1Function: idealmul 2Section: number_fields 3C-Name: idealmul0 4Prototype: GGGD0,L, 5Help: idealmul(nf,x,y,{flag=0}): product of the two ideals x and y in the 6 number field nf. If (optional) flag is nonzero, reduce the result. 7Description: 8 (gen, gen, gen, ?0):gen idealmul($1, $2, $3) 9 (gen, gen, gen, 1):gen idealmulred($1, $2, $3) 10 (gen, gen, gen, #small):gen $"invalid flag in idealmul" 11 (gen, gen, gen, small):gen idealmul0($1, $2, $3, $4) 12Doc: ideal multiplication of the ideals $x$ and $y$ in the number field 13 \var{nf}; the result is the ideal product in HNF. If either $x$ or $y$ 14 are extended ideals\sidx{ideal (extended)}, their principal part is suitably 15 updated: i.e. multiplying $[I,t]$, $[J,u]$ yields $[IJ, tu]$; multiplying 16 $I$ and $[J, u]$ yields $[IJ, u]$. 17 \bprog 18 ? nf = nfinit(x^2 + 1); 19 ? idealmul(nf, 2, x+1) 20 %2 = 21 [4 2] 22 23 [0 2] 24 ? idealmul(nf, [2, x], x+1) \\ extended ideal * ideal 25 %3 = [[4, 2; 0, 2], x] 26 ? idealmul(nf, [2, x], [x+1, x]) \\ two extended ideals 27 %4 = [[4, 2; 0, 2], [-1, 0]~] 28 @eprog\noindent 29 If $\fl$ is nonzero, reduce the result using \kbd{idealred}. 30Variant: 31 \noindent See also 32 \fun{GEN}{idealmul}{GEN nf, GEN x, GEN y} ($\fl=0$) and 33 \fun{GEN}{idealmulred}{GEN nf, GEN x, GEN y} ($\fl\neq0$). 34