7.20 Modular Solve and Roots

The operators (m_solve) and (m_roots) are for modular polynomials and modular polynomial systems.⁶ The moduli need not be primes. m_solve requires a modulus to be set. m_roots takes the modulus as a second argument. For example:

on modular; setmod 8;
m_solve(2x=4);            ->  {{X=2},{X=6}}
m_solve({x^2-y^3=3});
    ->  {{X=0,Y=5}, {X=2,Y=1}, {X=4,Y=5}, {X=6,Y=1}}
m_solve({x=2,x^2-y^3=3}); ->  {{X=2,Y=1}}
off modular;
m_roots(x^2-1,8);         ->  {1,3,5,7}
m_roots(x^3-x,7);         ->  {0,1,6}

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