fixade lösning 20240822

TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org#

@@ -41,20 +41,19 @@ def H_L_tree(f, p: int, r: int):
 #+end_src
 
 
-#+begin_src sage
-  :session 
-   p = 5
-   k = 4
-   q = p^k
-   R.<x> = ZZ[]
-   f = x^4 + 2*x + 3
-   [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
-   df = f.diff()
-   df, df(3)
+#+begin_src sage :session 
+  p = 5
+  k = 4
+  q = p^k
+  R.<x> = ZZ[]
+  f = x^4 + 2*x + 4
+  [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
+  df = f.diff()
+  df, df(3)
 #+end_src
 
 #+RESULTS:
-: [(0, [0]), (1, [3]), (2, []), (3, []), (4, [])]
+: [(0, [0]), (1, []), (2, []), (3, []), (4, [])]
 : (4*x^3 + 2, 110)
 
 #+begin_src sage :session :results file :file "nu1.png"
@@ -78,17 +77,16 @@ def H_L_tree(f, p: int, r: int):
 
 Parametrisera med lutning, rationell punkt (-1,0)
 
-#+begin_src sage
-  :session
-  var('s,t,x,y')
-  kurva = x^2 + 2*y^2-1
-  linje = y - t*(x+1)
-  soln = solve([kurva,linje],[x,y])
-  soln
-  rp = soln[0]
-  rp
-  soln2 = solve([linje],[t])
-  soln2
+#+begin_src sage :session
+var('s,t,x,y')
+kurva = x^2 + 2*y^2-1
+linje = y - t*(x+1)
+soln = solve([kurva,linje],[x,y])
+soln
+rp = soln[0]
+rp
+soln2 = solve([linje],[t])
+soln2
 #+end_src
 
 #+RESULTS:
@@ -106,12 +104,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) )
 [[file:nu2.png]]
 
 ** U3
-#+begin_src sage :session
-  legendre_symbol(187,23)
-#+end_src
 
-#+RESULTS:
-: 1
 
 ** U4 
 #+begin_src latex
@@ -122,8 +115,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) )
     \]
 #+end_src
 
-#+begin_s
-rc sage :session
+#+begin_src sage :session
 n=20
 [(k,number_of_divisors(k),floor(n/k)) for k in range(1,n+1)]
 
@@ -138,7 +130,6 @@ def w(n):
 #+end_src
 
 #+RESULTS:
-
 #+begin_example
 [(1, 1, 20),
  (2, 2, 10),
@@ -183,8 +174,6 @@ def w(n):
 #+end_example
 
 ** U5
-
-
 #+begin_src latex
 
 #+end_src
@@ -198,8 +187,7 @@ Hur många har
 #+end_export
 
 
-#+begin_src s
-age :session
+#+begin_src sage :session
 p = 23
 a = 11*17
 a
@@ -210,6 +198,9 @@ f = x^2 -23
 f.roots(Integers(187),multiplicities=False)
 f.roots(Integers(11),multiplicities=False)
 f.roots(Integers(17),multiplicities=False)
+
+g = x^2 -187
+g.roots(Integers(23),multiplicities=False)
 #+end_src
 
 #+RESULTS:
@@ -218,6 +209,7 @@ f.roots(Integers(17),multiplicities=False)
 : []
 : [10, 1]
 : []
+: [16, 7]
 
 ** U7
 #+begin_src latex
@@ -240,6 +232,7 @@ r=p/q
 cf = continued_fraction(r)
 cf
 best = cf.convergent(2)
+best
 fel = abs(p/q - best)
 "kedjebråkapprox fel", fel
 
@@ -254,6 +247,7 @@ for j in range(2,q):
 #+RESULTS:
 #+begin_example
 [0; 1, 58, 2]
+58/59
 ('kedjebråkapprox fel', 1/7021)
 2 0.483193277310924 0.0168067226890756 0.000142429853297251
 3 0.316526610644258 0.0168067226890756 0.000142429853297251

TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org

-jansn@jansn19-thinkpad.130192:1724236765
\ No newline at end of file
+jansn@jansn19-thinkpad.315947:1724236765
\ No newline at end of file

