// this program is a magma translation of the maple program biquadratic, // so that that explanations are not rewritten in this file. This program // allows us to compute the biquadratic forms for a general curve of genus // 3 defined by a polynomial of degree 7. // This programs requires about 4 hours and 150 Mo of memory on a Pentium II 600Mhz // The file of this result is biquad.gz cdb:=PolynomialRing(Rationals()); polf:=PolynomialRing(cdb,8); ratf:=FieldOfFractions(polf); polsansx:=PolynomialRing(ratf,24); ratsansx:=FieldOfFractions(polsansx); pol:=PolynomialRing(ratsansx,3); rat:=FieldOfFractions(pol); f:=function(x) return f7*x^7+f6*x^6+f5*x^5+f4*x^4+f3*x^3+f2*x^2+f1*x+f0; end function; sym2:=function(P) local Q,C,Q1,Q2,Q3; Q:=P; while Q ne Evaluate(pol!Q,[u,v,x3]) do Q1:=Evaluate(pol!Q,[x1,0,x3]); Q2:=Q-Evaluate(pol!Q1,[x1+x2,x2,x3]); Q3:=pol!(Q2/x1/x2); Q:=Evaluate(pol!Q1,[s12,x2,x3])+p12*Q3; end while; Q:=pol!Q; C:=Coefficients(Q); if #C eq 0 then return polsansx!0; else return polsansx!C[1]; end if; end function; sym3:=function(P) local Q,Q1,Q2,Q3,Q4,Q5,verif; Q:=pol!P; while Q ne Evaluate(Q,[u,v,w]) do Q1:=Evaluate(Q,[x1,x2,0]); Q2:=sym2(Q1); Q3:=Evaluate(Q2,[s,b,p,x1+x2+x3,x1*x2+x1*x3+x2*x3,A0,A1,A2,A3,C0,C1,C2,C3,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w]); Q4:=Q-Q3; Q5:=pol!(Q4/(x1*x2*x3)); Q:=Evaluate(Q2,[s,b,p,s,b,A0,A1,A2,A3,C0,C1,C2,C3,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w])+p*Q5; end while; Q:=pol!Q; C:=Coefficients(Q); if #C eq 0 then return polsansx!0; else return polsansx!C[1]; end if; end function; B123:=pol!((x1*f(x2)-x2*f(x1)-x3*f(x2)+x3*f(x1)-x1*f(x3)+x2*f(x3))/((x1-x2)*(x2-x3)*(x3-x1))); B23:=pol!((f(x2)-f(x3))/(x2-x3)); retourapol:=function(Q,corps) local Ky,Y1,Y2,Y3,Q2,P,coeff,mono,size; Ky:=PolynomialRing(corps,3); Q2:=MultivariatePolynomial(Ky,Q,Y1); coeff:=Coefficients(Q2); mono:=Monomials(Q2); size:=#coeff; P:=Ky!0; for i:=1 to size do P:=P+Evaluate(coeff[i],[Y2,Y3])*mono[i]; end for; P:=Evaluate(P,[x1,x2,x3]); return pol!P; end function; simp:=function(P) local Q,corps,K; corps:= PolynomialRing(polsansx,2); K:=PolynomialRing(corps); Q:=Evaluate(pol!P,[X1,X2,X3]); b123:=Evaluate(B123,[X1,X2,X3]); Q:=Q mod b123; Q:=retourapol(Q,corps); corps:= PolynomialRing(polsansx,2); K:=PolynomialRing(corps); Q:=Evaluate(pol!Q,[X1,X2,X3]); b23:=Evaluate(B23,[X1,X2,X3]); Q:=Q mod b23; Q:=retourapol(Q,corps); corps:= PolynomialRing(polsansx,2); K:=PolynomialRing(corps); Q:=Evaluate(pol!Q,[X1,X2,X3]); F:=Evaluate(pol!f(x3),[X1,X2,X3]); Q:=Q mod F; Q:=retourapol(Q,corps); return Q; end function; a0:=1; a1:=x1+x2+x3; a2:=x1*x2+x1*x3+x2*x3; a3:=x1*x2*x3; c0:=-f7*s^3+f7*b*s-f6*s^2+3*f7*p+2*f6*b; c1:=-f7*s^4+3*f7*b*s^2-f6*s^3-f7*b^2-f7*p*s+2*f6*b*s-f5*s^2+2*f5*b; c2:=f7*b*s^3-2*f7*b^2*s+f6*b*s^2+f7*b*p-f6*b^2+f5*b*s-3*f5*p; c3:=f7*b^2*s^2-f7*p*s^3+f7*p*b*s-f7*b^3+f6*b^2*s-f6*p*s^2+f5*b^2-f5*p*s; simpsp:=function(P) local Q; Q:=polsansx!P; Q:=Evaluate(Q,[a1,a2,a3,s12,p12,A0,A1,A2,A3,C0,C1,C2,C3,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w]); Q:=simp(Q); Q:=sym3(Q); return