence. \ex ->\color {blue} l.527 {\ex \verb!A.sparse_matrix()!} \verb!A!'nın seyrek temsili\\ ! Undefined control sequence. \ex ->\color {blue} l.528 {\ex \verb!A.dense_rows()!} (yoÄŸun) satır vektörleri olarak \verb!A!\\ ! Undefined control sequence. \warn ->\bf \color {red} l.557 {\warn Not:} Farklı halkalar üzerinde farklı algoritmalar kullanıl... ! Undefined control sequence. \ex ->\color {blue} l.558 {\ex \verb!<nesne>.base_ring(R)!} vektör, matris gibi bir \verb!nesne! \\ ! Undefined control sequence. \ex ->\color {blue} l.560 {\ex \verb!<nesne>.change_ring(R)!} vektör, matris gibi bir \verb!nesne! ! Undefined control sequence. \ex ->\color {blue} l.562 {\ex \verb!R.is_ring()!} halka mı? ,\quad{\ex\verb!R.is_field()!} cis... ! Undefined control sequence. \ex ->\color {blue} l.562 ...\verb!R.is_ring()!} halka mı? ,\quad{\ex \verb!R.is_field()!} cisi... ! Undefined control sequence. \ex ->\color {blue} l.563 {\ex \verb!R.is_integral_domain()!},\quad{\ex\verb!R.is_exact()!} ! Undefined control sequence. \ex ->\color {blue} l.563 {\ex\verb!R.is_integral_domain()!},\quad{\ex \verb!R.is_exact()!} ! Undefined control sequence. \ex ->\color {blue} l.566 \skipin{\ex \verb!ZZ!}\quad tamsayılar, halka\\ ! Undefined control sequence. \ex ->\color {blue} l.567 \skipin{\ex \verb!QQ!}\quad kesir sayılar, cisim\\ ! Undefined control sequence. \ex ->\color {blue} l.568 \skipin{\ex \verb!QQbar!}\quad cebirsel cisim, kayıpsız\\ ! Undefined control sequence. \ex ->\color {blue} l.569 \skipin{\ex \verb!RDF!}\quad real double field, kayıpsız\\ ! Undefined control sequence. \ex ->\color {blue} l.570 \skipin{\ex \verb!RR!}\quad 53-bit hassas gerçeller, kayıplı\\ ! Undefined control sequence. \ex ->\color {blue} l.571 \skipin{\ex \verb!RealField(400)!}\quad 400-bit hassas gerçeller, kayÄ... ! Undefined control sequence. \ex ->\color {blue} l.572 \skipin{\ex \verb!CDF!,\quad\verb!CC!,\quad\verb!ComplexField(400)!}\qu... ! Undefined control sequence. \ex ->\color {blue} l.573 \skipin{\ex \verb!RIF!}\quad gerçel aralık cismi\\ ! Undefined control sequence. \ex ->\color {blue} l.574 \skipin{\ex \verb!GF(2)!}\quad mod 2, cisim, özel algoritmalar\\ ! Undefined control sequence. \ex ->\color {blue} l.575 \skipin{\ex \verb!GF(p) == FiniteField(p)!}\quad \verb!p! asal, sonlu c... ! Undefined control sequence. \ex ->\color {blue} l.576 \skipin{\ex \verb!Integers(6)!}\quad mod 6'da tamsayılar, yalnızca ha... ! Undefined control sequence. \ex ->\color {blue} l.577 \skipin{\ex \verb!CyclotomicField(7)!}\quad 1'in 7. kökleri eklenmiÅŸ ... ! Undefined control sequence. \ex ->\color {blue} l.578 \skipin{\ex \verb!QuadraticField(-5, 'x')!}\, kesirlere \verb!x=!$\sqrt... ! Undefined control sequence. \ex ->\color {blue} l.579 \skipin{\ex \verb!SR!}\quad simgesel ifadeler halkası [6] ! LaTeX Error: \begin{document} on input line 48 ended by \end{multicols*}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.603 \end{multicols*} [7] (./latex_196db71385b281e88596f68b95fb50851f88d04e_p.aux) ) (\end occurred inside a group at level 1) ### semi simple group (level 1) entered at line 48 (\begingroup) ### bottom level (see the transcript file for additional information) Output written on latex_196db71385b281e88596f68b95fb50851f88d04e_p.dvi (7 pages , 18260 bytes). Transcript written on latex_196db71385b281e88596f68b95fb50851f88d04e_p.log.
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