Hi Ángel, > Am 30.09.2018 um 11:35 schrieb Ángel del Río <adel...@um.es>: > > Hi, > > How can I get the coefficients of an element of a finite field in a basis?
Just like with any vector space: by using Coefficients(basis, vector). > For example, I would like to obtain the coefficients of z^189 in the > canonical basis of GF(2^32) with z a primitive element of F. The following > calculation shows that GAP knows them and I could manually read it but I > would like to have an automatic way to obtain the coefficients. > > gap> F:=GF(2^32); > GF(2^32) > gap> CB:=CanonicalBasis(F); > CanonicalBasis( GF(2^32) ) > gap> Elements(CB); > [ z0, z31, z30, z29, z28, z27, z26, z25, z24, z23, z22, z21, z20, z19, z18, > z17, z16, z15, z14, z13, z12, z11, z10, z9, z8, z7, z6, z5, z4, z3, z2, z ] > gap> z := PrimitiveElement(F); > z > gap> z^189; > 1+z3+z5+z11+z12+z13+z14+z15+z17+z22+z23+z24+z25+z28+z30 gap> v:=Coefficients(CB, z^189); <an immutable GF2 vector of length 32> gap> AsPlist(v); [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ] Cheers, Max > > Thanks, > > Ángel > > -- > Ángel del Río Mateos > Dep. Matemáticas > Universidad de Murcia > 30100 Murcia, Spain > adel...@um.es > Phone: +34 868 88 3537 > Fax: +34 868 88 4182 > > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
