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tomleslie

13821 Reputation

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14 years, 210 days
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These are answers submitted by tomleslie

If I...

tomleslie 13821
May 08 2023
2 0

get rid of all the redundant code, and correct all the syntax errors in your worksheet, then I come up with the attached, which *may* be what you want.

> 

restart; Q[0] := 3; I2[0] := 1; for k from 0 to 8 do Q[k+1] := -(Q[k]+I2[k]+1/factorial(k))/(k+1); I2[k+1] := -(-Q[k]+I2[k])/(k+1) end do; Qt := add(Q[r]*t^r, r = 0 .. 6); plot(Qt, t = 0 .. 3)

3-5*t+t^2+(2/3)*t^3-(7/12)*t^4+(3/20)*t^5-(1/72)*t^6

  

 
> 

``

Download seri.mw

 

Your question...

tomleslie 13821
May 07 2023
1 3

is not completely clear (to me at least!), but maybe(?) the attached does what you want

> 

restart;
L:=[{{0, 1}, {0, 3}, {0, 5}, {0, 7}, {2, 9}}, {{0, 1}, {0, 3}, {0, 5}, {0, 7}, {4, 9}}, {{0, 1}, {0, 3}, {0, 5}, {0, 7}, {6, 9}}, {{0, 1}, {0, 3}, {0, 5}, {0, 7}, {8, 9}}, {{0, 1}, {0, 3}, {0, 5}, {0, 9}, {2, 7}}, {{0, 1}, {0, 3}, {0, 5}, {0, 9}, {4, 7}}, {{0, 1}, {0, 3}, {0, 5}, {0, 9}, {6, 7}}, {{0, 1}, {0, 3}, {0, 5}, {0, 9}, {7, 8}}, {{0, 1}, {0, 3}, {0, 7}, {0, 9}, {2, 5}}, {{0, 1}, {0, 3}, {0, 7}, {0, 9}, {4, 5}}, {{0, 1}, {0, 3}, {0, 7}, {0, 9}, {5, 6}}, {{0, 1}, {0, 3}, {0, 7}, {0, 9}, {5, 8}}, {{0, 1}, {0, 5}, {0, 7}, {0, 9}, {2, 3}}, {{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 4}}, {{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 6}}, {{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 8}}, {{0, 1}, {1, 2}, {1, 4}, {1, 6}, {3, 8}}, {{0, 1}, {1, 2}, {1, 4}, {1, 6}, {5, 8}}, {{0, 1}, {1, 2}, {1, 4}, {1, 6}, {7, 8}}, {{0, 1}, {1, 2}, {1, 4}, {1, 6}, {8, 9}}, {{0, 1}, {1, 2}, {1, 4}, {1, 8}, {3, 6}}, {{0, 1}, {1, 2}, {1, 4}, {1, 8}, {5, 6}}, {{0, 1}, {1, 2}, {1, 4}, {1, 8}, {6, 7}}, {{0, 1}, {1, 2}, {1, 4}, {1, 8}, {6, 9}}, {{0, 1}, {1, 2}, {1, 6}, {1, 8}, {3, 4}}, {{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 5}}, {{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 7}}, {{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 9}}, {{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 3}}, {{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 5}}, {{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 7}}, {{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 9}}, {{0, 1}, {2, 3}, {2, 5}, {2, 7}, {2, 9}}, {{0, 1}, {2, 3}, {3, 4}, {3, 6}, {3, 8}}, {{0, 1}, {2, 5}, {4, 5}, {5, 6}, {5, 8}}, {{0, 1}, {2, 7}, {4, 7}, {6, 7}, {7, 8}}, {{0, 1}, {2, 9}, {4, 9}, {6, 9}, {8, 9}}, {{0, 1}, {3, 4}, {4, 5}, {4, 7}, {4, 9}}, {{0, 1}, {3, 6}, {5, 6}, {6, 7}, {6, 9}}, {{0, 1}, {3, 8}, {5, 8}, {7, 8}, {8, 9}}, {{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 2}}, {{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 4}}, {{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 6}}, {{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 8}}, {{0, 3}, {1, 2}, {1, 4}, {1, 6}, {1, 8}}, {{0, 3}, {1, 2}, {2, 5}, {2, 7}, {2, 9}}, {{0, 3}, {1, 2}, {3, 4}, {3, 6}, {3, 8}}, {{0, 3}, {1, 4}, {2, 3}, {3, 6}, {3, 8}}, {{0, 3}, {1, 4}, {4, 5}, {4, 7}, {4, 9}}, {{0, 3}, {1, 6}, {2, 3}, {3, 4}, {3, 8}}, {{0, 3}, {1, 6}, {5, 6}, {6, 7}, {6, 9}}, {{0, 3}, {1, 8}, {2, 3}, {3, 4}, {3, 6}}, {{0, 3}, {1, 8}, {5, 8}, {7, 8}, {8, 9}}, {{0, 3}, {2, 3}, {3, 4}, {3, 6}, {5, 8}}, {{0, 3}, {2, 3}, {3, 4}, {3, 6}, {7, 8}}, {{0, 3}, {2, 3}, {3, 4}, {3, 6}, {8, 9}}, {{0, 3}, {2, 3}, {3, 4}, {3, 8}, {5, 6}}, {{0, 3}, {2, 3}, {3, 4}, {3, 8}, {6, 7}}, {{0, 3}, {2, 3}, {3, 4}, {3, 8}, {6, 9}}, {{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 5}}, {{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 7}}, {{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 9}}, {{0, 3}, {2, 5}, {3, 4}, {3, 6}, {3, 8}}, {{0, 3}, {2, 5}, {4, 5}, {5, 6}, {5, 8}}, {{0, 3}, {2, 7}, {3, 4}, {3, 6}, {3, 8}}, {{0, 3}, {2, 7}, {4, 7}, {6, 7}, {7, 8}}, {{0, 3}, {2, 9}, {3, 4}, {3, 6}, {3, 8}}, {{0, 3}, {2, 9}, {4, 9}, {6, 9}, {8, 9}}, {{0, 5}, {1, 2}, {1, 4}, {1, 6}, {1, 8}}, {{0, 5}, {1, 2}, {2, 3}, {2, 7}, {2, 9}}, {{0, 5}, {1, 2}, {4, 5}, {5, 6}, {5, 8}}, {{0, 5}, {1, 4}, {2, 5}, {5, 6}, {5, 8}}, {{0, 5}, {1, 4}, {3, 4}, {4, 7}, {4, 9}}, {{0, 5}, {1, 6}, {2, 5}, {4, 5}, {5, 8}}, {{0, 5}, {1, 6}, {3, 6}, {6, 7}, {6, 9}}, {{0, 5}, {1, 8}, {2, 5}, {4, 5}, {5, 6}}, {{0, 5}, {1, 8}, {3, 8}, {7, 8}, {8, 9}}, {{0, 5}, {2, 3}, {3, 4}, {3, 6}, {3, 8}}, {{0, 5}, {2, 3}, {4, 5}, {5, 6}, {5, 8}}, {{0, 5}, {2, 5}, {3, 4}, {5, 6}, {5, 8}}, {{0, 5}, {2, 5}, {3, 6}, {4, 5}, {5, 8}}, {{0, 5}, {2, 5}, {3, 8}, {4, 5}, {5, 6}}, {{0, 5}, {2, 5}, {4, 5}, {5, 6}, {7, 8}}, {{0, 5}, {2, 5}, {4, 5}, {5, 6}, {8, 9}}, {{0, 5}, {2, 5}, {4, 5}, {5, 8}, {6, 7}}, {{0, 5}, {2, 5}, {4, 5}, {5, 8}, {6, 9}}, {{0, 5}, {2, 5}, {4, 7}, {5, 6}, {5, 8}}, {{0, 5}, {2, 5}, {4, 9}, {5, 6}, {5, 8}}, {{0, 