Down below I am sharing with you the question and what I wrote as a solution so far. It includes the commands, functions, outputs, and errors. I am struggling with fixing my errors as I have tried numerous ways to correct them. However, I either get new errors or previous errors. Was wondering if someone can look at it and provide me advice, and a possible solution to the problem. 

In this question, you are given a cypher that was obtained using a Vigenere cypher, care of question 2, and are asked to decipher it.  You will use the approach outlined in Section 5.2 of the text.  There are two steps:  1)  Determine the key length by finding the shift which produces the maximum number of coincidences, 2)  use frequency analysis on the subsequences obtained by selecting symbols from the cypher at multiples of the key length to determine the key.  The details of these steps will be outlined below.  You will be asked to write several maple procedures that assist in this process.

restart;
with(StringTools):

with(LinearAlgebra):
cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";
cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveol\

  qlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvv\

  zhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgy\

  klhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvoji\

  komtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhha\

  pdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpv\

  euzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyin\

  ky"

n := Length(cstr);
                            n := 429

a)  Determine the key length.  Write a Maple function to determine the key length given the ciphertext obtained from a Vigenere cipher with unknown key using a specified alphabet.  Use one of the methods outlined in section 5.2 of the text: the Kasiski test (using trigrams) or the index of coincidence test. For the Kasiski test, the key length is suggested by the greatest common divisor of the distances between most of the repeated trigrams. For the index of coincidence test, construct the subsequences described in part (b) for various values of 
k;
. The 
k;
 value that yields the highest average index of coincidence of these subsequences most likely is the key length. 

KasiskiTest := proc(str)
  local i, j, n, trigrams, distances, gcds, freqs;
  n := StringTools:-Length(str);
  trigrams := table();
  distances := table();
  gcds := table();
  freqs := table();
  for i from 1 to n-2 do
    trigrams[str[i..i+2]] := [op(trigrams[str[i..i+2]]),i];
  end do;
  for j in trigrams do
    if nops(trigrams[j]) > 1 then
      distances[j] := map(diff,trigrams[j]);
      gcds[j] := igcd(op(distances[j]));
      freqs[gcds[j]] := freqs[gcds[j]] + 1;
    end if;
  end do;
  return maxloc(freqs);
end;

IndexCoincidenceTest := proc(str)
  local i, k, n, m, L, C, Convert, IC, avgIC;
  Convert := table();  n := StringTools:-Length(str);  
  for i from 1 to n do
    Convert[str[i]] := i-1;
  end do;
  L := Letter2Number(str,Convert); 
  IC := [];
  avgIC := [];
  for k from 1 to n/2 do
    C := [];
    for i from 1 to k do
      C[i] := seq(L[i+j*k],j=0..floor((n-i)/k));
    end do;
    IC[k] := map(DotProduct,C,C)/nops(C)^2;
    avgIC[k] := add(IC[k])/k;
  end do;
  return maxloc(avgIC);
end;

KasiskiTest(cstr);

                         maxloc(freqs)

IndexCoincidenceTest(cstr);
Error, (in IndexCoincidenceTest) expression sequences cannot be assigned to lists

b) Construct subsequences of the cypher by selecting characters at multiples of the key length.  I.E.  If k is the key length, then construct subsequences:  c1 = cstr[1],cstr[1+k],...,cstr[1+n/k],...,ck = cstr[k],cstr[2*k],...,cstr[floor(n/k)*k].  

Maple hint:  use seq and cat to form these strings.

cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";
cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveol\

  qlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvv\

  zhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgy\

  klhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvoji\

  komtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhha\

  pdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpv\

  euzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyin\

  ky"

Subsequences := proc(str,k)
  local i, n, C, S;
  n := StringTools:-Length(str);
  C := [];
  S := [];
  for i from 1 to k do
    C[i] := seq(str[i+j*k],j=0..floor((n-i)/k));
    S[i] := cat(op(C[i]));
  end do;
  return S;
end;

Warning, (in Subsequences) `j` is implicitly declared local
 Subsequences := proc (str, k) local i, n, C, S, j; n := 

    StringTools:-Length(str); C := []; S := []; for i to k do 

    C[i] := seq(str[i+j*k], j = 0 .. floor((n-i)/k)); S[i] := 

    cat(op(C[i])) end do; return S end proc

Subsequences(cstr,4);
Error, (in Subsequences) expression sequences cannot be assigned to lists

c) Calculate the character frequencies in the substrings formed from (b).  You should construct a list F=[f1/n,...,ft/n], where fi is the number of occurrences of symbol i in the string and n is the number of symbols in the string, and t is the number of symbols in the alphabet.  Don't forget that you can use evalf() to get a floating point approximation to the fractions fi/n, and you can use CountCharacterOccurrences() from the StringTools package to obtain the number of occurrences of the ith symbol. For the alphabet use a,...,z.  See question 1.

alphabet := Iota("a".."z");
            alphabet := "abcdefghijklmnopqrstuvwxyz"

CharacterFrequencies := proc(str,alphabet)
  local i, n, t, F, C;
  n := StringTools:-Length(str);
  t := StringTools:-Length(alphabet);
  F := [];
  C := StringTools:-CountCharacterOccurrences(str);
  for i from 1 to t do
    F[i] := evalf(C[alphabet[i]]/n);
  end do;
  return F;
end;

Error, attempting to assign to `StringTools:-CharacterFrequencies` which is protected
alphabet := "abcdefghijklmnopqrstuvwxyz";
S := Subsequences(cstr,4);
CharacterFrequencies(S[1],alphabet);

            alphabet := "abcdefghijklmnopqrstuvwxyz"

Error, (in Subsequences) expression sequences cannot be assigned to lists
Error, (in StringTools:-CharacterFrequencies) first argument must be a string

d) Determine the Ceasar shifts for the 5 subsequences from (b) and hence determine the key.  This is done by comparing the frequencies computed in (c) with the standard English letter probabilities given in the list FE.

You are to write a function FindShift(F1,F2) which takes as input F1 = the standard frequencies and F2 = the shifted frequencies.  The function FindShift(F1,F2) find the shift 
                              "s"

 which minimizes the error between the two lists of frequencies.  I.E.  For each possible shift 
                  "s=0,1,...,25 = nops(F1), "

compute the sum of the squares of the difference F1[i]-F2[i+s mod 26].  Find the value of 
                              "s"

 that minimizes this sum.  This will be the most likely shift.

Note that in the above sum, you will need to correct the indexing due to the fact that Maple indexes lists and arrays starting at 1 rather than 0.

Use the function FindShift to find the key used to create the cypher cstr.

