c = CC() print "c:", c c = c.one() print "c:", c c = CC((2, ), (3, )) print "c:", c print "c^5:", c**5 + c.one() print c = CC((2, ), rn) print "c: ", c print "1/c: " + str(1 / c) print zm = ZM(19, 11) print "zm: " + str(zm) print "zm^2: " + str(zm * zm) print "1/zm: " + str(1 / zm) #print "zm.ring: " + str(zm.ring.toScript()); print r = PolyRing(QQ(), "x,y", PolyRing.lex) print "Ring: " + str(r) print # sage like: with generators for the polynomial ring #is automatic: [one,x,y] = r.gens(); zero = r.zero() try:
print "z1 = " + str(z1); z2 = z1**2 + 12345678901234567890; print "z2 = " + str(z2); print; print "------- QQ = BigRational ------------"; r1 = QQ(1,12345678901234567890); print "r1 = " + str(r1**3); r2 = r1**2 + (1,12345678901234567890); print "r2 = " + str(r2); print; print "------- ZM = ModInteger ------------"; m1 = ZM(19,12345678901234567890); print "m1 = " + str(m1); m2 = m1**2 + 12345678901234567890; print "m2 = " + str(m2); print; print "------- GF = ModInteger ------------"; m1 = GF(19,12345678901234567890); print "m1 = " + str(m1); m2 = m1**2 + 12345678901234567890; print "m2 = " + str(m2); print; print "------- DD = BigDecimal ------------";
#
# jython examples for jas.
# $Id$
#
import sys
from java.lang import System
from jas import Ring, PolyRing
from jas import ZM, QQ, AN, RF
from jas import terminate, startLog
# polynomial examples: factorization over Z_p(x)(sqrt{p}(x))[y]
Q = PolyRing(ZM(5), "x", PolyRing.lex)
print "Q = " + str(Q)
[e, a] = Q.gens()
#print "e = " + str(e);
print "a = " + str(a)
Qr = RF(Q)
print "Qr = " + str(Qr.factory())
[er, ar] = Qr.gens()
#print "er = " + str(er);
#print "ar = " + str(ar);
print
Qwx = PolyRing(Qr, "wx", PolyRing.lex)
print "Qwx = " + str(Qwx)
[ewx, ax, wx] = Qwx.gens()
print "------- ZZ = BigInteger ------------" z1 = ZZ(12345678901234567890) print "z1 = " + str(z1) z2 = z1**2 + 12345678901234567890 print "z2 = " + str(z2) print print "------- QQ = BigRational ------------" r1 = QQ(1, 12345678901234567890) print "r1 = " + str(r1**3) r2 = r1**2 + (1, 12345678901234567890) print "r2 = " + str(r2) print print "------- ZM = ModInteger ------------" m1 = ZM(19, 12345678901234567890) print "m1 = " + str(m1) m2 = m1**2 + 12345678901234567890 print "m2 = " + str(m2) print print "------- GF = ModInteger ------------" m1 = GF(19, 12345678901234567890) print "m1 = " + str(m1) m2 = m1**2 + 12345678901234567890 print "m2 = " + str(m2) print print "------- DD = BigDecimal ------------" d1 = DD(12345678901234567890) print "d1 = " + str(d1)
from java.lang import System, Integer from jas import PolyRing, ZZ, QQ, ZM from jas import terminate, startLog from basic_sigbased_gb import sigbased_gb from basic_sigbased_gb import ggv, ggv_first_implementation from basic_sigbased_gb import coeff_free_sigbased_gb from basic_sigbased_gb import arris_algorithm, min_size_mons from basic_sigbased_gb import f5, f5z from staggered_linear_basis import staglinbasis #r = PolyRing( QQ(), "(B,S,T,Z,P,W)", PolyRing.lex ); #r = PolyRing( ZZ(), "(B,S,T,Z,P,W)", PolyRing.lex ); r = PolyRing(ZM(32003), "(B,S,T,Z,P,W)", PolyRing.lex) #r = PolyRing( ZM(19), "(B,S,T,Z,P,W)", PolyRing.lex ); print "Ring: " + str(r) print [one, B, S, T, Z, P, W] = r.gens() p1 = 45 * P + 35 * S - 165 * B - 36 p2 = 35 * P + 40 * Z + 25 * T - 27 * S p3 = 15 * W + 25 * S * P + 30 * Z - 18 * T - 165 * B**2 p4 = -9 * W + 15 * T * P + 20 * S * Z p5 = P * W + 2 * T * Z - 11 * B**3 p6 = 99 * W - 11 * B * S + 3 * B**2 p7 = 10000 * B**2 + 6600 * B + 2673 F = [p1, p2, p3, p4, p5, p6, p7]
import sys from jas import Ring, PolyRing, ParamIdeal, QQ, ZM, RR from jas import startLog, terminate # Boolean coefficient boolean GB # see S. Inoue and A. Nagai "On the Implementation of Boolean Groebner Bases" in ASCM 2009 # Z_2 regular ring coefficent example r = PolyRing(RR(ZM(2), 3), "a,x,y", PolyRing.lex) print "r = " + str(r) #print len(r.gens()) [s1, s2, s3, a, x, y] = r.gens() one = r.one() print "one = " + str(one) print "s1 = " + str(s1) print "s2 = " + str(s2) print "s3 = " + str(s3) print "a = " + str(a) print "x = " + str(x) print "y = " + str(y) #brel = [ a**2 - a, x**2 - x, y**2 - y ]; brel = [x**2 - x, y**2 - y] #print "brel = " + str(brel[0]) + ", " + str(brel[1]) + ", " + str(brel[2]); print "brel = " + str(brel[0]) + ", " + str(brel[1]) pl = [(one + s1 + s2) * (x * y + x + y), s1 * x + s1, a * y + a, x * y]