Q; end function; k:=[1,s,b,p,c0,c1,c2,c3]; K2:=Matrix(8,8,[1, s,b,p,-f7*s^3-f6*s^2+f7*s*b+2*f6*b+3*f7*p,-f7*s^4-f6*s^3+ 3*f7*s^2*b-f5*s^2+2*f6*s*b-f7*s*p-f7*b^2+2*f5*b,f7*s^3*b+ f6*s^2*b-2*f7*s*b^2+f5*s*b-f6*b^2+f7*b*p-3*f5*p,-f7*s^3*p+ f7*s^2*b^2-f6*s^2*p+f6*s*b^2+f7*s*b*p-f5*s*p-f7*b^3+f5*b^2,s, s^2,s*b,s*p,-f7*s^4-f6*s^3+f7*s^2*b+2*f6*s*b+3*f7*s*p,-f7*s^3*b -f6*s^2*b+2*f7*s^2*p+f4*s^2+2*f7*s*b^2+2*f6*s*p+f3*s+f6*b^2- 2*f7*b*p-f4*b+f5*p+f2,f7*s^3*p+f7*s^2*b^2+f6*s^2*p+f6*s*b^2- 3*f7*s*b*p-f4*s*b-2*f5*s*p-f7*b^3+f5*b^2-2*f6*b*p-f3*b+f7*p^2 +f4*p+f1,f7*s*b^3+f7*s*p^2+f4*s*p+f1*s+f6*b^3-2*f7*b^2*p- f4*b^2+f5*b*p+f2*b,b,s*b,b^2,b*p,-f7*s^3*b-f6*s^2*b+f7*s*b^2+ 2*f6*b^2+3*f7*b*p,-f7*s^3*p-f6*s^2*p+3*f7*s*b*p+f4*s*b-f5*s*p+ f5*b^2+2*f6*b*p+f3*b-f7*p^2-f4*p-f1,2*f7*s^2*b*p+2*f6*s*b*p- f7*s*p^2+f1*s-2*f7*b^2*p-f4*b^2-f5*b*p+f2*b-f6*p^2-f3*p-f0, -f7*s^2*p^2+f1*s^2+2*f7*s*b^2*p+f2*s*b-f6*s*p^2-f3*s*p-f0*s+ 2*f6*b^2*p+f3*b^2-f7*b*p^2-f4*b*p-f1*b,p,s*p,b*p,p^2,-f7*s^3*p -f6*s^2*p+f7*s*b*p+2*f6*b*p+3*f7*p^2,f7*s*p^2+f4*s*p+f5*b*p+ f6*p^2+f3*p+f0,f7*s^2*p^2+f6*s*p^2-f0*s-f7*b*p^2-f4*b*p- 2*f5*p^2+f2*p,-f0*s^2+f7*s*b*p^2+f2*s*p+f6*b*p^2+f3*b*p+f0*b, -f7*s^3-f6*s^2+f7*s*b+2*f6*b+3*f7*p,-f7*s^4-f6*s^3+f7*s^2*b+ 2*f6*s*b+3*f7*s*p,-f7*s^3*b-f6*s^2*b+f7*s*b^2+2*f6*b^2+3*f7*b*p, -f7*s^3*p-f6*s^2*p+f7*s*b*p+2*f6*b*p+3*f7*p^2,-f5*f7*s^4-f6*f7*s^3*b -7*f7^2*s^3*p+(-f4*f7-f5*f6)*s^3+4*f7^2*s^2*b^2-f6^2*s^2*b- 9*f6*f7*s^2*p+(-f3*f7-f4*f6)*s^2+4*f6*f7*s*b^2+(-f4*f7+ 2*f5*f6)*s*b+(f5*f7-2*f6^2)*s*p+(-f2*f7-f3*f6)*s-2*f7^2*b^3+ (2*f5*f7+3*f6^2)*b^2+10*f6*f7*b*p+(-2*f3*f7+f4*f6)*b+11*f7^2*p^2+ (2*f4*f7-f5*f6)*p+2*f1*f7-f2*f6,-f4*f7*s^4-f5*f7*s^3*b- 3*f6*f7*s^3*p+(-f3*f7-f4*f6)*s^3+f6*f7*s^2*b^2-3*f7^2*s^2*b*p+ (f4*f7-f5*f6)*s^2*b+(f5*f7-3*f6^2)*s^2*p+(-f2*f7-f3*f6)*s^2+ f7^2*s*b^3+(f5*f7+f6^2)*s*b^2+2*f6*f7*s*b*p+2*f4*f6*s*b+ 6*f7^2*s*p^2+(5*f4*f7-2*f5*f6)*s*p+(f1*f7-f2*f6)*s-f7^2*b^2*p+ (-f4*f7+3*f5*f6)*b^2+(3*f5*f7+2*f6^2)*b*p+(f2*f7+f3*f6)*b+ 3*f6*f7*p^2+(4*f3*f7-f4*f6)*p+4*f0*f7-f1*f6,f4*f7*s^3*b+ 3*f5*f7*s^3*p+2*f6*f7*s^2*b*p+(f3*f7+f4*f6)*s^2*b+4*f7^2*s^2*p^2+ 3*f5*f6*s^2*p-2*f1*f7*s^2-f6*f7*s*b^3-f7^2*s*b^2*p+(-4*f5*f7+ 2*f6^2)*s*b*p+(-f2*f7+f3*f6)*s*b+4*f6*f7*s*p^2+2*f3*f7*s*p- f7^2*b^4+(f5*f7-f6^2)*b^3-3*f6*f7*b^2*p+(-f3*f7-f4*f6)*b^2+ (-f4*f7-5*f5*f6)*b*p+(f1*f7+f2*f6)*b-7*f5*f7*p^2+2*f2*f7*p, -f4*f7*s^3*p-2*f1*f7*s^3+f4*f7*s^2*b^2-f5*f7*s^2*b*p-2*f2*f7*s^2*b- 2*f6*f7*s^2*p^2+(f3*f7-f4*f6)*s^2*p+f5*f7*s*b^3+f6*f7*s*b^2*p+ (-f3*f7+f4*f6)*s*b^2+3*f7^2*s*b*p^2+(3*f4*f7-f5*f6)*s*b*p+ 2*f1*f7*s*b-2*f6^2*s*p^2+(f2*f7-f3*f6)*s*p-3*f7^2*b^3*p+(-f4*f7+ f5*f6)*b^3+(2*f5*f7+f6^2)*b^2*p+(f2*f7+f3*f6)*b^2+f6*f7*b*p^2+ 2*f3*f7*b*p+(4*f0*f7-f1*f6)*b+2*f7^2*p^3+(2*f4*f7-f5*f6)*p^2+ (2*f1*f7-f2*f6)*p,-f7*s^4-f6*s^3+3*f7*s^2*b-f5*s^2+2*f6*s*b- f7*s*p-f7*b^2+2*f5*b,-f7*s^3*b-f6*s^2*b+2*f7*s^2*p+f4*s^2+ 2*f7*s*b^2+2*f6*s*p+f3*s+f6*b^2-2*f7*b*p-f4*b+f5*p+f2, -f7*s^3*p-f6*s^2*p+3*f7*s*b*p+f4*s*b-f5*s*p+f5*b^2+2*f6*b*p+ f3*b-f7*p^2-f4*p-f1,f7*s*p^2+f4*s*p+f5*b*p+f6*p^2+f3*p+f0, -f4*f7*s^4-f5*f7*s^3*b-3*f6*f7*s^3*p+(-f3*f7-f4*f6)*s^3+f6*f7*s^2*b^2 -3*f7^2*s^2*b*p+(f4*f7-f5*f6)*s^2*b+(f5*f7-3*f6^2)*s^2*p+(-f2*f7 -f3*f6)*s^2+f7^2*s*b^3+(f5*f7+f6^2)*s*b^2+2*f6*f7*s*b*p+ 2*f4*f6*s*b+6*f7^2*s*p^2+(5*f4*f7-2*f5*f6)*s*p+(f1*f7-f2*f6)*s- f7^2*b^2*p+(-f4*f7+3*f5*f6)*b^2+(3*f5*f7+2*f6^2)*b*p+(f2*f7+ f3*f6)*b+3*f6*f7*p^2+(4*f3*f7-f4*f6)*p+4*f0*f7-f1*f6,-f3*f7*s^4- f4*f7*s^3*b-3*f5*f7*s^3*p+(-f2*f7-f3*f6)*s^3+f5*f7*s^2*b^2- 2*f6*f7*s^2*b*p+(2*f3*f7-f4*f6)*s^2*b+2*f7^2*s^2*p^2+(4*f4*f7- 3*f5*f6)*s^2*p+(-f2*f6-f3*f5+f4^2)*s^2+f6*f7*s*b^3-3*f7^2*s*b^2*p +(f4*f7+f5*f6)*s*b^2+(8*f5*f7-2*f6^2)*s*b*p+(2*f2*f7+f3*f6+ f4*f5)*s*b+4*f6*f7*s*p^2+(f3*f7+4*f4*f6-3*f5^2)*s*p+(2*f0*f7- f2*f5+f3*f4)*s+f7^2*b^4+(-2*f5*f7+f6^2)*b^3-f6*f7*b^2*p+ 2*f5^2*b^2+2*f7^2*b*p^2+(-f4*f7+3*f5*f6)*b*p+(f2*f6+2*f3*f5- f4^2)*b+(-3*f5*f7+2*f6^2)*p^2+(-f2*f7+2*f3*f6-f4*f5)*p+2*f0*f6- 2*f1*f5+f2*f4,f3*f7*s^3*b+f4*f7*s^3*p-f1*f7*s^3+f4*f7*s^2*b^2+ f5*f7*s^2*b*p+f3*f6*s^2*b+2*f6*f7*s^2*p^2+(f3*f7+f4*f6)*s^2*p- f1*f6*s^2-f6*f7*s*b^2*p+(-2*f3*f7+f4*f6)*s*b^2+3*f7^2*s*b*p^2+ (-3*f4*f7+f5*f6)*s*b*p+(2*f1*f7+f3*f5-f4^2)*s*b+(-4*f5*f7+ 2*f6^2)*s*p^2+(f2*f7+f3*f6-2*f4*f5)*s*p-f7^2*b^3*p-f4*f7*b^3- f6^2*b^2*p-f3*f6*b^2+f6*f7*b*p^2+(-2*f4*f6-2*f5^2)*b*p+(-2*f0*f7+ f1*f6+f2*f5-f3*f4)*b-2*f7^2*p^3+(-f4*f7-2*f5*f6)*p^2+(-2*f1*f7+ f2*f6-3*f3*f5+f4^2)*p-3*f0*f5+f1*f4,-f3*f7*s^3*p-f0*f7*s^3+ f3*f7*s^2*b^2-f1*f7*s^2*b-2*f5*f7*s^2*p^2-f3*f6*s^2*p+(-f0*f6+ f1*f5)*s^2+f4*f7*s*b^3+2*f5*f7*s*b^2*p+f3*f6*s*b^2+2*f3*f7*s*b*p+ (f0*f7-f1*f6+f2*f5)*s*b+2*f7^2*s*p^3+(2*f4*f7-2*f5*f6)*s*p^2+ (-2*f3*f5+f4^2)*s*p+(-f0*f5+f1*f4)*s+(-f3*f7+f4*f6)*b^3+ (-2*f4*f7+2*f5*f6)*b^2*p+(f1*f7+2*f3*f5-f4^2)*b^2+(f2*f7+ f3*f6)*b*p+(2*f0*f6-2*f1*f5+f2*f4)*b+2*f6*f7*p^3+(f3*f7+f4*f6- f5^2)*p^2+(f0*f7+f1*f6-f2*f5)*p,f7*s^3*b+f6*s^2*b-2*f7*s*b^2+ f5*s*b-f6*b^2+f7*b*p-3*f5*p,f7*s^3*p+f7*s^2*b^2+f6*s^2*p+ f6*s*b^2-3*f7*s*b*p-f4*s*b-2*f5*s*p-f7*b^3+f5*b^2-2*f6*b*p- f3*b+f7*p^2+f4*p+f1,2*f7*s^2*b*p+2*f6*s*b*p-f7*s*p^2+f1*s- 2*f7*b^2*p-f4*b^2-f5*b*p+f2*b-f6*p^2-f3*p-f0,f7*s^2*p^2+ f6*s*p^2-f0*s-f7*b*p^2-f4*b*p-2*f5*p^2+f2*p,f4*f7*s^3*b+ 3*f5*f7*s^3*p+2*f6*f7*s^2*b*p+(f3*f7+f4*f6)*s^2*b+4*f7^2*s^2*p^2+ 3*f5*f6*s^2*p-2*f1*f7*s^2-f6*f7*s*b^3-f7^2*s*b^2*p+(-4*f5*f7+ 2*f6^2)*s*b*p+(-f2*f7+f3*f6)*s*b+4*f6*f7*s*p^2+2*f3*f7*s*p- f7^2*b^4+(f5*f7-f6^2)*b^3-3*f6*f7*b^2*p+(-f3*f7-f4*f6)*b^2+ (-f4*f7-5*f5*f6)*b*p+(f1*f7+f2*f6)*b-7*f5*f7*p^2+2*f2*f7*p, f3*f7*s^3*b+f4*f7*s^3*p-f1*f7*s^3+f4*f7*s^2*b^2+f5*f7*s^2*b*p+ f3*f6*s^2*b+2*f6*f7*s^2*p^2+(f3*f7+f4*f6)*s^2*p-f1*f6*s^2- f6*f7*s*b^2*p+(-2*f3*f7+f4*f6)*s*b^2+3*f7^2*s*b*p^2+(-3*f4*f7+ f5*f6)*s*b*p+(2*f1*f7+f3*f5-f4^2)*s*b+(-4*f5*f7+2*f6^2)*s*p^2+ (f2*f7+f3*f6-2*f4*f5)*s*p-f7^2*b^3*p-f4*f7*b^3-f6^2*b^2*p- f3*f6*b^2+f6*f7*b*p^2+(-2*f4*f6-2*f5^2)*b*p+(-2*f0*f7+f1*f6+ f2*f5-f3*f4)*b-2*f7^2*p^3+(-f4*f7-2*f5*f6)*p^2+(-2*f1*f7+f2*f6- 3*f3*f5+f4^2)*p-3*f0*f5+f1*f4,f1*f7*s^4+f2*f7*s^3*b-f3*f7*s^3*p+ (-3*f0*f7+f1*f6)*s^3-4*f4*f7*s^2*b*p+(-2*f1*f7+f2*f6)*s^2*b- 4*f5*f7*s^2*p^2+(2*f2*f7-f3*f6)*s^2*p+(-3*f0*f6+f1*f5)*s^2- 2*f2*f7*s*b^2+2*f6*f7*s*b*p^2+(2*f3*f7-4*f4*f6)*s*b*p+(3*f0*f7- f1*f6+f2*f5)*s*b-2*f7^2*s*p^3-4*f5*f6*s*p^2+(2*f2*f6-f3*f5)*s*p+ (3*f0*f5-f1*f4)*s+2*f7^2*b^2*p^2+4*f4*f7*b^2*p+(-f2*f6+f4^2)*b^2+ (2*f5*f7+2*f6^2)*b*p^2+(-f2*f7+f3*f6+2*f4*f5)*b*p-f2*f4*b- 2*f6*f7*p^3+(-f3*f7+5*f5^2)*p^2+(-f0*f7-f1*f6-4*f2*f5+f3*f4)*p+ f0*f4,-f0*f7*s^4+f1*f7*s^3*b+f2*f7*s^3*p-f0*f6*s^3+f2*f7*s^2*b^2+ f3*f7*s^2*b*p+(-f0*f7+f1*f6)*s^2*b+(-3*f1*f7+f2*f6)*s^2*p+(2*f0*f5 -f1*f4)*s^2-2*f4*f7*s*b^2*p+(-f1*f7+f2*f6)*s*b^2-3*f5*f7*s*b*p^2+ (-f2*f7+f3*f6)*s*b*p+(-2*f0*f6+f1*f5-f2*f4)*s*b+2*f6*f7*s*p^3+ 2*f3*f7*s*p^2+(3*f0*f7-3*f1*f6-2*f2*f5+f3*f4)*s*p+f0*f4*s- f2*f7*b^3+(-f3*f7-2*f4*f6)*b^2*p+(-f0*f7+f2*f5-f3*f4)*b^2+ 2*f7^2*b*p^3+(2*f4*f7-3*f5*f6)*b*p^2+(-2*f3*f5+f4^2)*b*p+(-3*f0*f5 +f1*f4)*b+(-2*f5*f7+2*f6^2)*p^3+(-f2*f7+2*f3*f6-f4*f5)*p^2+ (2*f0*f6-f1*f5)*p,-f7*s^3*p+f7*s^2*b^2-f6*s^2*p+f6*s*b^2+f7*s*b*p -f5*s*p-f7*b^3+f5*b^2,f7*s*b^3+f7*s*p^2+f4*s*p+f1*s+f6*b^3- 2*f7*b^2*p-f4*b^2+f5*b*p+f2*b,-f7*s^2*p^2+f1*s^2+2*f7*s*b^2*p+ f2*s*b-f6*s*p^2-f3*s*p-f0*s+2*f6*b^2*p+f3*b^2-f7*b*p^2-f4*b*p -f1*b,-f0*s^2+f7*s*b*p^2+f2*s*p+f6*b*p^2+f3*b*p+f0*b, -f4*f7*s^3*p-2*f1*f7*s^3+f4*f7*s^2*b^2-f5*f7*s^2*b*p-2*f2*f7*s^2*b- 2*f6*f7*s^2*p^2+(f3*f7-f4*f6)*s^2*p+f5*f7*s*b^3+f6*f7*s*b^2*p+ (-f3*f7+f4*f6)*s*b^2+3*f7^2*s*b*p^2+(3*f4*f7-f5*f6)*s*b*p+ 2*f1*f7*s*b-2*f6^2*s*p^2+(f2*f7-f3*f6)*s*p-3*f7^2*b^3*p+(-f4*f7+ f5*f6)*b^3+(2*f5*f7+f6^2)*b^2*p+(f2*f7+f3*f6)*b^2+f6*f7*b*p^2+ 2*f3*f7*b*p+(4*f0*f7-f1*f6)*b+2*f7^2*p^3+(2*f4*f7-f5*f6)*p^2+ (2*f1*f7-f2*f6)*p,-f3*f7*s^3*p-f0*f7*s^3+f3*f7*s^2*b^2-f1*f7*s^2*b -2*f5*f7*s^2*p^2-f3*f6*s^2*p+(-f0*f6+f1*f5)*s^2+f4*f7*s*b^3+ 2*f5*f7*s*b^2*p+f3*f6*s*b^2+2*f3*f7*s*b*p+(f0*f7-f1*f6+f2*f5)*s*b +2*f7^2*s*p^3+(2*f4*f7-2*f5*f6)*s*p^2+(-2*f3*f5+f4^2)*s*p+(-f0*f5 +f1*f4)*s+(-f3*f7+f4*f6)*b^3+(-2*f4*f7+2*f5*f6)*b^2*p+(f1*f7+ 2*f3*f5-f4^2)*b^2+(f2*f7+f3*f6)*b*p+(2*f0*f6-2*f1*f5+f2*f4)*b+ 2*f6*f7*p^3+(f3*f7+f4*f6-f5^2)*p^2+(f0*f7+f1*f6-f2*f5)*p, -f0*f7*s^4+f1*f7*s^3*b+f2*f7*s^3*p-f0*f6*s^3+f2*f7*s^2*b^2+ f3*f7*s^2*b*p+(-f0*f7+f1*f6)*s^2*b+(-3*f1*f7+f2*f6)*s^2*p+(2*f0*f5 -f1*f4)*s^2-2*f4*f7*s*b^2*p+(-f1*f7+f2*f6)*s*b^2-3*f5*f7*s*b*p^2+ (-f2*f7+f3*f6)*s*b*p+(-2*f0*f6+f1*f5-f2*f4)*s*b+2*f6*f7*s*p^3+ 2*f3*f7*s*p^2+(3*f0*f7-3*f1*f6-2*f2*f5+f3*f4)*s*p+f0*f4*s- f2*f7*b^3+(-f3*f7-2*f4*f6)*b^2*p+(-f0*f7+f2*f5-f3*f4)*b^2+ 2*f7^2*b*p^3+(2*f4*f7-3*f5*f6)*b*p^2+(-2*f3*f5+f4^2)*b*p+(-3*f0*f5 +f1*f4)*b+(-2*f5*f7+2*f6^2)*p^3+(-f2*f7+2*f3*f6-f4*f5)*p^2+ (2*f0*f6-f1*f5)*p,-3*f0*f7*s^3*b-f1*f7*s^3*p+f1*f7*s^2*b^2+ 2*f2*f7*s^2*b*p-3*f0*f6*s^2*b+(4*f0*f7-f1*f6)*s^2*p+f1*f3*s^2+ f2*f7*s*b^3+3*f3*f7*s*b^2*p+(-f0*f7+f1*f6)*s*b^2+(-6*f1*f7+ 2*f2*f6)*s*b*p+(-f1*f4+f2*f3)*s*b-2*f5*f7*s*p^3-4*f2*f7*s*p^2+ (2*f0*f6+f1*f5-f3^2)*s*p+(-f0*f3+f1*f2)*s+f2*f6*b^3+(-2*f2*f7+ 3*f3*f6)*b^2*p+(f0*f6-f2*f4+f3^2)*b^2+(4*f0*f7-2*f1*f6+f2*f5- f3*f4)*b*p+(f0*f4-2*f1*f3+f2^2)*b+3*f7^2*p^4+(4*f4*f7- 2*f5*f6)*p^3+(4*f1*f7-2*f2*f6-f3*f5+f4^2)*p^2+(-f0*f5+2*f1*f4- f2*f3)*p-f0*f2+f1^2]); V:=[K2[1,5],K2[1,6],K2[1,7],K2[2,5],K2[2,6],K2[2,7],K2[2,8],K2[3,5],K2[3,6],K2[3,7],K2[3,8],K2[4,5],K2[4,6],K2[4,7],K2[4,8],K2[5,5],K2[5,6],K2[5,7],K2[5,8],K2[6,6],K2[6,7],K2[6,8],K2[7,7],K2[7,8],K2[8,8]]; Z:=Matrix(polsansx,1,25,[C0,C1,C2,A1*C0,A1*C1,A1*C2,A1*C3,A2*C0,A2*C1,A2*C2,A2*C3,A3*C0,A3*C1,A3*C2,A3*C3,C0*C0,C0*C1,C0*C2,C0*C3,C1*C1,C1*C2,C1*C3,C2*C2,C2*C3,C3*C3]); coef2:=function(cs,cb,cp,es) return