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Context("Congruence") - Provides contexts that allow the entry of congruence solutions


These contexts allow you to enter congruence solutions. Either the general solution or all possible solutions can be accepted based on settings.

There are three contexts included here: Context("Congruence"), which allows both types of solutions, Context("Congruence-General-Solution"), which requires the general solution, and Context("Congruence-All-Solutions"), which requires all solutions to be entered.

Congruences must be created with three paramters (a, b, m) from ax ≡ b (mod m).



  ax ≡ b (mod m)
  can initialize with Congruence(a, b, m);

  #ex: 15x ≡ 10 (mod 25)
        $C1 = Congruence(15, 10, 25); 
  $general_answer = Compute("4+5k");
  $all_answers = Compute("4+25k,9+25k,14+25k,19+25k,24+25k");
  $all_answers_diff_order = Compute("9+25k,4+25k,14+25k,19+25k,24+25k");

  $C1->compare($general_answer); # is true
  $C1->compare($all_answers); # is true
  $C1->compare($all_answers_diff_order); # is true

  Can an force general solution only with

        Context()->flags->set(requireGeneralSolution => 1);
  $C1->compare($general_answer); # is true
  $C1->compare($all_answers); # is false

  Can an force all solutions only with

        Context()->flags->set(requireAllSolutions => 1);
  $C1->compare($general_answer); # is false
  $C1->compare($all_answers); # is true

  Students can enter 'none' when there is no solution
  #ex: 15x ≡ 10 (mod 24)
        $C2 = Congruence(15, 10, 24); 
  $none = Compute("None");
  $n = Compute("n");

  $C2->compare($none); # is true
  $C2->compare($n); # is true
  $C1->compare($none); # is false

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