5}, {2, 7}, {4, 5}, {5, 6}, {5, 8}}, {{0, 5}, {2, 7}, {4, 7}, {6, 7}, {7, 8}}, {{0, 5}, {2, 9}, {4, 5}, {5, 6}, {5, 8}}, {{0, 5}, {2, 9}, {4, 9}, {6, 9}, {8, 9}}, {{0, 7}, {1, 2}, {1, 4}, {1, 6}, {1, 8}}, {{0, 7}, {1, 2}, {2, 3}, {2, 5}, {2, 9}}, {{0, 7}, {1, 2}, {4, 7}, {6, 7}, {7, 8}}, {{0, 7}, {1, 4}, {2, 7}, {6, 7}, {7, 8}}, {{0, 7}, {1, 4}, {3, 4}, {4, 5}, {4, 9}}, {{0, 7}, {1, 6}, {2, 7}, {4, 7}, {7, 8}}, {{0, 7}, {1, 6}, {3, 6}, {5, 6}, {6, 9}}, {{0, 7}, {1, 8}, {2, 7}, {4, 7}, {6, 7}}, {{0, 7}, {1, 8}, {3, 8}, {5, 8}, {8, 9}}, {{0, 7}, {2, 3}, {3, 4}, {3, 6}, {3, 8}}, {{0, 7}, {2, 3}, {4, 7}, {6, 7}, {7, 8}}, {{0, 7}, {2, 5}, {4, 5}, {5, 6}, {5, 8}}, {{0, 7}, {2, 5}, {4, 7}, {6, 7}, {7, 8}}, {{0, 7}, {2, 7}, {3, 4}, {6, 7}, {7, 8}}, {{0, 7}, {2, 7}, {3, 6}, {4, 7}, {7, 8}}, {{0, 7}, {2, 7}, {3, 8}, {4, 7}, {6, 7}}, {{0, 7}, {2, 7}, {4, 5}, {6, 7}, {7, 8}}, {{0, 7}, {2, 7}, {4, 7}, {5, 6}, {7, 8}}, {{0, 7}, {2, 7}, {4, 7}, {5, 8}, {6, 7}}, {{0, 7}, {2, 7}, {4, 7}, {6, 7}, {8, 9}}, {{0, 7}, {2, 7}, {4, 7}, {6, 9}, {7, 8}}, {{0, 7}, {2, 7}, {4, 9}, {6, 7}, {7, 8}}, {{0, 7}, {2, 9}, {4, 7}, {6, 7}, {7, 8}}, {{0, 7}, {2, 9}, {4, 9}, {6, 9}, {8, 9}}, {{0, 9}, {1, 2}, {1, 4}, {1, 6}, {1, 8}}, {{0, 9}, {1, 2}, {2, 3}, {2, 5}, {2, 7}}, {{0, 9}, {1, 2}, {4, 9}, {6, 9}, {8, 9}}, {{0, 9}, {1, 4}, {2, 9}, {6, 9}, {8, 9}}, {{0, 9}, {1, 4}, {3, 4}, {4, 5}, {4, 7}}, {{0, 9}, {1, 6}, {2, 9}, {4, 9}, {8, 9}}, {{0, 9}, {1, 6}, {3, 6}, {5, 6}, {6, 7}}, {{0, 9}, {1, 8}, {2, 9}, {4, 9}, {6, 9}}, {{0, 9}, {1, 8}, {3, 8}, {5, 8}, {7, 8}}, {{0, 9}, {2, 3}, {3, 4}, {3, 6}, {3, 8}}, {{0, 9}, {2, 3}, {4, 9}, {6, 9}, {8, 9}}, {{0, 9}, {2, 5}, {4, 5}, {5, 6}, {5, 8}}, {{0, 9}, {2, 5}, {4, 9}, {6, 9}, {8, 9}}, {{0, 9}, {2, 7}, {4, 7}, {6, 7}, {7, 8}}, {{0, 9}, {2, 7}, {4, 9}, {6, 9}, {8, 9}}, {{0, 9}, {2, 9}, {3, 4}, {6, 9}, {8, 9}}, {{0, 9}, {2, 9}, {3, 6}, {4, 9}, {8, 9}}, {{0, 9}, {2, 9}, {3, 8}, {4, 9}, {6, 9}}, {{0, 9}, {2, 9}, {4, 5}, {6, 9}, {8, 9}}, {{0, 9}, {2, 9}, {4, 7}, {6, 9}, {8, 9}}, {{0, 9}, {2, 9}, {4, 9}, {5, 6}, {8, 9}}, {{0, 9}, {2, 9}, {4, 9}, {5, 8}, {6, 9}}, {{0, 9}, {2, 9}, {4, 9}, {6, 7}, {8, 9}}, {{0, 9}, {2, 9}, {4, 9}, {6, 9}, {7, 8}}, {{1, 2}, {2, 3}, {2, 5}, {2, 7}, {4, 9}}, {{1, 2}, {2, 3}, {2, 5}, {2, 7}, {6, 9}}, {{1, 2}, {2, 3}, {2, 5}, {2, 7}, {8, 9}}, {{1, 2}, {2, 3}, {2, 5}, {2, 9}, {4, 7}}, {{1, 2}, {2, 3}, {2, 5}, {2, 9}, {6, 7}}, {{1, 2}, {2, 3}, {2, 5}, {2, 9}, {7, 8}}, {{1, 2}, {2, 3}, {2, 7}, {2, 9}, {4, 5}}, {{1, 2}, {2, 3}, {2, 7}, {2, 9}, {5, 6}}, {{1, 2}, {2, 3}, {2, 7}, {2, 9}, {5, 8}}, {{1, 2}, {2, 5}, {2, 7}, {2, 9}, {3, 4}}, {{1, 2}, {2, 5}, {2, 7}, {2, 9}, {3, 6}}, {{1, 2}, {2, 5}, {2, 7}, {2, 9}, {3, 8}}, {{1, 2}, {3, 4}, {4, 5}, {4, 7}, {4, 9}}, {{1, 2}, {3, 6}, {5, 6}, {6, 7}, {6, 9}}, {{1, 2}, {3, 8}, {5, 8}, {7, 8}, {8, 9}}, {{1, 4}, {2, 3}, {2, 5}, {2, 7}, {2, 9}}, {{1, 4}, {2, 3}, {4, 5}, {4, 7}, {4, 9}}, {{1, 4}, {2, 5}, {3, 4}, {4, 7}, {4, 9}}, {{1, 4}, {2, 7}, {3, 4}, {4, 5}, {4, 9}}, {{1, 4}, {2, 9}, {3, 4}, {4, 5}, {4, 7}}, {{1, 4}, {3, 4}, {4, 5}, {4, 7}, {6, 9}}, {{1, 4}, {3, 4}, {4, 5}, {4, 7}, {8, 9}}, {{1, 4}, {3, 4}, {4, 5}, {4, 9}, {6, 7}}, {{1, 4}, {3, 4}, {4, 5}, {4, 9}, {7, 8}}, {{1, 4}, {3, 4}, {4, 7}, {4, 9}, {5, 6}}, {{1, 4}, {3, 4}, {4, 7}, {4, 9}, {5, 8}}, {{1, 4}, {3, 6}, {4, 5}, {4, 7}, {4, 9}}, {{1, 4}, {3, 6}, {5, 6}, {6, 7}, {6, 9}}, {{1, 4}, {3, 8}, {4, 5}, {4, 7}, {4, 9}}, {{1, 4}, {3, 8}, {5, 8}, {7, 8}, {8, 9}}, {{1, 6}, {2, 3}, {2, 5}, {2, 7}, {2, 9}}, {{1, 6}, {2, 3}, {5, 6}, {6, 7}, {6, 9}}, {{1, 6}, {2, 5}, {3, 6}, {6, 7}, {6, 9}}, {{1, 6}, {2, 7}, {3, 6}, {5, 6}, {6, 9}}, {{1, 6}, {2, 9}, {3, 6}, {5, 6}, {6, 7}}, {{1, 6}, {3, 4}, {4, 5}, {4, 7}, {4, 9}}, {{1, 6}, {3, 4}, {5, 6}, {6, 7}, {6, 9}}, {{1, 6}, {3, 6}, {4, 5}, {6, 7}, {6, 9}}, {{1, 6}, {3, 6}, {4, 7}, {5, 6}, {6, 9}}, {{1, 6}, {3, 6}, {4, 9}, {5, 6}, {6, 7}}, {{1, 6}, {3, 6}, {5, 6}, {6, 7}, {8, 9}}, {{1, 6}, {3, 6}, {5, 6}, {6, 9}, {7, 8}}, {{1, 6}, {3, 6}, {5, 8}, {6, 7}, {6, 9}}, {{1, 6}, {3, 8}, {5, 6}, {6, 7}, {6, 9}}, {{1, 6}, {3, 8}, {5, 8}, {7, 8}, {8, 9}}, {{1, 8}, {2, 3}, {2, 5}, {2, 7}, {2, 9}}, {{1, 8}, {2, 3}, {5, 8}, {7, 8}, {8, 9}}, {{1, 8}, {2, 5}, {3, 8}, {7, 8}, {8, 9}}, {{1, 8}, {2, 7}, {3, 8}, {5, 8}, {8, 9}}, {{1, 8}, {2, 9}, {3, 8}, {5, 8}, {7, 8}}, {{1, 8}, {3, 4}, {4, 5}, {4, 7}, {4, 9}}, {{1, 8}, {3, 4}, {5, 8}, {7, 8}, {8, 9}}, {{1, 8}, {3, 6}, {5, 6}, {6, 7}, {6, 9}}, {{1, 8}, {3, 6}, {5, 8}, {7, 8}, {8, 9}}, {{1, 8}, {3, 8}, {4, 5}, {7, 8}, {8, 9}}, {{1, 8}, {3, 8}, {4, 7}, {5, 8}, {8, 9}}, {{1, 8}, {3, 8}, {4, 9}, {5, 8}, {7, 8}}, {{1, 8}, {3, 8}, {5, 6}, {7, 8}, {8, 9}}, {{1, 8}, {3, 8}, {5, 8}, {6, 7}, {8, 9}}, {{1, 8}, {3, 8}, {5, 8}, {6, 9}, {7, 8}}]:
  L1:=ListTools:-MakeUnique([seq( j[1], j in L)]):
  L2:=[seq( [seq(`if`(k[1]=j, convert(k,list), NULL), k in L)], j in L1)]:
  numelems(L2);
#
# Check a few entries in the output list
#
  L2[1];
  L2[2];
  L2[9];