Coefficient(Coefficient(Coefficient(polsansx!es,polsansx!s,cs),polsansx!b,cb),polsansx!p,cp); end function; matrice:=function() local M,t,i,j,l,m,Mi; M:=Matrix(polsansx,25,25,[<1,1,0>]); t:=0; for i:= 0 to 4 do for j:= 0 to 4-i do for l:= Maximum(3-i-j,0) to 4-i-j do t:=t+1; for m :=1 to 25 do M[t,m]:=coef2(i,j,l,V[m]); end for; end for; end for; end for; return M; end function; Mi:=Matrix(polsansx,25,25,[<7,20,1/2/f7>,<4,19,-1/2/f7>,<2,20,0>,<15,9,0>,<24,10,0>,<2,15,-1/4*f3/f7^2>,<17,14,0>,<25,1,0>,<8,6,1/4*f5*f4/f7^3>,<2,10,0>,<6,2,1/12/f7^3*(4*f7*f1-4*f2*f6-4*f4^2-f3*f5)>,<19,19,0>,<21,8,-1/4/f7^2>,<4,4,-1/8/f7^3*(8*f7*f0+f5*f2-2*f1*f6)>,<11,2,-1/3/f7^3*(3*f3*f7-f4*f6+f5^2)>,<13,13,1/2*f6^2/f7^3>,<6,1,1/4*f4/f7^2>,<12,19,0>,<16,12,0>,<17,3,0>,<21,13,0>,<23,13,0>,<5,23,-1/2*f6/f7^2>,<10,1,1/4*f5/f7^2>,<16,7,1/2/f7^2>,<15,20,0>,<22,14,0>,<4,11,-1/8/f7^3*(2*f7*f1-f2*f6)>,<24,13,0>,<5,10,0>,<5,17,1/2/f7>,<18,14,0>,<19,10,0>,<4,20,1/2*f4/f7^2>,<5,1,1/8*f3/f7^2>,<10,7,0>,<12,14,0>,<14,2,1/6/f7^3*(3*f3*f7-6*f4*f6+2*f5^2)>,<18,3,1/4/f7^2>,<9,14,0>,<16,18,0>,<24,12,0>,<2,3,-1/4*f3/f7^2>,<17,20,-1/2/f7^2>,<1,19,0>,<9,9,-1/f7^3*(3*f7*f5+2*f6^2)>,<4,10,0>,<14,7,0>,<20,9,3/4/f7^2>,<21,12,0>,<22,3,0>,<16,10,0>,<19,3,0>,<17,17,0>,<23,21,0>,<25,22,0>,<3,20,1/4*f5/f7^2>,<6,5,1/2*f6/f7^2>,<20,20,0>,<7,8,3/4*f5/f7^2>,<9,1,-1/4*f4/f7^2>,<20,14,0>,<3,15,-1/4/f7^3*(f5*f6+f4*f7)>,<22,19,0>,<25,17,0>,<9,12,1/2/f7>,<17,25,0>,<20,19,0>,<1,5,1/2*f3/f7^2>,<3,10,0>,<2,2,1/12/f7^3*(3*f3^2+f1*f5-2*f2*f4)>,<24,9,0>,<2,4,1/8/f7^3*(4*f7*f0+f5*f2-2*f1*f6)>,<5,20,1/4*f5/f7^2>,<10,4,-1/4/f7^3*(f3*f7-f5^2)>,<11,11,-1/4/f7^3*(2*f7*f5-f6^2)>,<16,15,0>,<23,20,0>,<3,5,1/4*f5/f7^2>,<6,18,-1/4*f5/f7^2>,<7,1,-1/8*f5/f7^2>,<9,21,3/4/f7>,<11,10,0>,<3,2,-1/12/f7^3*(24*f7*f0+3*f4*f3+2*f5*f2)>,<1,14,0>,<7,15,-1/2*f6/f7^2>,<12,12,-1/2/f7>,<19,9,0>,<9,4,-1/4/f7^3*(2*f7*f2+f5*f4-3*f3*f6)>,<11,14,0>,<1,9,-1/4/f7^3*(3*f7*f2+2*f5*f4+4*f3*f6)>,<5,14,0>,<11,20,0>,<12,6,-1/2/f7^3*(f3*f7-f5^2)>,<22,23,0>,<8,2,-1/12/f7^3*(28*f7*f0+f4*f3-4*f1*f6+4*f5*f2)>,<23,16,0>,<4,18,0>,<8,23,0>,<11,4,1/4/f7^3*(2*f4*f7+f5*f6)>,<13,11,-1/8/f7^3*(4*f4*f7-9*f5*f6)>,<3,4,3/8/f7^3*(2*f7*f1+f3*f5)>,<5,12,0>,<12,15,1/2/f7^3*(f7*f5-2*f6^2)>,<14,15,-1/2/f7>,<21,21,0>,<20,23,0>,<5,4,1/8/f7^3*(6*f7*f1+f3*f5)>,<14,24,0>,<3,3,-1/4*f4/f7^2>,<14,20,0>,<18,21,0>,<23,17,0>,<10,16,-3/2/f7>,<1,25,f6/f7^2>,<7,22,0>,<15,1,3/4/f7>,<20,10,0>,<21,9,0>,<12,18,1/2*f5/f7^2>,<8,22,0>,<10,12,0>,<13,18,-3/2*f6/f7^2>,<14,11,1/4/f7^3*(2*f7*f5-3*f6^2)>,<20,8,-1/4*f6/f7^3>,<22,10,0>,<25,12,0>,<2,18,-1/4*f3/f7^2>,<6,25,0>,<10,11,-1/4*f5*f6/f7^3>,<22,21,0>,<5,6,-1/2/f7^3*(f7*f2+f5*f4)>,<5,16,1/2/f7^3*(f7*f5-f6^2)>,<5,21,1/2*f6/f7^2>,<6,23,0>,<11,6,0>,<15,13,1/f7>,<2,13,1/4/f7^3*f3*f6>,<6,14,0>,<11,15,1/f7>,<15,8,3/2/f7>,<20,1,0>,<17,19,0>,<12,20,3/2*f6/f7^2>,<6,11,-1/4/f7^3*(2*f3*f7+f4*f6)>,<13