TATA54/TENTOR/tenta-TATA54-20240822-losning.log

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+ file:line:error style messages enabled.
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+**tenta-TATA54-20240822-losning.tex
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+LaTeX2e <2022-11-01> patch level 1
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 File: l3backend-pdftex.def 2023-01-16 L3 backend support: PDF output (pdfTeX)
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-=\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1
-/cmr/m/n/10 118$.
+Overfull \hbox (9.70393pt too wide) in paragraph at lines 86--91
+[]\OT1/cmr/bx/n/10 L[]osning: \OT1/cmr/m/n/10 Ked-jebr^^Waksutvecklingen []ar $
+117\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 118 = [0; 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n
+/10 58\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2]$ med kon-ver-gen-ter $0\OML/cmm/m/i
+t/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 =
+\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1/
+cmr/m/n/10 118$.
  []
 
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TATA54/TENTOR/tenta-TATA54-20240822-losning.tex

@@ -36,11 +36,8 @@ Examinator: Jan Snellman}
     x^4 +2x +4 \equiv 0 \mod 625 ?
   \end{displaymath}
 
-  \soln Kalla polynomet för \(f(x)\). Modulo 5 finns den enda lösningen
-  \(x \equiv 3 \mod 5\). Eftersom \(f'(3)=110 \equiv 0 \mod 5\)
-  så lyfter inga eller alla av \(3 + 5s\), \(s=0,1,2,3,4\),
-  till lösningar modulo 25. Eftersom \(f(3)=110 \not \equiv 0\)
-  så finns inga lösningar modulo 25, och alltså inga modulo 625.
+  \soln Kalla polynomet för \(f(x)\). Modulo 5 finns
+  inga lösningar; alltså finns inga lösningar modulo \(5^4\).
 
 \item   Hitta alla rationella punkter på kurvan
    \begin{displaymath}

TATA54/TENTOR/tenta-TATA54-20240822-skiss.org

@@ -46,7 +46,7 @@ def H_L_tree(f, p: int, r: int):
   k = 4
   q = p^k
   R.<x> = ZZ[]
-  f = x^4 + 2*x + 3
+  f = x^4 + 2*x + 4
   [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
   df = f.diff()
   df, df(3)

homepage/sitemap.org

 #+TITLE: Kurshemsida
 
+- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]]
+- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]]
 - [[file:index.org][TATA54 Talteori]]
-- [[file:senaste-nytt.org][senaste-nytt]]
 - [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]]
+- [[file:senaste-nytt.org][senaste-nytt]]
 - [[file:labs/lecture5.org][lecture5]]
 - [[file:labs/lecture4.org][lecture4]]
 - [[file:labs/lecture3.org][lecture3]]
@@ -10,6 +12,4 @@
 - [[file:labs/lecture1.org][lecture1]]
 - [[file:labs/lecture0.org][lecture0]]
 - [[file:labs/kedjebraklab.org][Sagemath-övningar på kedjebråk]]
-- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar på Hensellyft, primitiva rötter, och KRS]]
-- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]]
-- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]]
\ No newline at end of file
+- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar på Hensellyft, primitiva rötter, och KRS]]
\ No newline at end of file

public/sitemap.html

 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-08-22 -->
+<!-- 2024-08-23 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Kurshemsida</title>
@@ -206,9 +206,11 @@
 <header>
 <h1 class="title">Kurshemsida</h1>
 </header><ul class="org-ul">
+<li><a href="newlectures/newlecture.html">Föreläsningar i Talteori</a></li>
+<li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li>
 <li><a href="index.html">TATA54 Talteori</a></li>
-<li><a href="senaste-nytt.html">senaste-nytt</a></li>
 <li><a href="lectures/Henselfaktorisering.html">Henselfaktorisering</a></li>
+<li><a href="senaste-nytt.html">senaste-nytt</a></li>
 <li><a href="labs/lecture5.html">lecture5</a></li>
 <li><a href="labs/lecture4.html">lecture4</a></li>
 <li><a href="labs/lecture3.html">lecture3</a></li>
@@ -217,13 +219,11 @@
 <li><a href="labs/lecture0.html">lecture0</a></li>
 <li><a href="labs/kedjebraklab.html">Sagemath-övningar på kedjebråk</a></li>
 <li><a href="labs/HenselLyftLabHT2023.html">SageMath-övningar på Hensellyft, primitiva rötter, och KRS</a></li>
-<li><a href="newlectures/newlecture.html">Föreläsningar i Talteori</a></li>
-<li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li>
 </ul>
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-08-22</p>
+<p class="date">Created: 2024-08-23</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>