9

  

[[{0, 1}, {0, 3}, {0, 5}, {0, 7}, {2, 9}], [{0, 1}, {0, 3}, {0, 5}, {0, 7}, {4, 9}], [{0, 1}, {0, 3}, {0, 5}, {0, 7}, {6, 9}], [{0, 1}, {0, 3}, {0, 5}, {0, 7}, {8, 9}], [{0, 1}, {0, 3}, {0, 5}, {0, 9}, {2, 7}], [{0, 1}, {0, 3}, {0, 5}, {0, 9}, {4, 7}], [{0, 1}, {0, 3}, {0, 5}, {0, 9}, {6, 7}], [{0, 1}, {0, 3}, {0, 5}, {0, 9}, {7, 8}], [{0, 1}, {0, 3}, {0, 7}, {0, 9}, {2, 5}], [{0, 1}, {0, 3}, {0, 7}, {0, 9}, {4, 5}], [{0, 1}, {0, 3}, {0, 7}, {0, 9}, {5, 6}], [{0, 1}, {0, 3}, {0, 7}, {0, 9}, {5, 8}], [{0, 1}, {0, 5}, {0, 7}, {0, 9}, {2, 3}], [{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 4}], [{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 6}], [{0, 1}, {0, 5}, {0, 7}, {0, 9}, {3, 8}], [{0, 1}, {1, 2}, {1, 4}, {1, 6}, {3, 8}], [{0, 1}, {1, 2}, {1, 4}, {1, 6}, {5, 8}], [{0, 1}, {1, 2}, {1, 4}, {1, 6}, {7, 8}], [{0, 1}, {1, 2}, {1, 4}, {1, 6}, {8, 9}], [{0, 1}, {1, 2}, {1, 4}, {1, 8}, {3, 6}], [{0, 1}, {1, 2}, {1, 4}, {1, 8}, {5, 6}], [{0, 1}, {1, 2}, {1, 4}, {1, 8}, {6, 7}], [{0, 1}, {1, 2}, {1, 4}, {1, 8}, {6, 9}], [{0, 1}, {1, 2}, {1, 6}, {1, 8}, {3, 4}], [{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 5}], [{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 7}], [{0, 1}, {1, 2}, {1, 6}, {1, 8}, {4, 9}], [{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 3}], [{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 5}], [{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 7}], [{0, 1}, {1, 4}, {1, 6}, {1, 8}, {2, 9}], [{0, 1}, {2, 3}, {2, 5}, {2, 7}, {2, 9}], [{0, 1}, {2, 3}, {3, 4}, {3, 6}, {3, 8}], [{0, 1}, {2, 5}, {4, 5}, {5, 6}, {5, 8}], [{0, 1}, {2, 7}, {4, 7}, {6, 7}, {7, 8}], [{0, 1}, {2, 9}, {4, 9}, {6, 9}, {8, 9}], [{0, 1}, {3, 4}, {4, 5}, {4, 7}, {4, 9}], [{0, 1}, {3, 6}, {5, 6}, {6, 7}, {6, 9}], [{0, 1}, {3, 8}, {5, 8}, {7, 8}, {8, 9}]]

