# Singular

#### D.15.1.2 algemodStd

Procedure from library algemodstd.lib (see algemodstd_lib).

Usage:
algemodStd(I, #); I ideal, # optional parameters

Return:
standard basis of I over algebraic number field

Note:
The procedure passes to modStd if the ground field has no parameter. In this case, the optional parameters # (if given) are directly passed to modStd.

Example:
 LIB "algemodstd.lib"; ring r1 =(0,a),(x,y),dp; minpoly =a^2+1; ideal k=(a/2+1)*x^2+2/3y, 3*x-a*y+ a/7+2; ideal I=algemodStd(k); I; ==> I[1]=x+(-1/3a)*y+(1/21a+2/3) ==> I[2]=y2+(32/5a-178/35)*y+(-4/7a-195/49) ring r2 =(0,a),(x,y,z),dp; minpoly =a^3 +2; ideal k=(a^2+a/2)*x^2+(a^2 -2/3*a)*yz, (3*a^2+1)*zx-(a+4/7)*y+ a+2/5; ideal IJ=algemodStd(k); IJ; ==> IJ[1]=xz+(138/763a2+65/763a-46/763)*y+(-96/545a2-31/545a+32/545) ==> IJ[2]=x2+(28/45a2-14/45a+52/45)*yz ==> IJ[3]=yz2+(-3354/23653a2-6390/23653a-7683/47306)*xy+(993/6758a2+4104/1689\ 5a+4449/33790)*x ring r3=0,(x,y),dp;// ring without parameter ideal I = x2 + y, xy - 7y + 2x; I=algemodStd(I); I; ==> I[1]=y2-14x+51y ==> I[2]=xy+2x-7y ==> I[3]=x2+y