FE := [0.8167000000e-1, 0.1492000000e-1, 0.2782000000e-1, 0.4253000000e-1, .1270200000, 0.2228000000e-1, 0.2015000000e-1, 0.6094000000e-1, 0.6966000000e-1, 0.1530000000e-2, 0.7720000000e-2, 0.4025000000e-1, 0.2406000000e-1, 0.6749000000e-1, 0.7507000000e-1, 0.1929000000e-1, 0.9500000000e-3, 0.5987000000e-1, 0.6327000000e-1, 0.9056000000e-1, 0.2758000000e-1, 0.9780000000e-2, 0.2360000000e-1, 0.1500000000e-2, 0.1974000000e-1, 0.7400000000e-3];
[0.08167000000, 0.01492000000, 0.02782000000, 0.04253000000, 

  0.1270200000, 0.02228000000, 0.02015000000, 0.06094000000, 

  0.06966000000, 0.001530000000, 0.007720000000, 0.04025000000, 

  0.02406000000, 0.06749000000, 0.07507000000, 0.01929000000, 

  0.0009500000000, 0.05987000000, 0.06327000000, 0.09056000000, 

  0.02758000000, 0.009780000000, 0.02360000000, 0.001500000000, 

  0.01974000000, 0.0007400000000]

FindShift := proc(F1,F2)
  local i, s, n, t, S, M;
  n := nops(F1);
  t := nops(F2);
  S := [];
  for s from 0 to n-1 do
    S[s+1] := add((F1[i]-F2[(i+s) mod t + 1])^2,i=1..n);
  end do;
  M := minloc(S);
  return M[2]-1;
end;

 FindShift := proc (F1, F2) local i, s, n, t, S, M; n := 

    nops(F1); t := nops(F2); S := []; for s from 0 to n-1 do 

    S[s+1] := add((F1[i]-F2[(`mod`(i+s, t))+1])^2, i = 1 .. n) 

    end do; M := minloc(S); return M[2]-1 end proc

with(StringTools);
alphabet := "abcdefghijklmnopqrstuvwxyz";
cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";
FE := [0.8167000000e-1, 0.1492000000e-1, 0.2782000000e-1, 0.4253000000e-1, .1270200000, 0.2228000000e-1, 0.2015000000e-1, 0.6094000000e-1, 0.6966000000e-1, 0.1530000000e-2, 0.7720000000e-2, 0.4025000000e-1, 0.2406000000e-1, 0.6749000000e-1, 0.7507000000e-1, 0.1929000000e-1, 0.9500000000e-3, 0.5987000000e-1, 0.6327000000e-1, 0.9056000000e-1, 0.2758000000e-1, 0.9780000000e-2, 0.2360000000e-1, 0.1500000000e-2, 0.1974000000e-1, 0.7400000000e-3];
Subsequences := proc(str,k)
  local i, n, C, S;
  n := StringTools:-Length(str);
  C := [];
  S := [];
  for i from 1 to k do
    C[i] := seq(str[i+j*k],j=0..floor((n-i)/k));
    S[i] := cat(op(C[i]));
  end do;
  return S;
end;
CharacterFrequencies := proc(str,alphabet)
  local i, n, t, F, C;
  n := StringTools:-Length(str);
  t := StringTools:-Length(alphabet);
  F := [];
  C := StringTools:-CountCharacterOccurrences(str);
  for i from 1 to t do
    F[i] := evalf(C[alphabet[i]]/n);
  end do;
  return F;
end;
FindShift := proc(F1,F2)
  local i, s, n, t, S, M;
  n := nops(F1);
  t := nops(F2);
  S := [];
  for s from 0 to n-1 do
    S[s+1] := add((F1[i]-F2[(i+s) mod t + 1])^2,i=1..n);
  end do;
  M := minloc(S);
  return M[2]-1;
end;
S := Subsequences(cstr,4);
F := map(CharacterFrequencies,S,alphabet);
Shifts := map(FindShift,FE,F);
KeyLetters := map(Number2Letter,Shifts,alphabet);
Key := cat(op(KeyLetters));

[Anagrams, AndMap, ApproximateSearch, ApproximateSearchAll, 

  ArithmeticMean, Border, BorderArray, BorderLength, CamelCase, 

  Capitalize, CaseJoin, CaseSplit, Center, Centre, Char, 

  CharacterFrequencies, CharacterMap, Chomp, Chop, CommonPrefix, 

  CommonSuffix, Compare, CompareCI, Compress, 

  CountCharacterOccurrences, Decode, DecodeEntities, Delete, 

  DeleteSpace, DifferencePositions, Drop, EditDistance, Encode, 

  EncodeEntities, Entropy, Escape, Exchange, 

  ExpandCharacterClass, ExpandTabs, Explode, Fence, Fibonacci, 

  Fill, FirstFromLeft, FirstFromRight, FormatMessage, FormatTime, 

  FromByteArray, Generate, GenerateIdentifier, Group, 

  HammingDistance, HammingSearch, HammingSearchAll, Has, 

  HasASCII, HasAlpha, HasAlphaNumeric, HasBinaryDigit, 

  HasControlCharacter, HasDigit, HasGraphic, HasHexDigit, 

  HasIdentifier, HasIdentifier1, HasLower, HasOctalDigit, 

  HasPrintable, HasPunctuation, HasSpace, HasUpper, HasVowel, 

  Hash, Implode, Indent, IndexOfCoincidence, Insert, Iota, 

  IsASCII, IsAlpha, IsAlphaNumeric, IsAnagram, IsBalanced, 

  IsBinaryDigit, IsConjugate, IsControlCharacter, IsDerangement, 

  IsDigit, IsEodermdrome, IsGraphic, IsHexDigit, IsIdentifier, 

  IsIdentifier1, IsLower, IsMonotonic, IsOctalDigit, 

  IsPalindrome, IsPeriod, IsPermutation, IsPrefix, IsPrimitive, 

  IsPrintable, IsPunctuation, IsSorted, IsSpace, IsSubSequence, 

  IsSuffix, IsUpper, IsVowel, Join, Kasiski, LeftFold, 

  LeftRecursivePathOrder, Length, LengthSplit, Levenshtein, 

  LexOrder, LongestCommonSubSequence, LongestCommonSubString, 

  LowerCase, LyndonFactors, Map, MatchFence, MaxChar, 

  MaximalPalindromicSubstring, Metaphone, MinChar, 

  MinimumConjugate, MonotonicFactors, NGrams, NthWord, OrMap, 

  Ord, OtherCase, Overlap, PadLeft, PadRight, ParseTime, 

  PatternCanonicalForm, PatternDictionary, PatternEquivalent, 

  Period, Permute, PrefixDistance, PrimitiveRoot, Random, 

  Randomize, Readability, RegMatch, RegSplit, RegSub, RegSubs, 

  Remove, Repeat, Repeats, RevLexOrder, Reverse, RightFold, 

  RightRecursivePathOrder, Rotate, Search, SearchAll, Select, 

  SelectRemove, Sentences, Shift, ShortLexOrder, 

  ShortRevLexOrder, SimilarityCoefficient, Snarf, Sort, 

  SortPermutation, Soundex, Split, Squeeze, Stem, StringBuffer, 

  StringSplit, SubString, Subs, Substitute, SubstituteAll, 

  SuffixDistance, Support, SyllableLength, Tabulate, Take, 

  ThueMorse, ToByteArray, Trim, TrimLeft, TrimRight, Uncompress, 

  Unique, UpperCase, Visible, WildcardMatch, WordContaining, 

  WordCount, WordEnd, WordStart, Words, WrapText]

            alphabet := "abcdefghijklmnopqrstuvwxyz"

cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveol\

  qlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvv\

  zhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgy\

  klhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvoji\

  komtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhha\

  pdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpv\

  euzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyin\

  ky"

FE := [0.08167000000, 0.01492000000, 0.02782000000, 

  0.04253000000, 0.1270200000, 0.02228000000, 0.02015000000, 

  0.06094000000, 0.06966000000, 0.001530000000, 0.007720000000, 

  0.04025000000, 0.02406000000, 0.06749000000, 0.07507000000, 

  0.01929000000, 0.0009500000000, 0.05987000000, 0.06327000000, 

  0.09056000000, 0.02758000000, 0.009780000000, 0.02360000000, 

  0.001500000000, 0.01974000000, 0.0007400000000]