  

[[{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 2}], [{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 4}], [{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 6}], [{0, 3}, {0, 5}, {0, 7}, {0, 9}, {1, 8}], [{0, 3}, {1, 2}, {1, 4}, {1, 6}, {1, 8}], [{0, 3}, {1, 2}, {2, 5}, {2, 7}, {2, 9}], [{0, 3}, {1, 2}, {3, 4}, {3, 6}, {3, 8}], [{0, 3}, {1, 4}, {2, 3}, {3, 6}, {3, 8}], [{0, 3}, {1, 4}, {4, 5}, {4, 7}, {4, 9}], [{0, 3}, {1, 6}, {2, 3}, {3, 4}, {3, 8}], [{0, 3}, {1, 6}, {5, 6}, {6, 7}, {6, 9}], [{0, 3}, {1, 8}, {2, 3}, {3, 4}, {3, 6}], [{0, 3}, {1, 8}, {5, 8}, {7, 8}, {8, 9}], [{0, 3}, {2, 3}, {3, 4}, {3, 6}, {5, 8}], [{0, 3}, {2, 3}, {3, 4}, {3, 6}, {7, 8}], [{0, 3}, {2, 3}, {3, 4}, {3, 6}, {8, 9}], [{0, 3}, {2, 3}, {3, 4}, {3, 8}, {5, 6}], [{0, 3}, {2, 3}, {3, 4}, {3, 8}, {6, 7}], [{0, 3}, {2, 3}, {3, 4}, {3, 8}, {6, 9}], [{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 5}], [{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 7}], [{0, 3}, {2, 3}, {3, 6}, {3, 8}, {4, 9}], [{0, 3}, {2, 5}, {3, 4}, {3, 6}, {3, 8}], [{0, 3}, {2, 5}, {4, 5}, {5, 6}, {5, 8}], [{0, 3}, {2, 7}, {3, 4}, {3, 6}, {3, 8}], [{0, 3}, {2, 7}, {4, 7}, {6, 7}, {7, 8}], [{0, 3}, {2, 9}, {3, 4}, {3, 6}, {3, 8}], [{0, 3}, {2, 9}, {4, 9}, {6, 9}, {8, 9}]]

  

[[{1, 8}, {2, 3}, {2, 5}, {2, 7}, {2, 9}], [{1, 8}, {2, 3}, {5, 8}, {7, 8}, {8, 9}], [{1, 8}, {2, 5}, {3, 8}, {7, 8}, {8, 9}], [{1, 8}, {2, 7}, {3, 8}, {5, 8}, {8, 9}], [{1, 8}, {2, 9}, {3, 8}, {5, 8}, {7, 8}], [{1, 8}, {3, 4}, {4, 5}, {4, 7}, {4, 9}], [{1, 8}, {3, 4}, {5, 8}, {7, 8}, {8, 9}], [{1, 8}, {3, 6}, {5, 6}, {6, 7}, {6, 9}], [{1, 8}, {3, 6}, {5, 8}, {7, 8}, {8, 9}], [{1, 8}, {3, 8}, {4, 5}, {7, 8}, {8, 9}], [{1, 8}, {3, 8}, {4, 7}, {5, 8}, {8, 9}], [{1, 8}, {3, 8}, {4, 9}, {5, 8}, {7, 8}], [{1, 8}, {3, 8}, {5, 6}, {7, 8}, {8, 9}], [{1, 8}, {3, 8}, {5, 8}, {6, 7}, {8, 9}], [{1, 8}, {3, 8}, {5, 8}, {6, 9}, {7, 8}]]

 (1)
> 

;
> 

 

Download listlist.mw

Difficult to understand...

tomleslie 13821
May 06 2023
1 1

exactly what you do want because, there is no "animation" anywhere in your worksheet. Maybe the attached will help a little

 

 

 

1. La nature euclidienne de:  "{[[x^(2)+y^(2)=4],[y=z]] "
 

 

 

 

> 

restart
> 

with(plots)
> 

G1 := plot3d(`<,>`(2*cos(t), 2*sin(t), 2*sin(t)), t = -Pi .. Pi, color = "Black", thickness = 4, axes = none); G2 := display(plot3d(`<,>`(-sqrt(2), -sqrt(2), t), t = -6 .. 6, color = "Black", thickness = 4, axes = none), plot3d(`<,>`(sqrt(2), sqrt(2), t), t = -6 .. 6, color = "Black", thickness = 4, axes = none)); G3 := plot3d(`<,>`(2*cos(t), 2*sin(t), 4), t = -Pi .. Pi, color = "Black", thickness = 4, axes = none); L := 6; display([plot3d(`<,>`(2*cos(t), 2*sin(t), s), s = -L .. L, t = -Pi .. Pi, color = "Blue", transparency = .8), plot3d([s, t, t], s = -L .. L, t = -L .. L, color = "red", transparency = .8), G1, G2, G3])

 
 

 

 

 

 

2. La nature euclidienne de:  "{[[x^(2)+y^(2)=4],[x=y]] "
 

 

 

 

> 

display([plot3d(`<,>`(2*cos(t), 2*sin(t), s), s = -L .. L, t = -Pi .. Pi, color = "Blue", transparency = .8), plot3d([t, t, s], s = -L .. L, t = -L .. L, color = "red", transparency = .8), G1, G2, G3])

 
 

 

 

 

3.La nature euclidienne de:  "{[[x^(2)+y^(2)=4],[z=4]] "
 

 

 

 

> 

display([plot3d(`<,>`(2*cos(t), 2*sin(t), s), s = -4 .. 4, t = -Pi .. Pi, color = "Blue", scaling = constrained, transparency = .8), plot3d([s, t, 4], s = -L .. L, t = -L .. L, color = "red", transparency = .8), G1, G2, G3])

 
 

 

 

 

NULL

Download oddPlot.mw

As vv...

tomleslie 13821
May 05 2023
1 0

has demonstrated, the problem is so simple that you don't really need a geometry package, but you can use one if you want to, as in the attached.