,5,7/4/f7>,<23,25,0>,<21,5,0>,<25,15,0>,<16,2,-1/6*f1/f7^3>,<4,21,-3/4*f5/f7^2>,<15,18,0>,<24,7,0>,<5,8,1/4/f7^3*(f3*f7+f5^2+2*f4*f6)>,<7,18,0>,<10,22,0>,<13,22,0>,<25,19,0>,<12,9,-1/4/f7^3*(25*f7*f5+8*f6^2)>,<21,6,0>,<24,6,0>,<12,25,0>,<18,9,-1/4/f7^2>,<22,17,0>,<24,4,1/2/f7^2>,<4,5,1/2*f4/f7^2>,<10,13,0>,<21,7,0>,<18,7,0>,<8,20,1/2*f5/f7^2>,<14,10,0>,<6,6,-1/4/f7^3*(2*f3*f7+f5^2)>,<11,17,0>,<3,23,-1/2*f6/f7^2>,<6,21,-1/f7>,<11,22,0>,<6,24,0>,<15,22,0>,<20,2,-1/4*f3/f7^3>,<3,18,-1/4*f4/f7^2>,<4,22,0>,<6,10,0>,<14,18,0>,<21,4,-3/8*f5/f7^3>,<25,3,0>,<3,13,1/4/f7^3*f4*f6>,<10,15,3/4*f6/f7^2>,<10,19,0>,<7,16,2/f7>,<10,8,-3/4*f5/f7^2>,<16,9,1/2*f5/f7^3>,<17,16,-1/f7^2>,<25,16,0>,<9,10,0>,<10,24,0>,<14,13,f6/f7^2>,<17,15,1/2*f6/f7^3>,<24,22,0>,<25,13,0>,<10,10,0>,<15,24,0>,<19,7,0>,<16,14,0>,<19,6,0>,<15,25,0>,<1,12,0>,<23,6,1/2/f7^2>,<3,9,-1/4/f7^3*(7*f4*f7+2*f5*f6)>,<18,19,0>,<21,10,0>,<4,16,1/4/f7^3*(4*f4*f7+3*f5*f6)>,<4,24,1/2*f6/f7^2>,<8,25,0>,<9,16,9/4*f6/f7^2>,<24,18,0>,<4,13,0>,<9,2,1/12/f7^3*(11*f7*f1-8*f2*f6+4*f4^2+3*f3*f5)>,<16,11,0>,<23,19,0>,<6,19,0>,<24,5,0>,<10,14,0>,<17,1,0>,<22,6,1/2/f7^2>,<2,24,-1/2*f6/f7^2>,<5,22,0>,<16,8,0>,<20,21,0>,<8,7,-f6/f7^2>,<13,2,1/6/f7^3*(f7*f2+3*f3*f6+7*f5*f4)>,<14,1,3/4*f6/f7^2>,<16,16,-1/2*f6/f7^3>,<20,16,0>,<1,20,1/2*f3/f7^2>,<7,21,0>,<19,24,0>,<7,24,0>,<12,7,-21/4/f7>,<23,11,0>,<5,11,-1/8/f7^3*f3*f6>,<8,15,1/4/f7^3*(f4*f7-2*f5*f6)>,<4,15,-1/2/f7^3*f4*f6>,<24,20,0>,<8,13,-1/4/f7^3*f4*f6>,<16,5,0>,<21,24,0>,<25,5,0>,<1,23,0>,<13,3,-1/2*f6/f7^2>,<22,15,0>,<4,3,0>,<10,20,-1/4/f7>,<17,7,0>,<4,2,1/12/f7^3*(-2*f2*f4+f1*f5)>,<7,9,-2*f6/f7^2>,<23,4,0>,<9,8,1/4/f7^3*(2*f4*f7+7*f5*f6)>,<13,24,0>,<2,16,-1/4*f5*f6/f7^3>,<10,25,0>,<17,21,0>,<17,11,0>,<21,11,3/8*f6/f7^3>,<21,17,0>,<2,11,1/8/f7^3*(2*f7*f1-f2*f6)>,<13,12,0>,<19,20,0>,<20,4,0>,<20,24,0>,<24,17,0>,<12,24,0>,<14,21,0>,<22,5,0>,<11,9,1/f7>,<19,17,0>,<1,7,-1/2*f4/f7^2>,<18,10,0>,<5,9,-3/2*f4/f7^2>,<14,3,-1/f7>,<5,7,1/2*f6/f7^2>,<24,14,0>,<15,3,0>,<21,16,0>,<23,10,0>,<12,17,0>,<18,18,1/4/f7^2>,<9,3,-3/4*f5/f7^2>,<20,11,0>,<23,5,0>,<4,23,0>,<8,1,-1/8*f3/f7^2>,<11,23,0>,<20,18,1/4/f7^2>,<23,15,0>,<25,8,0>,<7,23,0>,<18,20,0>,<22,25,0>,<9,5,f6/f7^2>,<10,9,5/2*f6/f7^2>,<11,12,0>,<18,16,0>,<3,21,f6/f7^2>,<19,15,0>,<23,3,0>,<9,22,0>,<17,4,0>,<19,25,0>,<24,2,0>,<3,16,1/2*f5/f7^2>,<12,2,1/12/f7^3*(3*f7*f1-8*f3*f5-8*f2*f6)>,<17,18,0>,<21,22,0>,<25,18,0>,<5,24,0>,<13,25,0>,<19,2,-1/6*f4/f7^3>,<23,2,0>,<25,14,0>,<3,11,-3/8/f7^3*f3*f6>,<7,5,1/2/f7>,<12,13,-1/2*f5*f6/f7^3>,<21,19,0>,<12,3,1/2*f5/f7^2>,<15,11,-3/4*f6/f7^2>,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tryon:=function(P) local Q,R,S,t,i,j,l,T,termesensbp; Q:=polsansx!P; R:=Matrix(polsansx,25,1,[<1,1,0>]); t:=0; for i:=0 to 4 do for j:=0 to 4-i do for l:=Maximum(3-i-j,0) to 4-i-j do t:=t+1; R[t,1]:=coef2(i,j,l,Q); end for; end for; end for; S:=Z*Mi*R; termesensbp:=Q-simpsp(Evaluate(S[1,1],[s,b,p,s12,p12,1,s,b,p,c0,c1,c2,c3,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w])); Q:=termesensbp+S[1,1]; Q:=A0^2*Evaluate(Q,[s,b,p,s12,p12,A0,A1/A0,A2/A0,A3/A0,C0/A0,C1/A0,C2/A0,C3/A0,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w]); Q:=Evaluate(polsansx!Q,[A1/A0,A2/A0,A3/A0,s12,p12,A0,A1,A2,A3,C0,C1,C2,C3,y1,y2,y3,y4,y5,y6,y7,y8,u,v,w]); return