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#
# jython examples for jas.
# $Id$
#
import sys
from java.lang import System
from jas import PolyRing, QQ, RF, DD
from jas import terminate, startLog
# system biology examples: GB in RF()
# see: Informatik Spektrum, 2009, February,
# Laubenbacher, Sturmfels: Computer Algebra in der Systembiologie
# example from: http://theory.bio.uu.nl/rdb/books/tb.pdf
# ------------ input rational expression --------------------
r = PolyRing(RF(PolyRing(QQ(),"A",PolyRing.lex)),"L, M, R",PolyRing.lex);
print "PolyRing: " + str(r);
print;
#automatic: [one,A,L,M,R] = r.gens();
c = 1;
gamma = 1;
v = 1;
c0 = QQ(5,100); # 0.05
h = 2;
n = 5;
delta = QQ(2,10); # 0.2
f1 = R - 1/(1+A**n);
f2 = M * L - delta * A - ( v * M * A ) / ( h + A );
f3 = c0 + c * ( 1 - 1 / ( 1 + A**n ) - gamma * M);
F = [f1,f2,f3];
print "f1 = " + str(f1);
print "f2 = " + str(f2);
print "f3 = " + str(f3);
print;
I = r.ideal( "", list=F );
print "Ideal: " + str(I);
print;
#sys.exit();
G = I.GB();
print "GB: " + str(G);
print;
# ------------ GB and CGB --------------------
r2 = PolyRing(PolyRing(QQ(),"L",PolyRing.lex),"A, M, R",PolyRing.lex);
#r2 = PolyRing(RF(PolyRing(QQ(),"L",PolyRing.lex)),"A, M, R",PolyRing.lex);
print "PolyRing: " + str(r2);
print;
#automatic: [one,L,A,M,R] = r2.gens();
fi1 = ( (21,20) * A**6 + (21,10) * A**5 + (1,20) * A + (1,10) ) * L - ( (1,5) * A**7 + (29,20) * A**6 + (1,5) * A**2 + (9,20) * A );
fi2 = ( A**5 + 1 ) * M - ( (21,20) * A**5 + (1,20) );
fi3 = ( A**5 + 1 ) * R - ( 1 );
#fi4 = L - 1;
Fi = [fi1,fi2,fi3];
print "fi1 = " + str(fi1);
print "fi2 = " + str(fi2);
print "fi3 = " + str(fi3);
#print "fi4 = " + str(fi4);
print;
Ii = r2.ideal( "", list=Fi );
print "Ideal: " + str(Ii);
print;
Gi = Ii.GB();
print "GB: " + str(Gi);
print;
Ipi = r2.paramideal( "", list=Gi.list );
print "ParamIdeal: " + str(Ipi);
print;
cgb = Ipi.CGB();
print "CGB: " + str(cgb);
print;
#sys.exit();
# ------------ real roots --------------------
r3 = PolyRing(QQ(),"A",PolyRing.lex);
print "PolyRing: " + str(r3);
print;
eps = QQ(1,10) ** DD().elem.DEFAULT_PRECISION;
print "eps = ", eps;
[one,A] = r3.gens();
plot={};
plotd={};
br = 1;
for i in range(1,30):
L = QQ(-1) + (i,10);
#L = QQ(9,10) + (i,100);
fr = QQ(5) * ( (1,5) ) * A**7 - ( (21,20) * L - (29,20) ) * A**6 - ( (21,10) * L ) * A**5 + ( (1,5) ) * A**2 - ( (1,20) * L - (9,20) ) * A - ( (1,10) * L );
print "L = " + str(DD(L));
#print "fr = " + str(fr);
#print;
t = System.currentTimeMillis();
R = r3.realRoots(fr);
t = System.currentTimeMillis() - t;
# print "R = " + str([ str(DD(r.elem.getRational())) for r in R ]);
print "R = " + str([ r.elem.decimalMagnitude() for r in R ]);
plot[float(DD(L))] = R;
#print "real roots time =", t, "milliseconds";
if len(R) != br:
br = len(R);
print "#(real roots) = %s" % br;
b = L - (11,100);
for j in range(1,12):
L = b + (j,100);
fri = QQ(5) * ( (1,5) ) * A**7 - ( (21,20) * L - (29,20) ) * A**6 - ( (21,10) * L ) * A**5 + ( (1,5) ) * A**2 - ( (1,20) * L - (9,20) ) * A - ( (1,10) * L );
R = r3.realRoots(fri);
print "L = %s, Ri = %s" %(DD(L),[ r.elem.decimalMagnitude() for r in R ]);
plot[float(DD(L))] = R;
R = r3.realRoots(fri,eps);
plotd[float(DD(L))] = [ r.elem.decimalMagnitude() for r in R ];
t = System.currentTimeMillis();
R = r3.realRoots(fr,eps);
plotd[float(DD(L))] = [ r.elem.decimalMagnitude() for r in R ];
t = System.currentTimeMillis() - t;
print "R = " + str([ r.elem.decimalMagnitude() for r in R ]);
print "real roots time =", t, "milliseconds";
print;
print "real algebraic numbers:";
pk = plot.keys();
pk.sort();
for l in pk:
print "%s, %s" %(l,[ str(p.elem) for p in plot[l]]);
print;
print "real root approxmations:";
pk = plotd.keys();
pk.sort();
for l in pk:
print "%s, %s" %(l,[ str(p) for p in plotd[l]]);
print;
# ------------ factor polynomial --------------------
r5 = PolyRing(QQ(),"L",PolyRing.lex);
print "PolyRing: " + str(r5);
print;
[one,L] = r5.gens();
frl = L**5 + (5,31) * L**4 - (10,31) * L**3 + (10,31) * L**2 - (5,31) * L + (1,31);
#frl = (1,4) * L - (1,4);
print "frl = " + str(frl);
print;
t = System.currentTimeMillis();
R = r5.realRoots(frl);
t = System.currentTimeMillis() - t;
print "R = " + str([ r.elem.decimalMagnitude() for r in R ]);
print "real roots time =", t, "milliseconds";
t = System.currentTimeMillis();
R = r5.realRoots(frl,eps);
t = System.currentTimeMillis() - t;
print "R = " + str([ r.elem.decimalMagnitude() for r in R ]);
print "real roots time =", t, "milliseconds";
t = System.currentTimeMillis();
fk = r5.squarefreeFactors(frl);
#fk = r5.factors(frl);
t = System.currentTimeMillis() - t;
#print "fk = " + str(fk);
#print "factor time =", t, "milliseconds";
g = one;
for h, i in fk.iteritems():
print "h**i = (", h, ")**" + str(i);
h = h**i;
g = g*h;
#startLog();
terminate();
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