> 

  restart:
  with(geometry):
  with(plots):
  point( B, [0,0] ):
  point( C, [10,0] ):
  point(DD, [5,0]):

  intersection( s,
                circle(c1, [B, 6], [x,y]),
                circle(c2, [C, 8], [x,y]),
                [i1, i2]
              ):
  if   coordinates(i1)[2]>0
  then point(A, coordinates(i1))
  else point(A, coordinates(i2))
  fi:
  
  triangle(T, [A, B, C]):
  midpoint(E, B, A):
  midpoint(F, C, A):
  segment(s1, [DD, E]):
  segment(s2, [DD, F]):

  intersection(H,
               line(l3, [C, E]),
               line(l4, [B, F])
              ):

  dist:=simplify(distance(DD, H));

  p1:= draw([ T,
              l3(color=blue),
              l4(color=blue),
              s1(color=green),
              s2(color=green),
              DD(color=black),
              H(color=black)
            ],
            axes=none
            ):
  p2:= textplot( [ [coordinates(A)[], "A", align=above],
                   [coordinates(B)[], "B", align=left],
                   [coordinates(C)[], "C", align=right],
                   [coordinates(DD)[], "D", align=below],
                   [coordinates(E)[], "E", align=left],
                   [coordinates(F)[], "F", align=right],
                   [coordinates(H)[], "H", align=above]
                 ],
                 axes=none,
                 font=[times, roman, 14]
               ):
  display([p1,p2]);
  

5/3

  

 
> 

 

> 

 

Download trivGeom.mw

My $0.02...

tomleslie 13821
April 24 2023
0 0

When using the elementwise operation ('~`), you must have the same number of 'elements'  on each side of the operator. You have a single element (a matrix) on the left side and a list of two elements on the right side. This is never going to work!

You could come up with a "clunky" solution by repeating the same element on the left side, using

pl_translist := evalf([TransMatrix, TransMatrix] .~ ptlist)

which will work, but Acer's mapping solutions are much 'tidier'

Just use...

tomleslie 13821
April 24 2023
1 21

dsolve() with the option 'numeric'  - as in the attached. So far as I know all methods used by Maple to solve BVPs can be classified as 'finite element'

> 

  local gamma:
  local GAMMA:

  odeSystem:= [ (1 + GAMMA)*diff(f(eta), eta$4) - S*(eta*diff(f(eta), eta$3) + 3*diff(f(eta), eta$2)
                +
                diff(f(eta), eta)*diff(f(eta), eta$2) - f(eta)*diff(f(eta), eta$3))
                -
                GAMMA*delta(2*diff(f(eta), eta$2)*diff(f(eta), eta$3)^2 + diff(f(eta), eta$2)^2*diff(f(eta), eta$4))
                -
                M^2*diff(f(eta), eta$2) = 0,

                (1 + (4*R)/3)*diff(theta(eta), eta$2) + Pr*S*(f(eta)*diff(theta(eta), eta)
                -
                eta*diff(theta(eta), eta) + Q*theta(eta)) = 0,

                diff(phi(eta), eta$2) + Sc*S*(f(eta)*diff(phi(eta), eta)
                -
                eta*diff(phi(eta), eta)) - Sc*gamma*phi(eta) = 0
              ]:

  params:= [ S = 0.5, GAMMA = 0.1, delta = 0.1, gamma = 0.1, M = 1,
             Pr = 1, Ec = 0.2, Sc = 0.6, R = 1, Q = 1
           ]:
  bcs :=[ f(0) = 0, (D@@2)(f)(0) = 0, f(1) = 1, D(f)(1) = 0, D(theta)(0) = 0,
          theta(1) = 1, phi(1) = 1, D(phi)(0) = 0
        ]:
 