Q; end function; Ws:=Matrix(polsansx,8,8,[ -f7^2*s^3*p+f7^2*s^2*b^2-f6*f7*s^2*p+f6*f7*s*b^2+f7^2*s*b*p- f5*f7*s*p-f7^2*b^3+f5*f7*b^2,-f7^2*s^3*b-f6*f7*s^2*b+2*f7^2*s*b^2- f5*f7*s*b+f6*f7*b^2-f7^2*b*p+f5*f7*p,f7^2*s^4+f6*f7*s^3- 3*f7^2*s^2*b+f5*f7*s^2-2*f6*f7*s*b+f7^2*s*p+f7^2*b^2+2*f6*f7*p, f7^2*s^3+f6*f7*s^2-f7^2*s*b-2*f5*f7*s+3*f7^2*p,-f7*p,-f7*b,-f7*s, f7,-f4*f7*s^4-f5*f7*s^3*b+2*f6*f7*s^3*p+(f3*f7-f4*f6)*s^3- 2*f6*f7*s^2*b^2+4*f7^2*s^2*b*p+(3*f4*f7-f5*f6)*s^2*b+2*f6^2*s^2*p+ (f3*f6-f4*f5)*s^2-2*f7^2*s*b^3+(2*f5*f7-2*f6^2)*s*b^2+ 2*f6*f7*s*b*p+(-f3*f7+2*f4*f6-f5^2)*s*b-2*f7^2*s*p^2+(-3*f4*f7+ 2*f5*f6)*s*p+(f3*f5-f4^2)*s+(f4*f7-f5*f6)*b^2+f5*f7*b*p, -f5*f7*s^4+f7^2*s^3*p+(f4*f7-f5*f6)*s^3-f7^2*s^2*b^2+3*f5*f7*s^2*b +f6*f7*s^2*p+(f4*f6-f5^2)*s^2-f6*f7*s*b^2-f7^2*s*b*p+(-3*f4*f7+ 2*f5*f6)*s*b-2*f5*f7*s*p+f7^2*b^3-2*f5*f7*b^2+(f3*f7-2*f4*f6+ f5^2)*b+2*f7^2*p^2+(3*f4*f7-2*f5*f6)*p-f3*f5+f4^2,-2*f6*f7*s^4+ (f5*f7-2*f6^2)*s^3+6*f6*f7*s^2*b+(2*f4*f7-f5*f6)*s^2+(-3*f5*f7+ 4*f6^2)*s*b-6*f6*f7*s*p+(-f3*f7+f5^2)*s-2*f6*f7*b^2-2*f7^2*b*p- 2*f4*f7*b+(3*f5*f7-4*f6^2)*p-2*f3*f6+2*f4*f5,-3*f7^2*s^4- 3*f6*f7*s^3+9*f7^2*s^2*b+3*f5*f7*s^2+6*f6*f7*s*b-11*f7^2*s*p+ (-4*f4*f7+6*f5*f6)*s-f7^2*b^2-4*f5*f7*b-6*f6*f7*p-3*f3*f7+ 3*f5^2,f7*s^4+f6*s^3-3*f7*s^2*b+f5*s^2-2*f6*s*b+3*f7*s*p+f4*s+ f7*b^2-f5*b+2*f6*p+f3,-f7*s^3-f6*s^2+3*f7*s*b-f5*s+2*f6*b- 2*f7*p-f4,2*f7*s^2+2*f6*s-2*f7*b+f5,f7*s,f3*f7*s^4+f4*f7*s^3*b -2*f5*f7*s^3*p+(-f2*f7+f3*f6)*s^3+2*f5*f7*s^2*b^2-4*f6*f7*s^2*b*p+ (-3*f3*f7+f4*f6)*s^2*b+2*f7^2*s^2*p^2+(2*f4*f7-2*f5*f6)*s^2*p+ (-f2*f6+f3*f5)*s^2+2*f6*f7*s*b^3-6*f7^2*s*b^2*p+(-4*f4*f7+ 2*f5*f6)*s*b^2+(4*f5*f7-4*f6^2)*s*b*p+(f2*f7-2*f3*f6+f4*f5)*s*b+ 2*f6*f7*s*p^2+(f3*f7+2*f4*f6-2*f5^2)*s*p+(-f2*f5+f3*f4)*s+ 2*f7^2*b^4+(-4*f5*f7+2*f6^2)*b^3-2*f6*f7*b^2*p+(f3*f7-3*f4*f6+ 2*f5^2)*b^2+2*f7^2*b*p^2+(3*f4*f7-2*f5*f6)*b*p+(-f3*f5+f4^2)*b, -f5*f7*s^3*b+(2*f4*f7-f5*f6)*s^2*b+2*f5*f7*s^2*p+2*f5*f7*s*b^2+ (2*f4*f6-f5^2)*s*b-2*f7^2*s*p^2+(-2*f4*f7+2*f5*f6)*s*p+(-2*f4*f7+ f5*f6)*b^2-3*f5*f7*b*p+(-f2*f7+f4*f5)*b-2*f6*f7*p^2+(-f3*f7- 2*f4*f6+2*f5^2)*p+f2*f5-f3*f4,-2*f6*f7*s^3*b+f7^2*s^3*p-f4*f7*s^3 -f7^2*s^2*b^2+(2*f5*f7-2*f6^2)*s^2*b+5*f6*f7*s^2*p-f4*f6*s^2+ 3*f6*f7*s*b^2+f7^2*s*b*p+3*f4*f7*s*b+(-f5*f7+4*f6^2)*s*p+(f2*f7- f4*f5)*s+f7^2*b^3+(-3*f5*f7+2*f6^2)*b^2-4*f6*f7*b*p+2*f5^2*b- 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f2^2,(-2*f2*f7^2-f2*f7+3*f4*f5*f7)*s^4+(-3*f3*f7^2+3*f5^2*f7)*s^3*b +(-3*f4*f7^2+3*f4*f7-6*f5*f6*f7)*s^3*p+(f1*f7^2+2*f1*f7- 2*f2*f6*f7-f2*f6-3*f3*f5*f7+3*f4*f5*f6)*s^3+6*f5*f6*f7*s^2*b^2+ (-9*f5*f7^2+3*f5*f7)*s^2*b*p+(6*f2*f7^2+3*f2*f7-3*f3*f6*f7- 9*f4*f5*f7+3*f5^2*f6)*s^2*b+(6*f6*f7^2-6*f6*f7)*s^2*p^2+(5*f3*f7^2- 3*f3*f7-3*f4*f6*f7+3*f4*f6-6*f5*f6^2)*s^2*p+(-f0*f7^2+f0*f7+ f1*f6*f7+2*f1*f6-2*f2*f5*f7-f2*f5-3*f3*f5*f6+3*f4*f5^2)*s^2+ 6*f5*f7^2*s*b^3+(3*f6*f7^2+3*f6*f7)*s*b^2*p+(4*f3*f7^2-6*f5^2*f7+ 