Warning, (in Subsequences) `j` is implicitly declared local
 Subsequences := proc (str, k) local i, n, C, S, j; n := 

    StringTools:-Length(str); C := []; S := []; for i to k do 

    C[i] := seq(str[i+j*k], j = 0 .. floor((n-i)/k)); S[i] := 

    cat(op(C[i])) end do; return S end proc

Error, attempting to assign to `StringTools:-CharacterFrequencies` which is protected
 FindShift := proc (F1, F2) local i, s, n, t, S, M; n := 

    nops(F1); t := nops(F2); S := []; for s from 0 to n-1 do 

    S[s+1] := add((F1[i]-F2[(`mod`(i+s, t))+1])^2, i = 1 .. n) 

    end do; M := minloc(S); return M[2]-1 end proc

Error, (in Subsequences) expression sequences cannot be assigned to lists
                             F := 

Error, invalid input: FindShift uses a 2nd argument, F2, which is missing
KeyLetters := Number2Letter(Shifts, "abcdefghijklmnopqrstuvwxyz")

            Key := Shiftsabcdefghijklmnopqrstuvwxyz

e) Decipher cstr using the key found in (d) and your DecryptVigenere routine from question 2.  Note that the encrypted text will have blanks removed.

with(StringTools);
[Anagrams, AndMap, ApproximateSearch, ApproximateSearchAll, 

  ArithmeticMean, Border, BorderArray, BorderLength, CamelCase, 

  Capitalize, CaseJoin, CaseSplit, Center, Centre, Char, 

  CharacterFrequencies, CharacterMap, Chomp, Chop, CommonPrefix, 

  CommonSuffix, Compare, CompareCI, Compress, 

  CountCharacterOccurrences, Decode, DecodeEntities, Delete, 

  DeleteSpace, DifferencePositions, Drop, EditDistance, Encode, 

  EncodeEntities, Entropy, Escape, Exchange, 

  ExpandCharacterClass, ExpandTabs, Explode, Fence, Fibonacci, 

  Fill, FirstFromLeft, FirstFromRight, FormatMessage, FormatTime, 

  FromByteArray, Generate, GenerateIdentifier, Group, 

  HammingDistance, HammingSearch, HammingSearchAll, Has, 

  HasASCII, HasAlpha, HasAlphaNumeric, HasBinaryDigit, 

  HasControlCharacter, HasDigit, HasGraphic, HasHexDigit, 

  HasIdentifier, HasIdentifier1, HasLower, HasOctalDigit, 

  HasPrintable, HasPunctuation, HasSpace, HasUpper, HasVowel, 

  Hash, Implode, Indent, IndexOfCoincidence, Insert, Iota, 

  IsASCII, IsAlpha, IsAlphaNumeric, IsAnagram, IsBalanced, 

  IsBinaryDigit, IsConjugate, IsControlCharacter, IsDerangement, 

  IsDigit, IsEodermdrome, IsGraphic, IsHexDigit, IsIdentifier, 

  IsIdentifier1, IsLower, IsMonotonic, IsOctalDigit, 

  IsPalindrome, IsPeriod, IsPermutation, IsPrefix, IsPrimitive, 

  IsPrintable, IsPunctuation, IsSorted, IsSpace, IsSubSequence, 

  IsSuffix, IsUpper, IsVowel, Join, Kasiski, LeftFold, 

  LeftRecursivePathOrder, Length, LengthSplit, Levenshtein, 

  LexOrder, LongestCommonSubSequence, LongestCommonSubString, 

  LowerCase, LyndonFactors, Map, MatchFence, MaxChar, 

  MaximalPalindromicSubstring, Metaphone, MinChar, 

  MinimumConjugate, MonotonicFactors, NGrams, NthWord, OrMap, 

  Ord, OtherCase, Overlap, PadLeft, PadRight, ParseTime, 

  PatternCanonicalForm, PatternDictionary, PatternEquivalent, 

  Period, Permute, PrefixDistance, PrimitiveRoot, Random, 

  Randomize, Readability, RegMatch, RegSplit, RegSub, RegSubs, 

  Remove, Repeat, Repeats, RevLexOrder, Reverse, RightFold, 

  RightRecursivePathOrder, Rotate, Search, SearchAll, Select, 

  SelectRemove, Sentences, Shift, ShortLexOrder, 

  ShortRevLexOrder, SimilarityCoefficient, Snarf, Sort, 

  SortPermutation, Soundex, Split, Squeeze, Stem, StringBuffer, 

  StringSplit, SubString, Subs, Substitute, SubstituteAll, 

  SuffixDistance, Support, SyllableLength, Tabulate, Take, 

  ThueMorse, ToByteArray, Trim, TrimLeft, TrimRight, Uncompress, 

  Unique, UpperCase, Visible, WildcardMatch, WordContaining, 

  WordCount, WordEnd, WordStart, Words, WrapText]

alphabet := "abcdefghijklmnopqrstuvwxyz";
            alphabet := "abcdefghijklmnopqrstuvwxyz"

cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";
cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveol\

  qlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvv\

  zhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgy\

  klhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvoji\

  komtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhha\

  pdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpv\

  euzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyin\

  ky"

Key := [19, 4, 18, 19];
                     Key := [19, 4, 18, 19]

DecryptVigenere := proc(str,key,alphabet)
  local i, n, m, L, K, C, Convert, plain;
  Convert := table();  n := StringTools:-Length(alphabet);  
  for i from 1 to n do
    Convert[alphabet[i]] := i-1;
  end do;
  L := Letter2Number(str,Convert); 
  K := Letter2Number(key,Convert);
  m := nops(K);
  C := [];
  for i from 1 to nops(L) do
    C := [op(C),L[i]-K[i mod m + 1] mod n];
  end do;  
  plain := Number2Letter(C,alphabet);
  return plain;
end;
DecryptVigenere := proc (str, key, alphabet) local i, n, m, L, 

   K, C, Convert, plain; Convert := table(); n := StringTools:-L\

  ength(alphabet); for i to n do Convert[alphabet[i]] := i-1 

   end do; L := Letter2Number(str, Convert); K := Letter2Number(\

  key, Convert); m := nops(K); C := []; for i to nops(L) do C 

   := [op(C), `mod`(L[i]-K[(`mod`(i, m))+1], n)] end do; plain 

   := Number2Letter(C, alphabet); return plain end proc

DecryptVigenere(cstr,Key,alphabet);
Number2Letter([Letter2Number("eqjyvxvgiuphmrrrgzhvwrrukmrtijfbto\

  didtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjt\

  hitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvl\

  oiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnf\

  jnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxu\

  asvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhys\

  lgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvp\

  bonjsoabcizotysxztyinky", Convert)[1]

   + 25 Letter2Number([19, 4, 18, 19], Convert)[2], Letter2Number("eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky", 

  Convert)[2] + 25 Letter2Number([19, 4, 18, 19], Convert)[1]], 

  "abcdefghijklmnopqrstuvwxyz")

f) Decipher the Vigenere ciphers from Computer Problems 8 and 9 from Section 2.14 of the text.

