tdiv

tdiv(poly1,poly2)

:: Tests whether poly2 divides poly1.

return

Quotient if poly2 divides poly1, 0 otherwise.

poly1 poly2

polynomial

• Tests whether poly2 divides poly1 in polynomial ring.
• One application of this function: Consider the case where a polynomial is certainly an irreducible factor of the other polynomial, but the multiplicity of the factor is unknown. Application of tdiv() to the polynomials repeatedly yields the multiplicity.

[11] Y=(x+y+z)^5*(x-y-z)^3;  
x^8+(2*y+2*z)*x^7+(-2*y^2-4*z*y-2*z^2)*x^6+(-6*y^3-18*z*y^2-18*z^2*y-6*z^3)*x^5
+(6*y^5+30*z*y^4+60*z^2*y^3+60*z^3*y^2+30*z^4*y+6*z^5)*x^3+(2*y^6+12*z*y^5
+30*z^2*y^4+40*z^3*y^3+30*z^4*y^2+12*z^5*y+2*z^6)*x^2+(-2*y^7-14*z*y^6
-42*z^2*y^5-70*z^3*y^4-70*z^4*y^3-42*z^5*y^2-14*z^6*y-2*z^7)*x-y^8-8*z*y^7
-28*z^2*y^6-56*z^3*y^5-70*z^4*y^4-56*z^5*y^3-28*z^6*y^2-8*z^7*y-z^8
[12] for(I=0,F=x+y+z,T=Y; T=tdiv(T,F); I++); 
[13] I;
5

References

section sdiv, sdivm, srem, sremm, sqr, sqrm.

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