> 

  with(plots):
  sol:=dsolve( eval( [odeSystem[], bcs[] ], params), numeric);
  odeplot( sol, [eta, f(eta)], eta=0..1);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .0, (2) = .13761679545133373, (3) = .34498164173439616, (4) = .5186818700028772, (5) = .6631755824919455, (6) = .7865103203155236, (7) = .8962952680189267, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 8, {(1, 1) = .0, (1, 2) = 1.4433937317396737, (1, 3) = .0, (1, 4) = -2.333121764948255, (1, 5) = .9711210336114556, (1, 6) = .0, (1, 7) = 1.1163392618484445, (1, 8) = .0, (2, 1) = .19761929156705052, (2, 2) = 1.421209729987723, (2, 3) = -.32375830204564643, (2, 4) = -2.392260734568203, (2, 5) = .9716725996393883, (2, 6) = 0.801340863076986e-2, (2, 7) = 1.1140755243321754, (2, 8) = -0.3287828715461909e-1, (3, 1) = .4817243251385398, (3, 2) = 1.3008434883136388, (3, 3) = -.8482708398270041, (3, 4) = -2.714257299186619, (3, 5) = .9745816070440784, (3, 6) = 0.2002590221467707e-1, (3, 7) = 1.1021602830549697, (3, 8) = -0.8188503410269617e-1, (4, 1) = .6924187029933173, (4, 2) = 1.1103171239033962, (4, 3) = -1.3599018273312409, (4, 4) = -3.2132349822084665, (4, 5) = .9789272904347387, (4, 6) = 0.29996555764223734e-1, (4, 7) = 1.0844381842992008, (4, 8) = -.12199622650773645, (5, 1) = .8369727164823445, (5, 2) = .8783677802907506, (5, 3) = -1.8648151994971516, (5, 4) = -3.8033927793066664, (5, 5) = .9838576171457577, (5, 6) = 0.3824284453448716e-1, (5, 7) = 1.0644511561493029, (5, 8) = -.15452011154869225, (6, 1) = .9298863513249988, (6, 2) = .6178998393102831, (6, 3) = -2.372140723196441, (6, 4) = -4.445722882837911, (6, 5) = .9890086375535491, (6, 6) = 0.4529345604521887e-1, (6, 7) = 1.0437137097072917, (6, 8) = -.1816709009089781, (7, 1) = .9824105305991222, (7, 2) = .3293564404735158, (7, 3) = -2.8969848977175445, (7, 4) = -5.134784677019601, (7, 5) = .9943285639648187, (7, 6) = 0.5163894363658305e-1, (7, 7) = 1.0224610163782957, (7, 8) = -.20544783400660863, (8, 1) = 1.0, (8, 2) = .0, (8, 3) = -3.467970343378204, (8, 4) = -5.895376469857138, (8, 5) = 1.0, (8, 6) = 0.5776651945857268e-1, (8, 7) = 1.0, (8, 8) = -.22770673143200507}, datatype = float[8], order = C_order); YP := Matrix(8, 8, {(1, 1) = 1.4433937317396737, (1, 2) = .0, (1, 3) = -2.333121764948255, (1, 4) = 0.909090909090909e-2, (1, 5) = .0, (1, 6) = 0.5826726201668733e-1, (1, 7) = .0, (1, 8) = -.23921555611038064, (2, 1) = 1.421209729987723, (2, 2) = -.32375830204564643, (2, 3) = -2.392260734568203, (2, 4) = -.8706265199209529, (2, 5) = 0.801340863076986e-2, (2, 6) = 0.5815610862229087e-1, (2, 7) = -0.3287828715461909e-1, (2, 8) = -.23830773107890446, (3, 1) = 1.3008434883136388, (3, 2) = -.8482708398270041, (3, 3) = -2.714257299186619, (3, 4) = -2.2516668049592052, (3, 5) = 0.2002590221467707e-1, (3, 6) = 0.5765337774071753e-1, (3, 7) = -0.8188503410269617e-1, (3, 8) = -.23377780794881264, (4, 1) = 1.1103171239033962, (4, 2) = -1.3599018273312409, (4, 3) = -3.2132349822084665, (4, 4) = -3.514170069502999, (4, 5) = 0.29996555764223734e-1, (4, 6) = 0.5717218544635511e-1, (4, 7) = -.12199622650773645, (4, 8) = -.22783777420049162, (5, 1) = .8783677802907506, (5, 2) = -1.8648151994971516, (5, 3) = -3.8033927793066664, (5, 4) = -4.67320491838056, (5, 5) = 0.3824284453448716e-1, (5, 6) = 0.5703750799602518e-1, (5, 7) = -.15452011154869225, (5, 8) = -.22234200077534186, (6, 1) = .6178998393102831, (6, 2) = -2.372140723196441, (6, 3) = -4.445722882837911, (6, 4) = -5.7586540389806125, (6, 5) = 0.4529345604521887e-1, (6, 6) = 0.5739231946567326e-1, (6, 7) = -.1816709009089781, (6, 8) = -.2180713836396526, (7, 1) = .3293564404735158, (7, 2) = -2.8969848977175445, (7, 3) = -5.134784677019601, (7, 4) = -6.807673541750535, (7, 5) = 0.5163894363658305e-1, (7, 6) = 0.5832564348070064e-1, (7, 7) = -.20544783400660863, (7, 8) = -.21530760475848917, (8, 1) = .0, (8, 2) = -3.467970343378204, (8, 3) = -5.895376469857138, (8, 4) = -7.872659871314089, (8, 5) = 0.5776651945857268e-1, (8, 6) = 0.6e-1, (8, 7) = -.22770673143200507, (8, 8) = -.214285714285714}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .13761679545133373, (3) = .34498164173439616, (4) = .5186818700028772, (5) = .6631755824919455, (6) = .7865103203155236, (7) = .8962952680189267, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 8, {(1, 1) = .0, (1, 2) = -0.25304799779016353e-7, (1, 3) = .0, (1, 4) = -0.4146201060728139e-7, (1, 5) = 0.6642099178776253e-10, (1, 6) = .0, (1, 7) = -0.1579491158740188e-9, (1, 8) = .0, (2, 1) = -0.3794935280955525e-8, (2, 2) = -0.25773773835013586e-7, (2, 3) = -0.6457770455915928e-8, (2, 4) = -0.42741332787261556e-7, (2, 5) = 0.6812660169151781e-10, (2, 6) = 0.1786453605430017e-10, (2, 7) = -0.16219194559467549e-9, (2, 8) = -0.43841559921129475e-10, (3, 1) = 0.11737819871794217e-8, (3, 2) = -0.19548408336688137e-7, (3, 3) = 0.13063141620755076e-7, (3, 4) = -0.29637882669106708e-7, (3, 5) = 0.319027499302564e-10, (3, 6) = 0.27100840068170564e-10, (3, 7) = -0.6764942302099327e-10, (3, 8) = -0.8861830614941501e-10, (4, 1) = 0.10333855462730343e-8, (4, 2) = -0.12598333706491768e-7, (4, 3) = 0.15625192446912097e-7, (4, 4) = -0.1143706411410182e-7, (4, 5) = 0.12948853793328739e-10, (4, 6) = 0.23700176593180382e-10, (4, 7) = -0.20398135871970748e-10, (4, 8) = -0.8565904428857674e-10, (5, 1) = 0.3746705824991127e-9, (5, 2) = -0.8117998927462989e-8, (5, 3) = 0.15954474921128882e-7, (5, 4) = 0.6271929994514497e-9, (5, 5) = 0.6634117733896975e-11, (5, 6) = 0.18224563700374814e-10, (5, 7) = -0.6969588139634506e-11, (5, 8) = -0.7325781989983735e-10, (6, 1) = -0.2586420516396408e-10, (6, 2) = -0.4985304741757289e-8, (6, 3) = 0.16666511083414864e-7, (6, 4) = 0.8635115054594654e-8, (6, 5) = 0.4299750819126624e-11, (6, 6) = 0.1341878516027326e-10, (6, 7) = -0.4134559084822396e-11, (6, 8) = -0.6142811269372842e-10, (7, 1) = -0.14354514375013203e-9, (7, 2) = -0.24203028138466706e-8, (7, 3) = 0.1787205688898178e-7, (7, 4) = 0.14480649784508743e-7, (7, 5) = 0.2630248422989425e-11, (7, 6) = 0.8855383001023343e-11, (7, 7) = -0.31053237369603176e-11, (7, 8) = -0.49986065431972777e-10, (8, 1) = .0, (8, 2) = .0, (8, 3) = 0.1946243199488989e-7, (8, 4) = 0.19107020336419163e-7, (8, 5) = .0, (8, 6) = 0.30639368059718205e-11, (8, 7) = .0, (8, 8) = -0.3584956405964587e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(4.2741332787261556e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [8, 8, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), phi(eta), diff(phi(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(8, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 8, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(8, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 8, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), phi(eta), diff(phi(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 8)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[8] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(4.2741332787261556e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [8, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 8, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(8, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0.}); `dsolve/numeric/hermite`(8, 8, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 8)] end proc, (2) = Array(0..0, {}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), phi(eta), diff(phi(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), phi(eta), diff(phi(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = res[i+1], i = 1 .. 8)] catch: error end try end proc

  

 
> 

 


 

Download odeSol.mw

Well...

tomleslie 13821
April 19 2023
0 1

After the basic syntax errors have been fixed, one still has the problem that in the first integrand 'A' does not depend on 'x'. Hence its derivative wrt to 'x' is 0, so the first integral is always 0. Changing 'A' to 'A(x)', gives the attached
 

> 

restart
> 

D__11*(int((diff(A(x), x, x))*(diff(A(x), x, x)), x = 0 .. a))*(int(B*B, y = 0 .. b))

D__11*(int((diff(diff(A(x), x), x))^2, x = 0 .. a))*B^2*b

 (1)
> 

 


Download intOdd.mw

 

I'm not sure...

tomleslie 13821
April 18 2023
0 0

exacly what you are trying to achieve. The attached worksheet starts with ou two squares, then performs the following transformations

  1. a translation so that the midpoints of the two squares concide
  2. a rotation, so that the diagonals of the two squares coincide
  3. a scaling so that the corners of the two squares conincide
> 

  restart;  
  with(geometry):
  _EnvHorizontalName = 'x':  _EnvVerticalName = 'y':

  point(A, 0, 1):
  point(B, 1, 1):
  point(C, 1, 0):
  point(E, 0, 0):
  square(Sq0, [A, B, C, E]):

  Phi := (1 + sqrt(5))/2:
  point(N, (2 - Phi)/(Phi - 1), 1):
  MakeSquare(Sq1, [N, C, 'diagonal']):

  dsegment
  ( ds1,
    [ midpoint( m2,
                segment(s2, [N, C])
              ),
      midpoint( m1,
                segment(s1, [A, C])
              )
    ]
  ):
  translation( Sq2, Sq1, ds1):

  ang:= simplify
        ( FindAngle
          ( line( l1, [A,C]),
            line( l2, [N,C])
          )
        ):
  rotation( Sq3,
            Sq2,
            ang,
            counterclockwise,
            m1
          ):

  dilatation( Sq4,
              Sq3,
              diagonal(Sq0)/simplify(diagonal(Sq3)),
              m1
            ):

  draw( [ Sq0(color=black),
          Sq1(color=blue),
          Sq2(color=green),                 # Sq1 translated
          Sq3(color=red),                   # Sq2 rotated
          Sq4(color=lightgrey, filled=true) # Sq3 scaled
        ],
        axes=none
      );

