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D.15.14.2 nfmodStd
Procedure from library nfmodstd.lib (see nfmodstd_lib).
- Usage:
- nfmodStd(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 "nfmodstd.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=nfmodStd(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=nfmodStd(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=nfmodStd(I);
I;
==> I[1]=y2-14x+51y
==> I[2]=xy+2x-7y
==> I[3]=x2+y
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See also:
modStd.
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