xkju:= "xkjurowmllpxwznpimbvbqjcnowxpcchhvvfvsllfvxhazityxohulxqojaxelxzxmyjaqfs\
tsrulhhucdskbxknjqidallpqslluhiaqfpbpcidsvcihwhwewthbtxrljnrsncihuvffuxvoukjlj\
swmaqfvjwjsdyljogjxdboxajultucpzmpliwmlubzxvoodybafdskxgqfadshxnxehsaruojaqfpf\
kndhsaafvulluwtaqfrupwjrszxgpfutjqiynrxnyntwmhcukjfbirzsmehhsjshyonddzzntzmpli\
lrwnmwmlvuryonthuhabwnvw";
ocwy:= "ocwyikoooniwugpmxwktzdwgtssayjzwyemdlbnqaaavsuwdvbrflauplooubfgqhgcscmgz\
latoedcsdeidpbhtmuovpiekifpimfnoamvlpqfxejsmxmpgkccaykwfzpyuavtelwhrhmwkbbvgtg\
uvtefjlodfefkvpxsgrsorvgtajbsauhzrzalkwuowhgedefnswmrciwcpaaavogpdnfpktdbalsis\
urlnpsjyeatcuceesohhdarkhwotikbroqrdfmzghgucebvgwcdqxgpbgqwlpbdaylooqdmuhbdqgm\
yweuik";
xkju := "xkjurowmllpxwznpimbvbqjcnowxpcchhvvfvsllfvxhazityxohulx\

  qojaxelxzxmyjaqfstsrulhhucdskbxknjqidallpqslluhiaqfpbpcidsvcih\

  whwewthbtxrljnrsncihuvffuxvoukjljswmaqfvjwjsdyljogjxdboxajultu\

  cpzmpliwmlubzxvoodybafdskxgqfadshxnxehsaruojaqfpfkndhsaafvullu\

  wtaqfrupwjrszxgpfutjqiynrxnyntwmhcukjfbirzsmehhsjshyonddzzntzm\

  plilrwnmwmlvuryonthuhabwnvw"

ocwy := "ocwyikoooniwugpmxwktzdwgtssayjzwyemdlbnqaaavsuwdvbrflau\

  plooubfgqhgcscmgzlatoedcsdeidpbhtmuovpiekifpimfnoamvlpqfxejsmx\

  mpgkccaykwfzpyuavtelwhrhmwkbbvgtguvtefjlodfefkvpxsgrsorvgtajbs\

  auhzrzalkwuowhgedefnswmrciwcpaaavogpdnfpktdbalsisurlnpsjyeatcu\

  ceesohhdarkhwotikbroqrdfmzghgucebvgwcdqxgpbgqwlpbdaylooqdmuhbd\

  qgmyweuik"

 

 

We have just released updates to Maple and MapleSim.

Maple 2023.1 includes improvements to the math engine, Plot Builder, import/export, and more.  We recommend that all Maple 2023 users install this update.

This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2023.1 download page, where you can find more details.

In particular, please note that this update includes fixes to problems with Quantifier Elimination and Group  Theory, and improves performance after a period of inactivity, all of which were reported on MaplePrimes. Thanks for the feedback!

At the same time, we have also released an update to MapleSim, which contains a variety of improvements to MapleSim and its add-ons. You can find more information on the MapleSim 2023.1 download page.

I'm using Windows, and putting 

Typesetting:−Settings(parserwarnings=false):

into my maple.ini didn't seem to work.  The command

rsolve({u(0) = a, u(1) = b, u(n + 1) = 2*u(n) - (-e^2 + 1)*u(n - 1)}, u(n))

generated a (to me, useless) warning that "e" is sometimes used by people to represent the base of the natural logarithms, and if I meant that, then I'd have to use the palette or exp(1).  Well, as Freud once said, sometimes "e" is just a symbol, not necessarily the base of the natural logarithms.

If I issue the command *in the worksheet* it works.  But, I really *never* want to see that warning so I would like to put it in my maple.ini file.  I have some other things in that file, which *do* get executed, so...

But maybe this is a Windows thing?

My question: how do I turn those warnings off, so I never, ever see them?

The initialization file in question:

#
# Minimal maple.ini file
# RMC 2023-05-01
plots:-setoptions(font = ["Arial", 16], labelfont = ["Arial", 16],
                  axes = boxed,
                  gridlines = true,
                  colour = black ):
Typesetting:−Settings(parserwarnings=false):
print(" Initialization complete. " );

I am trying to see the closed form solution to the following equation where the know constants are phi1, a, and b:

Z := phi__1 = arctan(a*sin(alpha__1)/(a*cos(alpha__1) - b))

I am attempting to use the "solve" command as follows:

(solve(Z, alpha__1, useassumptions) assuming (0 < a and 0 < b))

 and I definitely do not understand what Maple is producing.

Thank you.

I made the upgrade to Maple 2023 today and for fun I compiled a simple procedure. I got an error in Maple 2023. So I ran the same lines of code in Maple 2022 and eveything works. Does anyone sees this problem?

>  restart: kernelopts(version); (1) >  p := proc( x :: float ) :: float; 2.3 * x end proc: >  cp:=Compiler:-Compile(p) Error, (in Compiler:-Compile) linker exited with nonzero status 1:   >  cp(1.1) (2) >

Download compile_ex.mw

Suppose that a procedure P is declared with option threadsafe and it has a local child procedure PC (possibly anonymous). Is their any benefit, or perhaps any detriment, to also declaring PC with option threadsafe? For example, is there any benefit or detriment to the yellow option threadsafe in this code below?:

P:= proc()
option threadsafe;
local PC:= proc() option threadsafe; (* some code *) end proc;
    (* some code *)
    PC();
    (* some code *)
end proc;

Recently, Maple takes quite long to start here, and I wonder if there are any hints about how to speed up.

Maple itself starts quickly, but opening the start page takes quite long.

Antivirus? Other settings?

Why can't a singular call fully simplify them? 
 

>  restart; >  (* in △ABC *) >  >  >  (1) >  (2) >  (3)

 

Download trigReduce.mw

Is there any limitation of `simplify/trig`?

 

I have a function that I want to plot from x=0..5 , when I ask it to plot over this range it will not plot from x=0..1 it will just go from x=1..5. However, If I ask it to plot from x=0..1 it will plot that... so then I have to splice the images together in display. 

Has anyone seen this problem? Is it something easy and stupid that I am missing? 

Function of interest attached in file. 

PlotIssue.mw

With a low numerical accuracy (for instance, Digits ≔ 10, 18, 22, 30, 50, …), the numeric calculation may fail (due to loss of precision). However, if I set the precision to 1011 digits, the error message will suggest that I need 2022 effective digits, and if I set the number of digits to 2023, the new error message will indicate that I need 4046 digits instead! 
 

