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sdiv
, sdivm
, srem
, sremm
, sqr
, sqrm
sdiv()
, sdivm()
, srem()
, sremm()
: polynomial sqr()
, sqrm()
: a list [quotient,remainder]
sdiv()
and
srem()
compute
the polynomial quotient and remainder of poly1 divided by poly2.
sdivm()
, sremm()
, sqrm()
execute the same
operation over GF(mod).
sqr()
to get both the quotient and remainder at once.
idiv()
, irem()
for integer quotient.
%
.
[0] sdiv((x+y+z)^3,x^2+y+a); x+3*y+3*z [1] srem((x+y+z)^2,x^2+y+a); (2*y+2*z)*x+y^2+(2*z-1)*y+z^2-a [2] X=(x+y+z)*(x-y-z)^2; x^3+(-y-z)*x^2+(-y^2-2*z*y-z^2)*x+y^3+3*z*y^2+3*z^2*y+z^3 [3] Y=(x+y+z)^2*(x-y-z); x^3+(y+z)*x^2+(-y^2-2*z*y-z^2)*x-y^3-3*z*y^2-3*z^2*y-z^3 [4] G=gcd(X,Y); x^2-y^2-2*z*y-z^2 [5] sqr(X,G); [x-y-z,0] [6] sqr(Y,G); [x+y+z,0] [7] sdiv(y*x^3+x+1,y*x+1); divsp: cannot happen return to toplevel |
idiv
, irem
, 6.3.10 %
.
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