6*f5*f6^2)*s*b^2+(6*f7^3-12*f7^2)*s*b*p^2+(f4*f7^2-9*f4*f7- 3*f5*f6*f7+3*f5*f6)*s*b*p+(3*f1*f7^2-6*f1*f7+4*f2*f6*f7+2*f2*f6- 6*f4*f5*f6+3*f5^3)*s*b+(4*f5*f7^2+6*f6^2*f7-6*f6^2)*s*p^2+(f2*f7^2 -6*f2*f7+5*f3*f6*f7-3*f3*f6+6*f4*f5*f7+3*f4*f5-6*f5^2*f6)*s*p+ (f1*f5*f7+2*f1*f5-3*f2*f4*f7-f2*f4+f3^2*f7-3*f3*f5^2+ 3*f4^2*f5)*s+(3*f7^3+3*f7^2)*b^3*p+(-6*f5*f7^2-6*f5*f7+3*f6^2*f7+ 3*f6^2)*b^2*p+(-f2*f7+f3*f6*f7-3*f4*f5*f7+3*f5^2*f6)*b^2- 6*f6*f7*b*p^2+(-2*f3*f7^2+3*f3*f7-2*f4*f6*f7-6*f4*f6+3*f5^2)*b*p+ (-3*f0*f7^2+3*f0*f7+3*f1*f6*f7-3*f1*f6+f2*f5*f7+f2*f5- 2*f3*f4*f7)*b+(-6*f7^3+10*f7^2)*p^3+(-8*f4*f7^2+12*f4*f7+ 4*f5*f6*f7-6*f5*f6)*p^2+(-6*f1*f7^2+6*f1*f7+3*f2*f6*f7-3*f2*f6+ 2*f3*f5*f7-3*f3*f5-2*f4^2*f7+3*f4^2)*p+f0*f5*f7-f0*f5-2*f1*f4*f7 +2*f1*f4+f2*f3*f7-f2*f3,f2*f7*s^4+f3*f7*s^3*b+(-f1*f7+f2*f6)*s^3 -2*f5*f7*s^2*b*p+(-3*f2*f7+f3*f6)*s^2*b+(-f1*f6+f2*f5)*s^2- 2*f6*f7*s*b^2*p-2*f3*f7*s*b^2+2*f7^2*s*b*p^2+(2*f4*f7-2*f5*f6)*s*b*p +(f1*f7-2*f2*f6+f3*f5)*s*b+f2*f7*s*p+(-f1*f5+f2*f4)*s- 2*f7^2*b^3*p+(4*f5*f7-2*f6^2)*b^2*p+(f2*f7-f3*f6)*b^2+ 2*f6*f7*b*p^2+(f3*f7+2*f4*f6-2*f5^2)*b*p+(-f2*f5+f3*f4)*b, -f3*f7*s^4-f4*f7*s^3*b+2*f5*f7*s^3*p+(f2*f7-f3*f6)*s^3- 2*f5*f7*s^2*b^2+4*f6*f7*s^2*b*p+(3*f3*f7-f4*f6)*s^2*b-2*f7^2*s^2*p^2 +(-2*f4*f7+2*f5*f6)*s^2*p+(f2*f6-f3*f5)*s^2-2*f6*f7*s*b^3+ 6*f7^2*s*b^2*p+(4*f4*f7-2*f5*f6)*s*b^2+(-4*f5*f7+4*f6^2)*s*b*p+ (-f2*f7+2*f3*f6-f4*f5)*s*b-2*f6*f7*s*p^2+(-f3*f7-2*f4*f6+ 2*f5^2)*s*p+(f2*f5-f3*f4)*s-2*f7^2*b^4+(4*f5*f7-2*f6^2)*b^3+ 2*f6*f7*b^2*p+(-f3*f7+3*f4*f6-2*f5^2)*b^2-2*f7^2*b*p^2+(-3*f4*f7+ 2*f5*f6)*b*p+(f3*f5-f4^2)*b,f4*f7*s^4+f5*f7*s^3*b-2*f6*f7*s^3*p+ (-f3*f7+f4*f6)*s^3+2*f6*f7*s^2*b^2-4*f7^2*s^2*b*p+(-3*f4*f7+ f5*f6)*s^2*b-2*f6^2*s^2*p+(-f3*f6+f4*f5)*s^2+2*f7^2*s*b^3+ (-2*f5*f7+2*f6^2)*s*b^2-2*f6*f7*s*b*p+(f3*f7-2*f4*f6+f5^2)*s*b+ 2*f7^2*s*p^2+(3*f4*f7-2*f5*f6)*s*p+(-f3*f5+f4^2)*s+(-f4*f7+ f5*f6)*b^2-f5*f7*b*p,-f7^2*s^3*p+f7^2*s^2*b^2-f6*f7*s^2*p+ f6*f7*s*b^2+f7^2*s*b*p-f5*f7*s*p-f7^2*b^3+f5*f7*b^2]); WW:=Matrix(polsansx,4680,1,[<1,1,0>]); compare:=function(u,v) local aa; aa:=0; if u[1] ge v[1] then else aa:=1; end if; if u[1] eq v[1] and u[2] le v[2] then aa:=1; end if; return aa; end function; time for i:=1 to 8 do print(i); for j:=1 to 8 do if i eq 8 then print(j); end if; for k:=1 to 8 do for l:=1 to 8 do if compare([k,l],[i,j]) eq 1 then WW[i+8*j+8*8*k+8*8*8*l,1]:=tryon(simpsp(Ws[i,j]*Ws[k,l])); end if; end for; end for; end for; end for; time for i:=1 to 8 do for j:=1 to 8 do for k:=1 to 8 do for l:=1 to 8 do if compare([k,l],[i,j]) eq 0 then WW[i+8*j+8*8*k+8*8*8*l,1]:=WW[k+8*l+8*8*i+8*8*8*j,1]; end if; end for; end for; end for; end for; Phi:=Matrix(polsansx,8,8,[<1,1,0>]); a:=Matrix(polsansx,8,1,[y1,y2,y3,y4,y5,y6,y7,y8]); time for i:=1 to 8 do for j:=1 to 8 do s:=0; for k:=1 to 8 do for l:=1 to 8 do s:=s+WW[i+8*k+8*8*j+8*8*8*l,1]*a[k,1]*a[l,1]; end for; end for; toreplace:=Coefficient(polsansx!Coefficient(polsansx!s,polsansx!y1,1),polsansx!y8,1); Phi[i,j]:=s-toreplace*y1*y8+toreplace*(y2*y7+y3*y6+y4*y5+2*f5*y2*y4-f5*y3^2-2*f6*y3*y4-3*f7*y4^2); end for; end for; PrintFileMagma("Phi",Phi);