>  restart; (* kernelopts(assertlevel = 2): *) >  f__||(1..2):=seq(:-Implies(:-And((x,y,z)>=~0,x+y+z>=x*y*z-2),(x+y+z-`k`)**2+12*`K`>=`K`*(y*z+z*x+x*y)+(6-`k`)**2),`k`in[-1,2]): >  >  >  Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   >  >  >  Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   >  >  >  Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   Error, (in CADCell:-incrementalCADMerge) intervals the same at this precision   >  >  >  Error, (in evalr/shake) -1745522223305217995292661862391649380423964537/713623846352979940529142984724747568191373312 .. -872761111652608997646330931195824690211982147/356811923176489970264571492362373784095686656 is an invalid range   Error, (in CADCell:-getRootOf) assertion failed, QuantifierElimination:-CADCell:-getRootOf expects its return value to be of type Or(realalgfun,polynom), but computed -4/(K-2)   >  >  >  Error, (in fsolve) 51953924463883761901792418789194928235174905950382670549953648710446970664310543651007323799780435683230006536652706682836424797844925527680493588036601389375573240391357941112051916610030393510104292907027389236710859112839952847980210175362475743230722948239736701720236829869491083611577725129304524699348873290677105040453671573567321637853939258015148604288142746130200523992493313329625476885430355670361959662016545723317992326796888354706811339520905282493925959682290128861158489269192756541573370159292296031148260734007880772071719402902769848742402757080259718232411901509888033214784334659015401671/30819898673354155827250363053007080040401556653705104858522744586491255892627612012097550784609712089241712532922647494787330207014552041144455101381729395981436612479496952144384572744741108042522485388168399399067680567400569683229292005861736460180837293483768754046332908526936593826873352431415491471788324674024265615864453291689457482809883285556150743539884381923037553971012554468298204987396409146047538379400693757398222304489423414139178941357835089904048085865698642930722386457182818721265486280995041559157415387409546850813117528120412289939445116172250012974400824049572899006074481824503955456 .. 103907848927767523803584837578389856470349811900765341099907297420893941328621087302014647599560871366460013073305413365672849595689851055360987176073202778751146480782715882224103833220060787020208585814054778473421718225679905695960420350724951486461445896479473403440473659738982167223155450258609049398697746581354210080907343147134643275707878516030297208576285492260401047984986626659250953770860711340723919324033091446635984653593776709413622679041810564987851919364580257722316978538385513083146740318584592062296521468015761544143438805805539697484805514160519436464823803019776066429568669328491156545/61639797346708311654500726106014160080803113307410209717045489172982511785255224024195101569219424178483425065845294989574660414029104082288910202763458791962873224958993904288769145489482216085044970776336798798135361134801139366458584011723472920361674586967537508092665817053873187653746704862830982943576649348048531231728906583378914965619766571112301487079768763846075107942025108936596409974792818292095076758801387514796444608978846828278357882715670179808096171731397285861444772914365637442530972561990083118314830774819093701626235056240824579878890232344500025948801648099145798012148963649007910912 is an invalid range   Error, (in QuantifierElimination:-makeIntervalsDisjoint) intervals the same at this precision   >  >  >  Error, (in QuantifierElimination:-CylindricalAlgebraicDecompose) could not deduce sign of expression -342/25*RootOf(19*_Z^2+38*_Z-12,-4987910358199862617695009215709741605709429723398915706935981134367159645137702755744811848649748363964619233272334637596908427108379140961254846049673609374649230279927501442010021927667514449257826614057994448539998131000148492036947851465573508992822358525609812547821711206993013464583756238982808480726743494241044879932540380141333843955234896674594593548858060217618984313571272446618558610719387174513219009335839077580775050010186121998765445974558764352314930517401142857800948902933757634601020640904937469362743714271628486160227454116983764409999636638394510618606021312024472773815702904498322013237669791547497017096378031053343768560075850663597929486261657611626497278288155649674743772219645453376069718849586569846366137879582969431774492624897836480589922659958172908351367904597399703973894410690193526222594908197737029927077207602713412071670101566072357427300354219930601407610842782444349564488842636963556768876362858397663083302382595638845298193545672264754619772234178272290746956937279156515624590145750509771810057257684689393280341696527499483583228747445979211697575964881432846981852813748325889619627566484956410900755790611831189266287867465483821614902144107200456548248296812798080610603299934574758229/2190242231433355605713622580784790257176337184818218989800356017935910506010367663745430846303103999469714369076399728939211315611038213435059310088109666395374919565272594510439485989473503083630539455881503721340537549806680592080012228027942618514056665699358193649600501485383437221341624748544828173727431527449245595018874125036164766112100289249925552604295781042498954120430296550327376602551694310632084558811115265278732133694885722844329665311749311648443155699857726046036733671350799899480858664936372681036344974146721644440898110681165136923137290519909746607233907552787706349690264162243952654925480709861488974859234405170031021488597060203095413643180377467031761467054899561926327819660155232715013691046430578595248173829090757022165068459240233126520336989047813133418836332022225509059532367109158642449881902354788176931193425240152480134741178073848049456750152420954534977358016033159177392382388120254638070390740274321873764804488799398344035670289074976972793812288435440057985727882576434370707829983166800843365502001207193311581981631050252308788689282672795587582994136507873542034063961735413414980448082151652674767077303650987359007543869672189311605552663328523263480296563526975531705493155616571523072 .. -2493955179099931308847504607854870802854714861699457853467990567183579822568851377872405924324874181982309616636167318798454213554189570480627423024836804687324615139963750721005010963833757224628913307028997224269999065500074246018473925732786754496411179262804906273910855603496506732291878119491404240363371747120522439966270190070666921977617448337297296774429030108809492156785636223309279305359693587256609504667919538790387525005093060999382722987279382176157465258700571428900474451466878817300510320452468734681371857135814243080113727058491882204999818319197255309303010656012236386907851452249161006618834895773748508548189015526671884280037925331798964743130828805813248639144077824837371886109822726688034859424793284923183068939791484715887246312448918240294961329979086454175683952298699851986947205345096763111297454098868514963538603801356706035835050783036178713650177109965300703805421391222174782244421318481778384438181429198831541651191297819422649096772836132377309886117089136145373478468639578257812295072875254885905028628842344696640170848263749741791614373722989605848787982440716423490926406874162944809813783242478205450377895305915594633143933732741910807451072053600228274124148406399040305301649967287369273/1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808285761536)+328/25 from intermediate relation -342/25*RootOf(19*_Z^2+38*_Z-12,-4987910358199862617695009215709741605709429723398915706935981134367159645137702755744811848649748363964619233272334637596908427108379140961254846049673609374649230279927501442010021927667514449257826614057994448539998131000148492036947851465573508992822358525609812547821711206993013464583756238982808480726743494241044879932540380141333843955234896674594593548858060217618984313571272446618558610719387174513219009335839077580775050010186121998765445974558764352314930517401142857800948902933757634601020640904937469362743714271628486160227454116983764409999636638394510618606021312024472773815702904498322013237669791547497017096378031053343768560075850663597929486261657611626497278288155649674743772219645453376069718849586569846366137879582969431774492624897836480589922659958172908351367904597399703973894410690193526222594908197737029927077207602713412071670101566072357427300354219930601407610842782444349564488842636963556768876362858397663083302382595638845298193545672264754619772234178272290746956937279156515624590145750509771810057257684689393280341696527499483583228747445979211697575964881432846981852813748325889619627566484956410900755790611831189266287867465483821614902144107200456548248296812798080610603299934574758229/2190242231433355605713622580784790257176337184818218989800356017935910506010367663745430846303103999469714369076399728939211315611038213435059310088109666395374919565272594510439485989473503083630539455881503721340537549806680592080012228027942618514056665699358193649600501485383437221341624748544828173727431527449245595018874125036164766112100289249925552604295781042498954120430296550327376602551694310632084558811115265278732133694885722844329665311749311648443155699857726046036733671350799899480858664936372681036344974146721644440898110681165136923137290519909746607233907552787706349690264162243952654925480709861488974859234405170031021488597060203095413643180377467031761467054899561926327819660155232715013691046430578595248173829090757022165068459240233126520336989047813133418836332022225509059532367109158642449881902354788176931193425240152480134741178073848049456750152420954534977358016033159177392382388120254638070390740274321873764804488799398344035670289074976972793812288435440057985727882576434370707829983166800843365502001207193311581981631050252308788689282672795587582994136507873542034063961735413414980448082151652674767077303650987359007543869672189311605552663328523263480296563526975531705493155616571523072 .. 