 
> 

 

> 

 

Download geoProb.mw

Another way...

tomleslie 13821
April 17 2023
1 1

which actually uses some of Maple's regular expreeion capability
 

> 

  restart:
  with(StringTools):
  sstr1 := "124e34e243e45e56e76f34e45e23ea12e98e34e43";
  RegSplit( "[a-z]+", sstr1);
  parse~([%])[];

"124e34e243e45e56e76f34e45e23ea12e98e34e43"

  

"124", "34", "243", "45", "56", "76", "34", "45", "23", "12", "98", "34", "43"

  

124, 34, 243, 45, 56, 76, 34, 45, 23, 12, 98, 34, 43

 (1)
> 

 


Download strSplit.mw

Several ways to do this...

tomleslie 13821
April 17 2023
0 0

One of the simplest is shown in the attached.

> 

  restart:
  with(LinearAlgebra):
  A := Matrix( [ [1, 3, 9, 2, 3, 7, 1, 1, 5, 4, 7],
                 [7, 5, 5, 4, 9, 3, 4, 5, 3, 5, 3],
                 [5, 2, 1, 6, 5, 4, 2, 9, 6, 6, 6],
                 [2, 4, 1, 9, 5, 1, 1, 2, 1, 1, 7],
                 [1, 9, 2, 3, 2, 9, 8, 2, 2, 7, 3],
                 [5, 5, 3, 7, 2, 1, 5, 2, 7, 8, 3],
                 [2, 2, 1, 7, 8, 7, 8, 2, 1, 4, 5],
                 [8, 9, 6, 4, 9, 4, 1, 5, 4, 2, 5],
                 [5, 7, 4, 5, 3, 2, 8, 3, 6, 2, 6],
                 [6, 7, 8, 9, 9, 9, 8, 4, 8, 9, 3]
               ]
             ):
  LinearSolve( SubMatrix(A, [1..-1], [1, 3..-1]),
               SubMatrix(A, [1..-1], [2])
             );
  entries(%[4], nolist);

Vector(10, {(1) = 9634894/3220003, (2) = 5813279/6440006, (3) = 7777841/6440006, (4) = -7667558/3220003, (5) = 4345665/3220003, (6) = 218052/3220003, (7) = 758435/6440006, (8) = -13225751/6440006, (9) = -1398056/3220003, (10) = -934323/6440006})

  

-7667558/3220003

 (1)
> 

 

Download matLin.mw

Well...

tomleslie 13821
April 12 2023
0 0

adding a simplify() command, makes th result much more compact - whether or not it is what you expect, I have no idea


 

> 

restart; with(LinearAlgebra)
> 

i := 1; w := c[i]*(x/a)^(i+1)*(1-x/a)^2*(y/b)^(i+1)*(1-y/b)^2

1

  

c[1]*x^2*(1-x/a)^2*y^2*(1-y/b)^2/(a^2*b^2)

 (1)
> 

al_eq1 := (1/2)*(int(int(D__11*(diff(w, x, x))^2+2*D__12*(diff(w, x, x))*(diff(w, y, y))+4*D__66*(diff(w, x, y))^2+D__22*(diff(w, y, y))^2-2*q__0*w, x = 0 .. a), y = 0 .. b))

-(7/45)*D__11*c[1]^2*b/a^3+(1/14)*((1/7)*(288*D__12*c[1]^2/(a^8*b^8)+1024*D__66*c[1]^2/(a^8*b^8))*a^7+(1/6)*(-864*D__12*c[1]^2/(a^7*b^8)-3072*D__66*c[1]^2/(a^7*b^8))*a^6+(1/5)*(864*D__11*c[1]^2/(a^8*b^6)+912*D__12*c[1]^2/(a^6*b^8)+3328*D__66*c[1]^2/(a^6*b^8))*a^5+(1/4)*(-1728*D__11*c[1]^2/(a^7*b^6)-384*D__12*c[1]^2/(a^5*b^8)-1536*D__66*c[1]^2/(a^5*b^8))*a^4+(1/3)*(1152*D__11*c[1]^2/(a^6*b^6)+48*D__12*c[1]^2/(a^4*b^8)+256*D__66*c[1]^2/(a^4*b^8))*a^3-120*D__11*c[1]^2/(a^3*b^6))*b^7+(1/12)*((1/7)*(-864*D__12*c[1]^2/(a^8*b^7)-3072*D__66*c[1]^2/(a^8*b^7))*a^7+(1/6)*(2592*D__12*c[1]^2/(a^7*b^7)+9216*D__66*c[1]^2/(a^7*b^7))*a^6+(1/5)*(-576*D__11*c[1]^2/(a^8*b^5)-2736*D__12*c[1]^2/(a^6*b^7)-9984*D__66*c[1]^2/(a^6*b^7))*a^5+(1/4)*(1152*D__11*c[1]^2/(a^7*b^5)+1152*D__12*c[1]^2/(a^5*b^7)+4608*D__66*c[1]^2/(a^5*b^7))*a^4+(1/3)*(-768*D__11*c[1]^2/(a^6*b^5)-144*D__12*c[1]^2/(a^4*b^7)-768*D__66*c[1]^2/(a^4*b^7))*a^3+80*D__11*c[1]^2/(a^3*b^5))*b^6+(1/10)*(-56*D__22*c[1]^2*a/b^8+(1/7)*(912*D__12*c[1]^2/(a^8*b^6)+3328*D__66*c[1]^2/(a^8*b^6)+864*D__22*c[1]^2/(a^6*b^8))*a^7+(1/6)*(-2736*D__12*c[1]^2/(a^7*b^6)-9984*D__66*c[1]^2/(a^7*b^6)-576*D__22*c[1]^2/(a^5*b^8))*a^6+(1/5)*(144*D__11*c[1]^2/(a^8*b^4)+2888*D__12*c[1]^2/(a^6*b^6)+10816*D__66*c[1]^2/(a^6*b^6)+144*D__22*c[1]^2/(a^4*b^8)-2*q__0*c[1]/(a^4*b^4))*a^5+(1/4)*(-288*D__11*c[1]^2/(a^7*b^4)-1216*D__12*c[1]^2/(a^5*b^6)-4992*D__66*c[1]^2/(a^5*b^6)+4*q__0*c[1]/(a^3*b^4))*a^4+(1/3)*(192*D__11*c[1]^2/(a^6*b^4)+152*D__12*c[1]^2/(a^4*b^6)+832*D__66*c[1]^2/(a^4*b^6)-2*q__0*c[1]/(a^2*b^4))*a^3-20*D__11*c[1]^2/(a^3*b^4))*b^5+(1/8)*(112*D__22*c[1]^2*a/b^7+(1/7)*(-384*D__12*c[1]^2/(a^8*b^5)-1536*D__66*c[1]^2/(a^8*b^5)-1728*D__22*c[1]^2/(a^6*b^7))*a^7+(1/6)*(1152*D__12*c[1]^2/(a^7*b^5)+4608*D__66*c[1]^2/(a^7*b^5)+1152*D__22*c[1]^2/(a^5*b^7))*a^6+(1/5)*(-1216*D__12*c[1]^2/(a^6*b^5)-4992*D__66*c[1]^2/(a^6*b^5)-288*D__22*c[1]^2/(a^4*b^7)+4*q__0*c[1]/(a^4*b^3))*a^5+(1/4)*(512*D__12*c[1]^2/(a^5*b^5)+2304*D__66*c[1]^2/(a^5*b^5)-8*q__0*c[1]/(a^3*b^3))*a^4+(1/3)*(-64*D__12*c[1]^2/(a^4*b^5)-384*D__66*c[1]^2/(a^4*b^5)+4*q__0*c[1]/(a^2*b^3))*a^3)*b^4+(1/6)*(-(224/3)*D__22*c[1]^2*a/b^6+(1/7)*(48*D__12*c[1]^2/(a^8*b^4)+256*D__66*c[1]^2/(a^8*b^4)+1152*D__22*c[1]^2/(a^6*b^6))*a^7+(1/6)*(-144*D__12*c[1]^2/(a^7*b^4)-768*D__66*c[1]^2/(a^7*b^4)-768*D__22*c[1]^2/(a^5*b^6))*a^6+(1/5)*(152*D__12*c[1]^2/(a^6*b^4)+832*D__66*c[1]^2/(a^6*b^4)+192*D__22*c[1]^2/(a^4*b^6)-2*q__0*c[1]/(a^4*b^2))*a^5+(1/4)*(-64*D__12*c[1]^2/(a^5*b^4)-384*D__66*c[1]^2/(a^5*b^4)+4*q__0*c[1]/(a^3*b^2))*a^4+(1/3)*(8*D__12*c[1]^2/(a^4*b^4)+64*D__66*c[1]^2/(a^4*b^4)-2*q__0*c[1]/(a^2*b^2))*a^3)*b^3-(1/63)*D__22*c[1]^2*a/b^3

