# Na02 denotes the example of Nagasaka' ISSAC02.

#Nagasaka, Kosaku. Towards certified irreducibility testing of bivariate approximate polynomials. In Mora, T., editor  ISSAC 2002 Procedings of 2002 International Symposium on Symbolic and Algebraic Computing, pages 192-199, New York, N.Y., 2002. ACM Press. ISBN 1-58113-484-3.

 Na02:=expand((x^2+u*x+2*u-1)*(x^3+u^2*x-u+7)+0.2*x);

 
#Sa01_2 denotes the example of Sasaki's second example in ISSAC01.

# Sasaki, Tateaki. Approximate multivariate polynomial factorization based on zero-sum relations. In Mourrain, B., editor  ISSAC 2001 Procedings of 2001 International Symposium on Symbolic and Algebraic Computing, pages 284-291, New York, N.Y., 2001. ACM Press. ISBN 1-58113-417-7.


G2:=x^5+(u-1)*x^4-(2*u^2+3)*x^3+(2*u^3-3*u^2-2)*x^2+(u^4-u^3+3*u-3)*x+(2*u^5-3*u^3-4*u^2+3):
H2:=x^5+(u+2)*x^4+(2*u^2-3*u-1)*x^3+(2*u^4+3*u^3-4*u^2-3*u)*x+(u^5+2*u^4-4*u^2-3):
DD2:=2*u*x^9+(3*u^3-4*u)*x^6+(u^5+3*u^2)*x^3-(3*u^7+4*u^3)*x:
Sa01_2:=evalf(expand(G2*H2+DD2*10^(-12))):


# Sa01_1 denotes the example of Sasaki's first example in ISSAC01.

G1:=x^10+(u+1)*x^9+(u^2-2)*x^8+(2*u^3-u^2+2)*x^7+(u^7-u^5-2*u+1)*x^3+(2*u^8-u^7+3*u^3-2)*x^2+(u^9+5*u^5-u^3+4)*x+(3*u^10+2*u^6+3*u^3+2):
H1:=x^10+(u-2)*x^9+(u^2+3*u-3)*x^7+(u^3+3*u^2+2)*x^5+(2*u^6-u^4+3*u^2-4)*x^4+(u^8+4*u^6-2*u^2+2)*x^2+(3*u^9-u^7+2*u^2-4)*x+(u^10-3*u^7-2*u^4+3):
DD1:=2*u*x^9-(3*u^3+u)*x^6+(u^5-3*u^2)*x^3+(3*u^7-4*u^3)*x:
Sa01_1:=evalf(expand(G1*H1+10^(-5)*DD1)):


#  Cor01 denotes the example of Corless, Giesbrech, Hoeij, Kotsireas, Watt  in  ISSAC01.

# Corless, Robert M., Geisbrecht, Mark W., van Hoeij, Mark, Kotsireas, Ilias S, and Watt, Stephen M. Towards factoring bivariate approximate polynomials. In Mourrain, B., editor  ISSAC 2001 Procedings of 2001 International Symposium on Symbolic and Algebraic Computing, pages 85-92, New York, N.Y., 2001. ACM Press. ISBN 1-58113-417-7.


G3:=-84+41*x+23*y+99*x^2*y^5-61*x^2*y^4-50*x^2*y^3-12*x^2*y^2-18*x^2*y-26*x*y^7-62*x*y^6+x*y^5-47*x*y^4-91*x*y^3-47*x*y^2+66*x^3*y-55*x^7*y-35*x^6*y^2+97*x^6*y+79*x^5*y^3+56*x^5*y^2+49*x^5*y+57*x^4*y^4-59*x^4*y^3+45*x^4*y^2-8*x^4*y^4+92*x^3*y^5+77*x^3*y^2+54*x^3+56*y^3+31*x^2-90*y^7-58*y^8-85*x^8-37*x^7-86*y^2+50*y^6+83*y^2+63*x^5+94*y^4-93*x^4-y^5-5*x^2*y^6-61*x*y+43*x^3*y^4-62*x^3*y^3:
H3:=-76-53*x+88*y+66*x^2*y^5-29*x^2*y^4-91*x^2*y^3-53*x^2*y^2-19*x^2*y+68*x*y^6-72*x*y^5-87*x*y^4+79*x*y^3+43*x*y^2+80*x^3*y-50*x^6*y-53*x^5*y^2+85*x^5*y+78*x^4*y^3+17*x^4*y^2+72*x^4*y+30*x^3*y^2+72*x^3-23*y^6-47*x^2-61*y^7+19*x^7-42*y^2+88*x^6-34*y^3+49*x^5+31*y^4-99*x^4-37*y^5-66*x*y-85*x^3*y^4-86*x^3*y^3:
Cor01:=evalf(expand(G3*H3+0.0003819));



# Cor02 denotes the example of Corless, Galligo, Kotsireas, Watt' ISSAC02:

#Corless, Robert M., Galligo, Andre, Kotsireas, Ilias S., and Watt, Stephen M. A geometric-numeric algorithm for absolute factorization of multivariate polynomials. In Mora, T., editor  ISSAC 2002 Procedings of 2002 International Symposium on Symbolic and Algebraic Computing, pages 192-199, New York, N.Y., 2002. ACM Press. ISBN 1-58113-484-3.


Cor02:=-3*x^9+8*x^6*y^3-5*x^3*y^6+y^9-4*x^7*y+3*x^4*y^4-8*x^7+8*x^6*y-x^5*y^2+6*x^4*y^3-10*x^3*y^4+x^2*y^5+3*y^7-4*x^5*y+3*x^4*y^2-5*x^3*y^3+4*x^2*y^4+3*y^6-4*x^5+5*x^4*y-11*x^3*y^2+5*x^2*y^3+4*x*y^4+3*y^5-2*x^4-16*x^3*y-x^2*y^2+8*x*y^3+6*y^4-11*x^3-16*x^2*y+4*x*y^2+8*y^3-20*x^2+3*y^2-16*x+7*y-3;