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< -328/25, and hence the truth of the relation at extremely high precision (2022 digits)   Error, (in QuantifierElimination:-makeIntervalsDisjoint) intervals the same at this precision   >  >  >  Error, (in QuantifierElimination:-CylindricalAlgebraicDecompose) could not deduce sign of expression 729/40*RootOf(675*_Z^2+4320*_Z+164,-1819051677054954937088966774080402766362059925703142152107946489025251982259488522542780558822517219639316402494749234977258281452721872596195467650700476020010399039940415953392604294876123760949630414571003345043058536169063535023925283379147685829107161736070003830151116673428248900332716375268508211684501695562616939133437174041034441376584698560240247761556592415321007416402048900440163892437015276176011310337300603150533018026563587072171241416168011632612357238259475097590157678620412464707919841087893184829799608291285025311386141897443342339895008930069979119261329436269651109803887141662013343345028327523396605031443141030592979074596095070340312564687602986967266200786007714529350708962680726180746170956434173926017391622625291269300493801401238866649332201049213884005284754844622216036725883210484281900413018082044160765680068545730501956460127342127985093814606350480667478728863376261758126837050880274579949598697992842161056923512008600132544448294200841589522500515326481026313488530269470428635356327011931075754801614951075174943281308119508487291913235980410376079341266842196873651243603900681632567868476973069932723815255465392820291318664946519344004970009655907607290026098369856940246699413112568838033475782130066576063234579076743137582968573831428223962433352098283374416391165256378809417689587775337229883660926670436787439976431849966558550993282514936484057496667144689512472917843887180133273405223385986170784235669630977598328782913236835975031624750449407439661249572312121089303775982530127100839700140234991905818113971710361731139305433120908241626049142242735873123856240503836917158412187864194547248768993721977403521327683731515035047114172696485817179248917490009209278478328750960045799740279062179161178468677252070278317310005303968311912857579673877649352912714860003562400484198803659486481750057023973660961789869836076670154829167736376240161200125847190646923144768413174724141120886850577811686805775815646094267765594470851387169800231908554869073543084999111082531238009835181748494035935970910076369437309379264050957253821751370830501980946293743365352524897540097111077417153535148530365946003377270456284573336614403275690819299705785249615255373207238268158894348748901694197861637204936251002306785950527925538395112283254810817125107801796287753263520088494441764001321707715354826697830996588138426232125594311787009795513953576866779767507238429611460775227571898834531649707618706825138461254621/285933079263816169413144541851492774693637760482340422924850373902918308816255528525172371495374549738837060300611787233194113976284527739171236679536490525249740812803687839049609334024581468693383571469393366403454569425825778777488435590962056082494036443800744733494479442306669356210402336518388024856372969899345962769818846576604495220532163650595992697790510902477525797117452376619251798034179672088688151793713781307108470359703815344098725460329322524768313640863088573187756591027103963342796421522373286918376660042483773002613205961723332709362826545169611843629757234387605551976455877457493693953865813941840969457108135977362737464798302288012028141980718501366399402353496206345614818918005816405967882467721191462092319071898367278404829820529516870466533723175323267228077946836568930189170080735522195049968325809069203955926060272787397547736675795575839590753375585122289558762124625511690002057915913780530623908096317180723335928736059212712565961282141471592273501222852732975249204340095038537218518879766135315526153052783478929783824841084245345183380418156767455659749391454874190497732942505042314702438270010844904380041358852660613332618990316041162958561059105087174721043578510585586037018883777607101285014631497074790660455512147172458162490403406088894897345491526917085359232859073781679212773956396743059366079758002448932173591047353092646642250006864939981144436091698023571410966211278546501056482344198531633282489087150074329774491807869868050368702609984703595771804565836834489179348160844445540193048550640645198792507523856969968059666939586495986645094799427038656373395532817515208024290860201966377672535670288007162093067705611187049909308660654075245387894773696125716308180689547874594724726991214072286726609194594123546046311834963573671594387313500100696164673659280086447417875426696581692494526458146176679301179150583290119986885804029722309121636372378706353823225860830979411024341155084344850606916792608195089470069296753772078845728052404012245837962382000412647514568685282879743958443532144854688880680220910410363245043375128815756426793704162475769162846126374606153687055467620078012707585042405830514056366452312205131267339483538726957115365182305926482979742520728404408517614517229931165788697582013983929288006130824110416050264053600345212465247222295960752013886006340831930220757762077006824543397765618303089731475111467870392577006916542521433340399181876582852066590459341170466040812929024 .. 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from intermediate relation 729/40*RootOf(675*_Z^2+4320*_Z+164,-1819051677054954937088966774080402766362059925703142152107946489025251982259488522542780558822517219639316402494749234977258281452721872596195467650700476020010399039940415953392604294876123760949630414571003345043058536169063535023925283379147685829107161736070003830151116673428248900332716375268508211684501695562616939133437174041034441376584698560240247761556592415321007416402048900440163892437015276176011310337300603150533018026563587072171241416168011632612357238259475097590157678620412464707919841087893184829799608291285025311386141897443342339895008930069979119261329436269651109803887141662013343345028327523396605031443141030592979074596095070340312564687602986967266200786007714529350708962680726180746170956434173926017391622625291269300493801401238866649332201049213884005284754844622216036725883210484281900413018082044160765680068545730501956460127342127985093814606350480667478728863376261758126837050880274579949598697992842161056923512008600132544448294200841589522500515326481026313488530269470428635356327011931075754801614951075174943281308119508487291913235980410376079341266842196873651243603900681632567868476973069932723815255465392820291318664946519344004970009655907607290026098369856940246699413112568838033475782130066576063234579076743137582968573831428223962433352098283374416391165256378809417689587775337229883660926670436787439976431849966558550993282514936484057496667144689512472917843887180133273405223385986170784235669630977598328782913236835975031624750449407439661249572312121089303775982530127100839700140234991905818113971710361731139305433120908241626049142242735873123856240503836917158412187864194547248768993721977403521327683731515035047114172696485817179248917490009209278478328750960045799740279062179161178468677252070278317310005303968311912857579673877649352912714860003562400484198803659486481750057023973660961789869836076670154829167736376240161200125847190646923144768413174724141120886850577811686805775815646094267765594470851387169800231908554869073543084999111082531238009835181748494035935970910076369437309379264050957253821751370830501980946293743365352524897540097111077417153535148530365946003377270456284573336614403275690819299705785249615255373207238268158894348748901694197861637204936251002306785950527925538395112283254810817125107801796287753263520088494441764001321707715354826697830996588138426232125594311787009795513953576866779767507238429611460775227571898834531649707618706825138461254621/285933079263816169413144541851492774693637760482340422924850373902918308816255528525172371495374549738837060300611787233194113976284527739171236679536490525249740812803687839049609334024581468693383571469393366403454569425825778777488435590962056082494036443800744733494479442306669356210402336518388024856372969899345962769818846576604495220532163650595992697790510902477525797117452376619251798034179672088688151793713781307108470359703815344098725460329322524768313640863088573187756591027103963342796421522373286918376660042483773002613205961723332709362826545169611843629757234387605551976455877457493693953865813941840969457108135977362737464798302288012028141980718501366399402353496206345614818918005816405967882467721191462092319071898367278404829820529516870466533723175323267228077946836568930189170080735522195049968325809069203955926060272787397547736675795575839590753375585122289558762124625511690002057915913780530623908096317180723335928736059212712565961282141471592273501222852732975249204340095038537218518879766135315526153052783478929783824841084245345183380418156767455659749391454874190497732942505042314702438270010844904380041358852660613332618990316041162958561059105087174721043578510585586037018883777607101285014631497074790660455512147172458162490403406088894897345491526917085359232859073781679212773956396743059366079758002448932173591047353092646642250006864939981144436091698023571410966211278546501056482344198531633282489087150074329774491807869868050368702609984703595771804565836834489179348160844445540193048550640645198792507523856969968059666939586495986645094799427038656373395532817515208024290860201966377672535670288007162093067705611187049909308660654075245387894773696125716308180689547874594724726991214072286726609194594123546046311834963573671594387313500100696164673659280086447417875426696581692494526458146176679301179150583290119986885804029722309121636372378706353823225860830979411024341155084344850606916792608195089470069296753772078845728052404012245837962382000412647514568685282879743958443532144854688880680220910410363245043375128815756426793704162475769162846126374606153687055467620078012707585042405830514056366452312205131267339483538726957115365182305926482979742520728404408517614517229931165788697582013983929288006130824110416050264053600345212465247222295960752013886006340831930220757762077006824543397765618303089731475111467870392577006916542521433340399181876582852066590459341170466040812929024 .. 