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asked 4 years ago

Cyrille gravatar image

Semmingly false answer by bool()

I plot the inequalities

var("x_1","x_2")
eq1=solve(3*x_1+4*x_2==14,x_2)
eq2=solve(5*x_1+6*x_2==-8,x_2)
eq3=solve(4*x_1-7*x_2==18,x_2)
eq4=solve(2*x_1-3*x_2==-8,x_2)
b=10
p=plot([eq1[0].rhs(),eq2[0].rhs(),eq3[0].rhs(),eq4[0].rhs()], (x_1, 0,b),color=["#c72b91","#2b37c7", "#cb7b2b","#2bcb4b"],axes_labels=["$x_1$","$x_2$"],legend_label=[r"$%s$"%latex(eq1[0].rhs()),r"$%s$"%latex(eq2[0].rhs()),r"$%s$"%latex(eq3[0].rhs()),r"$%s$"%latex(eq4[0].rhs())])
show(p)

which shows that the eq1 is always above for any x0 to eq2. The same for eq4. But there is an intersection with eq3. So the following code shoud return true for both bool

assume(x_1 >0)
show(bool(eq1[0][0].rhs()>eq2[0][0].rhs()))
show(bool(eq4[0][0].rhs()>eq2[0][0].rhs()))

and this is confirmed by the fact that

solve(eq4[0][0].rhs()>eq3[0][0].rhs()

return no solution. Is it my error ?

Semmingly false answer by bool()

I plot the inequalities

var("x_1","x_2")
eq1=solve(3*x_1+4*x_2==14,x_2)
eq2=solve(5*x_1+6*x_2==-8,x_2)
eq3=solve(4*x_1-7*x_2==18,x_2)
eq4=solve(2*x_1-3*x_2==-8,x_2)
b=10
p=plot([eq1[0].rhs(),eq2[0].rhs(),eq3[0].rhs(),eq4[0].rhs()], (x_1, 0,b),color=["#c72b91","#2b37c7", "#cb7b2b","#2bcb4b"],axes_labels=["$x_1$","$x_2$"],legend_label=[r"$%s$"%latex(eq1[0].rhs()),r"$%s$"%latex(eq2[0].rhs()),r"$%s$"%latex(eq3[0].rhs()),r"$%s$"%latex(eq4[0].rhs())])
show(p)

which shows that the eq1 is always above for any x0 to eq2. The same for eq4. But there is an intersection with eq3. So the following code shoud return true for both bool. And this is not the case.

assume(x_1 >0)
show(bool(eq1[0][0].rhs()>eq2[0][0].rhs()))
show(bool(eq4[0][0].rhs()>eq2[0][0].rhs()))

and this is confirmed by the fact that

solve(eq4[0][0].rhs()>eq3[0][0].rhs()

return no solution. Is it my error ?

Semmingly false answer by bool()

I plot the inequalities

var("x_1","x_2")
eq1=solve(3*x_1+4*x_2==14,x_2)
eq2=solve(5*x_1+6*x_2==-8,x_2)
eq3=solve(4*x_1-7*x_2==18,x_2)
eq4=solve(2*x_1-3*x_2==-8,x_2)
b=10
p=plot([eq1[0].rhs(),eq2[0].rhs(),eq3[0].rhs(),eq4[0].rhs()], (x_1, 0,b),color=["#c72b91","#2b37c7", "#cb7b2b","#2bcb4b"],axes_labels=["$x_1$","$x_2$"],legend_label=[r"$%s$"%latex(eq1[0].rhs()),r"$%s$"%latex(eq2[0].rhs()),r"$%s$"%latex(eq3[0].rhs()),r"$%s$"%latex(eq4[0].rhs())])
show(p)

which shows that the eq1 is always above for any x0 to eq2. The same for eq4. But there is an intersection with eq3. So the following code shoud return true for both bool. And this is not the case.

assume(x_1 >0)
show(bool(eq1[0][0].rhs()>eq2[0][0].rhs()))
show(bool(eq4[0][0].rhs()>eq2[0][0].rhs()))
show(bool(eq3[0][0].rhs()>eq2[0][0].rhs()))

and this is confirmed by the fact that

solve(eq4[0][0].rhs()>eq3[0][0].rhs()
solve(eq3[0][0].rhs()>eq3[0][0].rhs()

return no solution. for solution eq2[0][0], which is a way to answer to the same question that the one ask with bool. Is it my error ?

Semmingly false answer by bool()

I plot the inequalities

var("x_1","x_2")
eq1=solve(3*x_1+4*x_2==14,x_2)
eq2=solve(5*x_1+6*x_2==-8,x_2)
eq3=solve(4*x_1-7*x_2==18,x_2)
eq4=solve(2*x_1-3*x_2==-8,x_2)
b=10
p=plot([eq1[0].rhs(),eq2[0].rhs(),eq3[0].rhs(),eq4[0].rhs()], (x_1, 0,b),color=["#c72b91","#2b37c7", "#cb7b2b","#2bcb4b"],axes_labels=["$x_1$","$x_2$"],legend_label=[r"$%s$"%latex(eq1[0].rhs()),r"$%s$"%latex(eq2[0].rhs()),r"$%s$"%latex(eq3[0].rhs()),r"$%s$"%latex(eq4[0].rhs())])
show(p)

which shows that the eq1 is always above for any x0 to eq2. The same for eq4. But there is an intersection with eq3. So the following code shoud return true for both bool. And this is not the case.

assume(x_1 >0)
show(bool(eq1[0][0].rhs()>eq2[0][0].rhs()))
show(bool(eq3[0][0].rhs()>eq2[0][0].rhs()))

and this is confirmed by the fact that

solve(eq3[0][0].rhs()>eq3[0][0].rhs()

return for solution eq2[0][0], which is a way to answer to the same question that the one ask with bool. Is it my error ?