Learning Guide Learning Guide

58 • Chapter 3: Finding SolutionsFinding Solutions Modulo mThe msolve command solves equations in the integers modulo m (thepositive representation for integers), solving for all unknowns in the expression(s).> msolve({3*x-4*y=1,7*x+y=2},17);{y = 6, x = 14}> msolve({2^n=3},19);{n = 13 + 18 _Z1 ~}The tilde (~) on _Z1 indicates that msolve has placed an assumptionon _Z1, in this case that _Z1 is an integer.> about( _Z1 );Originally _Z1, renamed _Z1~:is assumed to be: integerSection 5.2 describes how you can place assumptions on unknowns.Solving Recurrence RelationsThe rsolve command solves recurrence equations, returning an expressionfor the general term of the function.> rsolve({f(n)=f(n-1)+f(n-2),f(0)=1,f(1)=1},{f(n)});⎧⎫√ 2⎪⎨ 5 (−f(n) = 2 1 + √ √ 25 )n 5 (−5 ⎪⎩1 + √ − 2 1 − √ 5 )n ⎪⎬5 5 1 − √ 5 ⎪⎭For more information, refer to ?LREtools.3.4 PolynomialsA polynomial in Maple is an expression containing unknowns. Each termin the polynomial contains a product of the unknowns. For example,