 (2)
> 

simplify(%)

-(1/900)*((4/7)*(-a^4*D__22-(4/7)*b^2*(D__12+2*D__66)*a^2-b^4*D__11)*c[1]+a^4*b^4*q__0)*c[1]/(b^3*a^3)

 (3)
> 

``
> 

 


 

Download simpl.mw

Very weird system...

tomleslie 13821
April 12 2023
1 0

I think all that the Maple error message is trying to tell you is that you have entered a very odd ODE system. The following is a (possibly non-exhaustive) list of things whihc are weird about it.

  1. You have twelve equations, Four of these are first-order ODEs, and eight of these are algebraic.
  2. The four first-order ODEs depend only on the variables theta__1(t) and theta__2(t). Because there are only two dependent variables, one should only need two such ODEs, which can be solved without reference to the other "dependent" variables, x__1(t), y__1(t), x__2(t), y__2(t)
  3. Your ODE systrem contains no initial/boundary conditions on theta__1(t) and theta__2(t). You are going to need two.
  4. If dsolve() can handle the fact that x__1(t), y__1(t), x__2(t), y__2(t), have no derivatives in your system (and I'm not sure about that), then there will still need to four initial/boundary conditions, for these dependent variables
  5. Your ODE system contains the unassigned names F__Ax, F__Ay, F__Bx, F__By, F__Ox, F__Oy. These will have to be given numerical values in order for a numerical solution to be obtained.
  6. You have confused the "simple" Greek letter 'pi', with 'Pi' (ration of circumference to diameter) throughout
  7. The reason that your attempts to produce a "Jacobian" failed, is that all of your "variables" are themselves dependent functions

There is a lot of stuff to fix here, and I don't understand the problem you are trying to solve well enough to do it. My advice would be]

  1. Focus on producing two ODEs which depend only on theta__1(t) and theta__2(t) - at the moment you have four
  2. Having obtained a solution for thes variables, if necessary then solve four algebraic equations for x__1(t), y__1(t), x__2(t), and y__2(t),

It is unclear...

tomleslie 13821
April 10 2023
0 0

(to me at leat) what "values" you actually want - but maybe the attached will help

(Compared with your original, I have discarded what appears to be completel;y redundant code)

If other "values" are required, then yyou will need to specify what they are.


 

> 

  restart:
  with(PDEtools):
  v_0 := 1:
  vstar := 10:
  r_0 := 1:
  k := 0.1:
  m := 0.1:
  PDE := diff(v(r, t), t) = k*(diff(v(r, t), r, r) + diff(v(r, t), r)/r):
  BC1 := eval(v(r, t) - v_0 = 0, r = 20):
  BC2 := D[1](v)(0, t) = 0:
  IC := v(r, 0) = v_0 + (vstar - v_0)*exp(-0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi)):
  conds := {BC1, BC2, IC}:

  u := r -> v_0 + (vstar - v_0)*exp((-1)*0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi)):
  plot(u(r), r = 0 .. 10);

  sol:= pdsolve(PDE, conds, numeric, time = t, range = 0 .. 20, spacestep = 0.1, timestep = 0.1):
  sol:-animate(t = 0 .. 20, frames = 100);
  sol:-plot3d(r = 0 .. 10, t = 0 .. 20);

  interface(rtablesize=[100,3]):
  Matrix( [ [r, t, v(r,t)],
            seq
            ( seq
              ( rhs~(sol:-value()(i,j)),
                j=0..10,2
              ),
              i=0..20,2
            )
          ]
        );
  interface(rtablesize=[10,10]):

 

 

 

Matrix(%id = 36893488148074342748)

 (1)
> 

 

> 

 


 

Download pdeStuff.mw

 

Correction to your "toy" worksheet...

tomleslie 13821
April 08 2023
1 3

print() statements in a procedure do not return any values to the calling environment. They merely cause something to be printed to the screen. Use a return statement instead, as in the attached.

> 

restart
> 

with(GraphTheory)
> 

with(SpecialGraphs)
> 

with(LinearAlgebra)
> 

A := proc (G::GRAPHLN, k) local M; M := AdjacencyMatrix(G); return M, MatrixPower(M, k) end proc
> 

B := proc (G::GRAPHLN, kl) return AdjacencyMatrix(G), AdjacencyMatrix(G)^kl end proc
> 

A(CycleGraph(3), 3)

Matrix(%id = 36893488148098420732), Matrix(%id = 36893488148098421812)

 (1)
> 

B(PathGraph(5), 5)

Matrix(%id = 36893488148098426748), Matrix(%id = 36893488148098428188)

 (2)
> 

RandomTools:-Generate(choose({A(CycleGraph(3), 3), B(PathGraph(5), 5)}))

Matrix(%id = 36893488148073309116)

 (3)
> 

``
> 

 

Download toyfix.mw

I think...

tomleslie 13821
April 07 2023
0 1

this one got answered in my rersponse to the op's other question here

https://www.mapleprimes.com/questions/236075-Pick-From-Excel-Sheet-And-Apply-Regular

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