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< -185517/1600, and hence the truth of the relation at extremely high precision (4046 digits)   Error, (in QuantifierElimination:-CylindricalAlgebraicDecompose) could not deduce sign of expression 268320*RootOf(_Z^2-4*_Z-3108,-492127911263632402423205713918799836904518676377048162992425734429860793731692159936602972936481041248623526526994722874660367271768174356169928553332951393419498776555955286893869001918647998412799011529468450574092033732574096246243075031960795210042594808195798865398335267427983632719074123660562225097737665568262936856232311715568036890231233556152048222985357975992190080693288389791302366783810231268184440077584519639030645274422543999884562893777193243508118616743834957282569981104272280385835288085232560051621140377993888298476658250637201897294462189693950496517725957548756442463996367694331835037672629250759616685287612144860043644654894247263008208959006749596183427232967937431422131992093153508395261469381823996699091048161869871322071652835568855691765196772918496299912543255329175183515700920916067877879984017407026209322547432665038498259378068022546783929817083415128153235344508927096692783925852196758999834951193030350855575649918467465480693402751011140405500094860137192509783115336658146795491835972228617740390843735892922168944588246907048524545667312466256649220165552267706084791685040495928909128159630953978136334359128846698928333954854907841861076262567269324227398973214419132527091503404022663598784745346467992010414933195414002982430699763388214297190092795055680666828359564692048273660527199926376627631594055083012084088435742248121611350735646981726816404043276661827996076294397135036065481195660831387872762010772027078907852012584267238876804835818549566339095826846386847023797071776488095353806918389884858737649798124892405607894636830504617083938369000898745839129545274037806848045896556982412424357215235329103644691716255214336081649377276962865227433439937120188638909850019231053644056344491101277662549251041205859845425237391856172192100920248639011897043923753529872561012003061403244043871735543387329617818369718253806449654460263067871454693475736765964789544285886195045254635603660126254287013897244681993052578074137534691266635113429902841966392451431249361489947985342817220109659665533629189264855187085250679258065129754474016088808974529737297953415496038520242422516199294764395494117459002846504408607409681823267832824633900558672300395031011267063694399498779745192690363028084634374813283330322179279293244551829295401546537527094160742631891193175961979095253696393062479670340536436137190591148134722469329390555337754710690848744601498992850092835433086458564473547950847570049066609295603769/9149858536442117421220625339247768790196408335434893533595211964893385882120176912805515887851985591642785929619577191462211647241104887653479573745167696807991706009718010849587498688786606998188274287020587724910546221626424920879629938910785794639809166201623831471823342153813419398732874768588416795403935036779070808634203090451343847057029236819071766329296348879280825507758476051816057537093749506838020857398841001827471051510522091011159214730538320792586036507618834342008210912867326826969485488715945181388053121359480736083622590775146646699610449445427578996152231500403377663246588078639798206523706046138911022627460351275607598873545673216384900543382992043724780875311878603059674205376186124990972238967078126786954210300747752908954554256944539854929079141610344551298494298770205766053442583536710241598986425890214526589633928729196721527573625458426866904108018723913265880387988016374080065853309240976979965059082149783146749719553894806802110761028527090952752039131287455207974538883041233190992604152516330096836897689071325753082394914695851045868173381016558581111980526555974095927454160161354070478024640347036940161323483285139626643807690113317214673953891362789591073394512338738753184604280883427241120468207906393301134576388709518661199692908994844636715055728861346731495451490361013734808766604695777899714552256078365829554913515298964692552000219678079396621954934336754285150918760913488033807435014353012265039650788802378552783737851835777611798483519510515064697746106778703653739141147022257286177553620500646361360240763423038977909342066767871572643033581665237003948657050160486656777307526462924085521141449216229186978166579557985597097877140930407852412632758276022921861782065531987031191263718850313175251494227011953473481978718834357491020394032003222277269557096962766317372013654290614159824846660677653737637732818665283839580345728951113891892363916118603322343227546591341152778916962699035219421337363462242863042217496120706523063297676928391866814796224013204720466197929052151806670193028635350044181767069133131623841388004122104205657398533199224613211076043987396917985774963842496406642721356986576449803726473990564200554863473239262627691685833789647455351760663308941072563664551357797305238322624447485737216196186371533313608449715211046798887911113470744064444352202906621767064248386464218385388728499785698871407203566971852562464221329360685866892773820050651266130894698917454913306013728768 .. 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from intermediate relation 268320*RootOf(_Z^2-4*_Z-3108,-492127911263632402423205713918799836904518676377048162992425734429860793731692159936602972936481041248623526526994722874660367271768174356169928553332951393419498776555955286893869001918647998412799011529468450574092033732574096246243075031960795210042594808195798865398335267427983632719074123660562225097737665568262936856232311715568036890231233556152048222985357975992190080693288389791302366783810231268184440077584519639030645274422543999884562893777193243508118616743834957282569981104272280385835288085232560051621140377993888298476658250637201897294462189693950496517725957548756442463996367694331835037672629250759616685287612144860043644654894247263008208959006749596183427232967937431422131992093153508395261469381823996699091048161869871322071652835568855691765196772918496299912543255329175183515700920916067877879984017407026209322547432665038498259378068022546783929817083415128153235344508927096692783925852196758999834951193030350855575649918467465480693402751011140405500094860137192509783115336658146795491835972228617740390843735892922168944588246907048524545667312466256649220165552267706084791685040495928909128159630953978136334359128846698928333954854907841861076262567269324227398973214419132527091503404022663598784745346467992010414933195414002982430699763388214297190092795055680666828359564692048273660527199926376627631594055083012084088435742248121611350735646981726816404043276661827996076294397135036065481195660831387872762010772027078907852012584267238876804835818549566339095826846386847023797071776488095353806918389884858737649798124892405607894636830504617083938369000898745839129545274037806848045896556982412424357215235329103644691716255214336081649377276962865227433439937120188638909850019231053644056344491101277662549251041205859845425237391856172192100920248639011897043923753529872561012003061403244043871735543387329617818369718253806449654460263067871454693475736765964789544285886195045254635603660126254287013897244681993052578074137534691266635113429902841966392451431249361489947985342817220109659665533629189264855187085250679258065129754474016088808974529737297953415496038520242422516199294764395494117459002846504408607409681823267832824633900558672300395031011267063694399498779745192690363028084634374813283330322179279293244551829295401546537527094160742631891193175961979095253696393062479670340536436137190591148134722469329390555337754710690848744601498992850092835433086458564473547950847570049066609295603769/9149858536442117421220625339247768790196408335434893533595211964893385882120176912805515887851985591642785929619577191462211647241104887653479573745167696807991706009718010849587498688786606998188274287020587724910546221626424920879629938910785794639809166201623831471823342153813419398732874768588416795403935036779070808634203090451343847057029236819071766329296348879280825507758476051816057537093749506838020857398841001827471051510522091011159214730538320792586036507618834342008210912867326826969485488715945181388053121359480736083622590775146646699610449445427578996152231500403377663246588078639798206523706046138911022627460351275607598873545673216384900543382992043724780875311878603059674205376186124990972238967078126786954210300747752908954554256944539854929079141610344551298494298770205766053442583536710241598986425890214526589633928729196721527573625458426866904108018723913265880387988016374080065853309240976979965059082149783146749719553894806802110761028527090952752039131287455207974538883041233190992604152516330096836897689071325753082394914695851045868173381016558581111980526555974095927454160161354070478024640347036940161323483285139626643807690113317214673953891362789591073394512338738753184604280883427241120468207906393301134576388709518661199692908994844636715055728861346731495451490361013734808766604695777899714552256078365829554913515298964692552000219678079396621954934336754285150918760913488033807435014353012265039650788802378552783737851835777611798483519510515064697746106778703653739141147022257286177553620500646361360240763423038977909342066767871572643033581665237003948657050160486656777307526462924085521141449216229186978166579557985597097877140930407852412632758276022921861782065531987031191263718850313175251494227011953473481978718834357491020394032003222277269557096962766317372013654290614159824846660677653737637732818665283839580345728951113891892363916118603322343227546591341152778916962699035219421337363462242863042217496120706523063297676928391866814796224013204720466197929052151806670193028635350044181767069133131623841388004122104205657398533199224613211076043987396917985774963842496406642721356986576449803726473990564200554863473239262627691685833789647455351760663308941072563664551357797305238322624447485737216196186371533313608449715211046798887911113470744064444352202906621767064248386464218385388728499785698871407203566971852562464221329360685866892773820050651266130894698917454913306013728768 .. 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< -210100816, and hence the truth of the relation at extremely high precision (4046 digits)   >  >  >  DBG> quit   Error, (in factors) time expired   Error, (in factor) time expired

 

Download cadpr.mw

So, how many digits of precision should be maintained for this question? 

Hi,

I'm looking for a harmonized layout for my weighted probability trees. Are there any possibilities to improve this code?

Thanks

Arbrepondéré.mw

The solve function is able to solve inequalities and return solutions that satisfy the inequalities. Unfortunately, it appears that for some toy problems, this command does not always perform efficiently: 
 

>  restart; >  >  >  >  Error, (in RegularChains:-TRDcadEvalBox) time expired   Error, (in RegularChains:-TRDexquo) time expired   >  >  Warning, solving 5 equations for 3 variables   Error, (in sdmp:-mul) time expired   Warning, solving 5 equations for 3 variables   Error, (in RegularChains:-TRDcadMultiplyInterval) time expired   >  >  Error, (in RegularChains:-TRDcadIsIntervalNormal) time expired   Error, (in RegularChains:-TRDnext_sub_resultant2) time expired   >  >  Error, (in RegularChains:-TRDsub_resultant_chain_monomial_basis) time expired   Error, (in modp1/DistDeg) time expired   >

 

Download x=y=z=3.mw

So none of them is capable of giving a complete description of the region defined by or  with a time limit of "ten seconds". (I believe that completing the evaluation may take a much long time; actually, if there is no constraint on the real time allowed, the symbolic solver will be stuck.) (Note that here it is not hard to find individual instances of values of variables that satisfy them (for example, via the 3-D region boundary plot above), yet they provide less insight into all solutions that exist.)
But in my view,  are too long for these two special systems.

Can Maple solve them more quickly at present? 

> eqns__1 := {x^2+y^2+z^2+x*y*z <= 2*(y*z+z*x+x*y), 2*(x^2+y^2+z^2) < y^2*z+z^2*x+x^2*y-27, x >= 0, y >= 0, z >= 0};
> eqns__2 := {x^2+y^2+z^2+x*y*z <= 2*(y*z+z*x+x*y), 2*(x^2+y^2+z^2) <= y^2*z+z^2*x+x^2*y-27, x > 0, y > 0, z > 0};

(It seems that a potential difficult part for Maple is likely attributable to proving completeness of the solution ….)

Hello community,

Could I please get help on how to invert a probability distribution (reciprocal of) and add the location and scale parameters? The distribution in question is from the built-in (Statistics package) of ChiSquare(n) transformed into a scaled inverse Chi Square with location (shift) parameters.

I have tried the following which results in verified (correct) empirical (sampled) data, but have not been equally successful in the theoretical moments and its quantiles.

>    >  restart; st:=time(): >  with(Statistics): >    >  InvChi2:=proc(a,b,n)         description "inverse chisquare distribution with a=location, b=scale, n=degrees of freedom";         local CHI := RandomVariable(ChiSquare(n)):                  Distribution(                 CDF = unapply(CDF(b*n/CHI+a,t),t),                 PDF = unapply(PDF(b*n/CHI+a,t),t),                 Mean = a+~Mean(b*n/CHI),                 Median = a+~Median(b*n/CHI),                 Variance = simplify(CentralMoment(a+b*n/CHI,2)),                 Skewness = simplify(CentralMoment(b*n/CHI, 3) / CentralMoment(b*n/CHI,2)^(3/2)),                 Kurtosis = simplify(CentralMoment(b*n/CHI, 4) / CentralMoment(b*n/CHI,2)^2),                 Conditions = [b > 0],                 RandomSample = proc(N::nonnegint)                                 a+~Sample(b*n/CHI,N)                         end proc                 );         end proc: >    >  T:= RandomVariable(InvChi2(2,4.32,3)) >    >    (1) >  evalf(Median(T)) (2) >  evalf(Mean(T)) (3) >  Variance(T) (4) >  Skewness(T) (5) >  Kurtosis(T) (6) >  Quantile(T,.25) (7) >  A:=Sample(T,10^5): >  Median(A) (8) >  Mean(A) (9) >  Variance(A) (10) >  Skewness(A) (11) >  Quantile(A,.25) (12) >  Quantile(A,.75) (13) >  printf("Time to execute worksheet = %a seconds", time() - st) Time to execute worksheet = 2.813 seconds   >

Download invChi2.mw

Thank you

How to randomly generate a matrix with the given determinant?

Many thanks!

Hi,

I can build my trigonometric circle, but I want to display irrational values ( instead of decimal values) in the tickmarks option. ideas? P.S : My code is quite long, because I wanted to display amplitudes in an optimal way.

 CERCLETEST.mwCERCLETEST.mw